# HG changeset patch
# User carandraug
# Date 1442246684 0
# Node ID 2f6ebbb02032c033a19d29dea4742b2bbddf7f76
# Parent 1f7c2d121557cb769a51ddccebd7adc84e4614f9
nurbs: move to individual hg repository
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/CITATION
--- a/extra/nurbs/CITATION Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,26 +0,0 @@
-
-To cite the Octave NURBS package use:
-
-[1] M. Spink, D. Claxton, C. de Falco, R. Vazquez,
- The NURBS toolbox,
- http://octave.sourceforge.net/nurbs/index.html.
-
-[2] C. de Falco, A. Reali, and R. Vazquez.
- Geopdes: A research tool for isogeometric analysis of pdes.
- Advances in Engineering Software, 42(12):1020-1034, 2011.
-
-BibTeX entries for LaTeX users are:
-
-@misc{NT,
- Author = {Spink, M. and Claxton, D. and de Falco, C. and V{\'a}zquez, R.},
- Howpublished = {\url{http://octave.sourceforge.net/nurbs/index.html}},
- Title = {The {NURBS} toolbox}}
-
-@article{geopdes,
- Author = {C. de Falco and A. Reali and R. V{\'a}zquez},
- Journal = {Advances in Engineering Software},
- Number = {12},
- Pages = {1020-1034},
- Title = {GeoPDEs: A research tool for Isogeometric Analysis of PDEs},
- Volume = {42},
- Year = {2011}}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/COPYING
--- a/extra/nurbs/COPYING Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,674 +0,0 @@
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-versions of the GNU General Public License can be used, that proxy's
-public statement of acceptance of a version permanently authorizes you
-to choose that version for the Program.
-
- Later license versions may give you additional or different
-permissions. However, no additional obligations are imposed on any
-author or copyright holder as a result of your choosing to follow a
-later version.
-
- 15. Disclaimer of Warranty.
-
- THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
-APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
-HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
-OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
-THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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-IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
-ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
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- 16. Limitation of Liability.
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-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
-THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
-GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
-USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
-DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
-PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
-EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
-SUCH DAMAGES.
-
- 17. Interpretation of Sections 15 and 16.
-
- If the disclaimer of warranty and limitation of liability provided
-above cannot be given local legal effect according to their terms,
-reviewing courts shall apply local law that most closely approximates
-an absolute waiver of all civil liability in connection with the
-Program, unless a warranty or assumption of liability accompanies a
-copy of the Program in return for a fee.
-
- END OF TERMS AND CONDITIONS
-
- How to Apply These Terms to Your New Programs
-
- If you develop a new program, and you want it to be of the greatest
-possible use to the public, the best way to achieve this is to make it
-free software which everyone can redistribute and change under these terms.
-
- To do so, attach the following notices to the program. It is safest
-to attach them to the start of each source file to most effectively
-state the exclusion of warranty; and each file should have at least
-the "copyright" line and a pointer to where the full notice is found.
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- Copyright (C)
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-
-Also add information on how to contact you by electronic and paper mail.
-
- If the program does terminal interaction, make it output a short
-notice like this when it starts in an interactive mode:
-
- Copyright (C)
- This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
- This is free software, and you are welcome to redistribute it
- under certain conditions; type `show c' for details.
-
-The hypothetical commands `show w' and `show c' should show the appropriate
-parts of the General Public License. Of course, your program's commands
-might be different; for a GUI interface, you would use an "about box".
-
- You should also get your employer (if you work as a programmer) or school,
-if any, to sign a "copyright disclaimer" for the program, if necessary.
-For more information on this, and how to apply and follow the GNU GPL, see
-.
-
- The GNU General Public License does not permit incorporating your program
-into proprietary programs. If your program is a subroutine library, you
-may consider it more useful to permit linking proprietary applications with
-the library. If this is what you want to do, use the GNU Lesser General
-Public License instead of this License. But first, please read
-.
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/DESCRIPTION
--- a/extra/nurbs/DESCRIPTION Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,11 +0,0 @@
-Name: Nurbs
-Version: 1.3.10
-Date: 2015-08-17
-Author: Mark Spink, Daniel Claxton, Carlo de Falco, Rafael Vazquez
-Maintainer: Carlo de Falco and Rafael Vazquez
-Title: Nurbs.
-Description: Collection of routines for the creation, and manipulation of Non-Uniform Rational B-Splines (NURBS), based on the NURBS toolbox by Mark Spink.
-Categories: splines
-Depends: octave (>= 3.8)
-License: GPLv3+
-Url: http://octave.sf.net
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/INDEX
--- a/extra/nurbs/INDEX Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,78 +0,0 @@
-nurbs >> Nurbs
-Basic operations for NURBS curves, surfaces and volumes
- nrbmak
- nrbkntins
- nrbdegelev
- nrbderiv
- nrbdeval
- nrbeval
- crvkntremove
-Operations for constructing NURBS curves and surfaces
- nrbtform
- nrbreverse
- nrbtransp
- nrbpermute
- nrbline
- nrbcirc
- nrbrect
- nrb4surf
- nrbcylind
- nrbextract
- nrbextrude
- nrbrevolve
- nrbruled
- nrbcoons
- nrbtestcrv
- nrbtestsrf
- nrbunclamp
- nrbmultipatch
-Plot and export
- nrbplot
- nrbctrlplot
- nrbkntplot
- nrbexport
- nrb2iges
-B-Spline functions
- bspeval
- bspderiv
- bspkntins
- bspdegelev
- basisfun
- basisfunder
- basiskntins
- findspan
- numbasisfun
- tbasisfun
-B-splines geometric entities
- curvederivcpts
- curvederiveval
- surfderivcpts
- surfderiveval
-NURBS geometric entities and functions
- nrbbasisfun
- nrbmeasure
- nrbbasisfunder
- nrbnumbasisfun
- nrbcrvderiveval
- nrbsurfderiveval
-Knots construction and refinement
- kntuniform
- kntrefine
- kntbrkdegreg
- kntbrkdegmult
-Vector and Transformation Utilities
- vecnorm
- vecmag
- vecmag2
- vecangle
- vecdot
- veccross
- vecrotx
- vecroty
- vecrotz
- vecrot
- vecscale
- vectrans
-Misc Utilities
- deg2rad
- rad2deg
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/NEWS
--- a/extra/nurbs/NEWS Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,60 +0,0 @@
-Summary of important user-visible changes for nurbs 1.3.10:
--------------------------------------------------------------------
-
- ** 1.3.10 is being released to allow compatibility with Octave 4.0
-
- * src/low_level_functions.cc(findspan): return an error if a point
- is outside the knotspan
-
- * inst/nrbexport: changed the format of geopdes files
-
- * inst/nrbbasisfun: fixed bug to return indices in the 1D case
-
- * inst/basiskntins: added new function to compute subdivision coefficients
-
-Summary of important user-visible changes for nurbs 1.3.9:
--------------------------------------------------------------------
-
- * inst/nrbexport: export multipatch geometries
-
-Summary of important user-visible changes for nurbs 1.3.8:
--------------------------------------------------------------------
-
- * inst/nrbkntremove.m: added new function
-
- * inst/nrbunclamp.m: added new function
-
- * inst/nrbmak.m: adapted for unclamped knot vector
-
- * inst/nrbplot.m: adapted for unclamped knot vector
-
- * inst/nrbkntplot.m: adapted for unclamped knot vector
-
- * inst/nrb2iges: added new function
-
- * inst/nrbmultipatch: added new function
-
-Summary of important user-visible changes for nurbs 1.3.7:
--------------------------------------------------------------------
-
- ** 1.3.7 is mainly a maintainance release to distribute small bug fixes
- that accumulated over time.
-
- * inst/nrbpermute.m: added new function
-
- * inst/nrbreverse.m: each direction can now be reversed independently
-
- * inst/nrbkntplot.m: now works for non-unitary interval
-
- * inst/nrbcrvderiveval: code vectorized
-
- * inst/nrbplot: fixed bug in affecting plot of trivariate nurbs, now works for
- non-unitary intervals
-
- * inst/nrbctrplot.m: plot the points only once
-
- * src/*.cc: avoid use of deprecated array constructors
-
-
-
-
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/PKG_ADD
--- a/extra/nurbs/PKG_ADD Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1 +0,0 @@
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/basisfun.m
--- a/extra/nurbs/inst/basisfun.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,91 +0,0 @@
-function B = basisfun (iv, uv, p, U)
-
-% BASISFUN: Basis function for B-Spline
-%
-% Calling Sequence:
-%
-% N = basisfun(iv,uv,p,U)
-%
-% INPUT:
-%
-% iv - knot span ( from FindSpan() )
-% uv - parametric points
-% p - spline degree
-% U - knot sequence
-%
-% OUTPUT:
-%
-% N - Basis functions vector(numel(uv)*(p+1))
-%
-% Adapted from Algorithm A2.2 from 'The NURBS BOOK' pg70.
-%
-% See also:
-%
-% numbasisfun, basisfunder, findspan
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2007 Daniel Claxton
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-B = zeros(numel(uv), p+1);
-
-for jj = 1:numel(uv)
-
- i = iv(jj) + 1; %% findspan uses 0-based numbering
- u = uv(jj);
-
- left = zeros(p+1,1);
- right = zeros(p+1,1);
-
- N(1) = 1;
- for j=1:p
- left(j+1) = u - U(i+1-j);
- right(j+1) = U(i+j) - u;
- saved = 0;
-
- for r=0:j-1
- temp = N(r+1)/(right(r+2) + left(j-r+1));
- N(r+1) = saved + right(r+2)*temp;
- saved = left(j-r+1)*temp;
- end
-
- N(j+1) = saved;
- end
-
- B (jj, :) = N;
-
-end
-
-end
-
-%!test
-%! n = 3;
-%! U = [0 0 0 1/2 1 1 1];
-%! p = 2;
-%! u = linspace (0, 1, 10);
-%! s = findspan (n, p, u, U);
-%! Bref = [1.00000 0.00000 0.00000
-%! 0.60494 0.37037 0.02469
-%! 0.30864 0.59259 0.09877
-%! 0.11111 0.66667 0.22222
-%! 0.01235 0.59259 0.39506
-%! 0.39506 0.59259 0.01235
-%! 0.22222 0.66667 0.11111
-%! 0.09877 0.59259 0.30864
-%! 0.02469 0.37037 0.60494
-%! 0.00000 0.00000 1.00000];
-%! B = basisfun (s, u, p, U);
-%! assert (B, Bref, 1e-5);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/basisfunder.m
--- a/extra/nurbs/inst/basisfunder.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,155 +0,0 @@
-function dersv = basisfunder (ii, pl, uu, u_knotl, nders)
-
-% BASISFUNDER: B-Spline Basis function derivatives.
-%
-% Calling Sequence:
-%
-% ders = basisfunder (ii, pl, uu, k, nd)
-%
-% INPUT:
-%
-% ii - knot span index (see findspan)
-% pl - degree of curve
-% uu - parametric points
-% k - knot vector
-% nd - number of derivatives to compute
-%
-% OUTPUT:
-%
-% ders - ders(n, i, :) (i-1)-th derivative at n-th point
-%
-% Adapted from Algorithm A2.3 from 'The NURBS BOOK' pg72.
-%
-% See also:
-%
-% numbasisfun, basisfun, findspan
-%
-% Copyright (C) 2009,2011 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- dersv = zeros(numel(uu), nders+1, pl+1);
-
- for jj = 1:numel(uu)
-
- i = ii(jj)+1; %% convert to base-1 numbering of knot spans
- u = uu(jj);
-
- ders = zeros(nders+1,pl+1);
- ndu = zeros(pl+1,pl+1);
- left = zeros(pl+1);
- right = zeros(pl+1);
- a = zeros(2,pl+1);
- ndu(1,1) = 1;
- for j = 1:pl
- left(j+1) = u - u_knotl(i+1-j);
- right(j+1) = u_knotl(i+j) - u;
- saved = 0;
- for r = 0:j-1
- ndu(j+1,r+1) = right(r+2) + left(j-r+1);
- temp = ndu(r+1,j)/ndu(j+1,r+1);
- ndu(r+1,j+1) = saved + right(r+2)*temp;
- saved = left(j-r+1)*temp;
- end
- ndu(j+1,j+1) = saved;
- end
- for j = 0:pl
- ders(1,j+1) = ndu(j+1,pl+1);
- end
- for r = 0:pl
- s1 = 0;
- s2 = 1;
- a(1,1) = 1;
- for k = 1:nders %compute kth derivative
- d = 0;
- rk = r-k;
- pk = pl-k;
- if (r >= k)
- a(s2+1,1) = a(s1+1,1)/ndu(pk+2,rk+1);
- d = a(s2+1,1)*ndu(rk+1,pk+1);
- end
- if (rk >= -1)
- j1 = 1;
- else
- j1 = -rk;
- end
- if ((r-1) <= pk)
- j2 = k-1;
- else
- j2 = pl-r;
- end
- for j = j1:j2
- a(s2+1,j+1) = (a(s1+1,j+1) - a(s1+1,j))/ndu(pk+2,rk+j+1);
- d = d + a(s2+1,j+1)*ndu(rk+j+1,pk+1);
- end
- if (r <= pk)
- a(s2+1,k+1) = -a(s1+1,k)/ndu(pk+2,r+1);
- d = d + a(s2+1,k+1)*ndu(r+1,pk+1);
- end
- ders(k+1,r+1) = d;
- j = s1;
- s1 = s2;
- s2 = j;
- end
- end
- r = pl;
- for k = 1:nders
- for j = 0:pl
- ders(k+1,j+1) = ders(k+1,j+1)*r;
- end
- r = r*(pl-k);
- end
-
- dersv(jj, :, :) = ders;
-
- end
-
-end
-
-%!test
-%! k = [0 0 0 0 1 1 1 1];
-%! p = 3;
-%! u = rand (1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 1);
-%! sumders = sum (squeeze(ders), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), 0, 1e-15);
-
-%!test
-%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
-%! p = 3;
-%! u = rand (1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 7);
-%! sumders = sum (squeeze(ders), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), zeros(rows(squeeze(ders))-1, 1), 1e-13);
-
-%!test
-%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
-%! p = 3;
-%! u = rand (100, 1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 7);
-%! for ii=1:10
-%! sumders = sum (squeeze(ders(ii,:,:)), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), zeros(rows(squeeze(ders(ii,:,:)))-1, 1), 1e-13);
-%! end
-%! assert (ders(:, (p+2):end, :), zeros(numel(u), 8-p-1, p+1), 1e-13)
-%! assert (all(all(ders(:, 1, :) <= 1)), true)
-
-
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/basiskntins.m
--- a/extra/nurbs/inst/basiskntins.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,172 +0,0 @@
-function S = basiskntins (deg,t,u)
-
-% Compute the coefficient matrix for non-uniform B-splines subdivision.
-%
-% This represents the B-spline basis given by a coarse knot vector
-% in terms of the B-spline basis of a finer knot vector.
-%
-% The function is implemented for the univariate case. It is based on
-% the paper:
-%
-% G. Casciola, L. Romani, A general matrix representation for non-uniform
-% B-spline subdivision with boundary control, ALMA-DL, University of Bologna (2007)
-%
-% Calling Sequence:
-%
-% S = basiskntins (deg, t, u);
-%
-% INPUT:
-%
-% deg - degree of the first knot vector
-% t - coarse knot vector
-% u - fine knot vector
-%
-% OUTPUT:
-%
-% B - Value of the basis functions at the points
-% size(B)=[numel(u),(p+1)] for curves
-% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
-%
-% N - Indices of the basis functions that are nonvanishing at each
-% point. size(N) == size(B)
-%
-% Copyright (C) 2015 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-nt = length(t);
-nu = length(u);
-S = sparse (nu-deg-1,nt-deg-1);
-[t_mult,t_single,nt_s] = knot_mult(deg,t);
-[u_mult,u_single,nu_s] = knot_mult(deg,u);
-st = deg+1;
-su = deg+1;
-row = 1;
-col = 1;
-Sl = bs2bs(deg,t,u,st,su);
-S(row:deg+row,col:deg+col) = Sl;
-t_single(nt+1) = t(nt-deg);
-i = 1;
-
-for j=1:nu_s
- if (u_single(j) == t_single(i))
- st = st+t_mult(i);
- col = col+t_mult(i);
- i = i+1;
- end
- su = su+u_mult(j);
- row = row+u_mult(j);
- Sl = bs2bs(deg,t,u,st,su);
- S(row:deg+row,col:deg+col) = Sl;
-end
-
-end
-
-
-function [t_mult,t_single,nt_s] = knot_mult(d,t)
-epsilon = 1e-14 * (t(end) - t(1));
-
-nt = length(t);
-nt_s = 0;
-m = 1;
-for i = d+2:nt-d-1
- if ((t(i+1) - t(i)) > epsilon)
- nt_s = nt_s+1;
- t_mult(nt_s) = m;
- t_single(nt_s) = t(i);
- m=1;
- else
- m = m+1;
- end
-end
-t_single(nt_s+1)=t(nt-d);
-t_mult(nt_s+1)=0;
-
-end
-
-function S = bs2bs(d,t,u,k,l)
-
-S = zeros(d+1);
-S(1,:) = bs2bs_first_row(d,t,u,k,l);
-
-for ir=1:d
- S(ir+1,:) = bs2bs_i_row(d,t,u,k,l,ir,S(ir,:));
-end
-end
-
-function S = bs2bs_first_row(d,t,u,k,l)
-
-S = eye(1,d+1);
-for h=1:d
- beta_2=0.0;
- uu=u(l+1-h);
- for j=h:-1:1
- d1=uu-t(k+j-h);
- d2=t(k+j)-uu;
- beta_1=S(j)/(d2+d1);
- S(j+1)=d1*beta_1+beta_2;
- beta_2=d2*beta_1;
- end
- S(1)=beta_2;
-end
-end
-
-function Si = bs2bs_i_row(d,t,u,k,l,ir,S)
-
-Si(1) = S(1)*(t(k+1)-u(l+ir))/(t(k+1)-u(l+ir-d));
-
-for j=1:d
- den=t(k+j+1)-u(l+ir-d);
- fact=(t(k+j+1)-t(k+j-d))/(t(k+j)-t(k+j-d-1));
- Si(j+1)=(fact*(S(j)*(u(l+ir)-t(k+j-d-1))-Si(j) * ...
- (u(l+ir-d)-t(k+j-d-1)))+S(j+1)*(t(k+j+1)-u(l+ir)))/den;
-end
-end
-
-%!test
-%! knt1 = [0 0 0 1/2 1 1 1];
-%! knt2 = [0 0 0 1/4 1/2 3/4 1 1 1];
-%! C = basiskntins (2, knt1, knt2);
-%! assert (full(C), [1 0 0 0; 1/2 1/2 0 0; 0 3/4 1/4 0; 0 1/4 3/4 0; 0 0 1/2 1/2; 0 0 0 1]);
-
-%!test
-%! crv = nrbtestcrv;
-%! crv2 = nrbkntins (crv, [0.1, 0.3, 0.4, 0.5, 0.6, 0.8, 0.96 0.98]);
-%! C = basiskntins (crv.order-1,crv.knots,crv2.knots);
-%! for ii = 1:4
-%! assert (max (abs(C*crv.coefs(ii,:)' - crv2.coefs(ii,:)')) < 1e-14 )
-%! end
-
-%!test
-%! crv = nrbtestcrv;
-%! crv2 = nrbkntins (crv, [0.50000001, 0.5000001, 0.500001, 0.50001, 0.5001]);
-%! C = basiskntins (crv.order-1,crv.knots,crv2.knots);
-%! for ii = 1:4
-%! assert (max (abs(C*crv.coefs(ii,:)' - crv2.coefs(ii,:)')) < 1e-14 )
-%! end
-
-%!test
-%! crv = nrbtestcrv;
-%! crv2 = nrbkntins (crv, [0.1, 0.3, 0.4, 0.5, 0.6, 0.8, 0.96 0.98]);
-%! C = basiskntins (crv.order-1,crv.knots,crv2.knots);
-%! x = linspace (0, 1, 10);
-%! s = findspan (crv.number-1, crv.order-1, x, crv.knots);
-%! s2 = findspan (crv2.number-1, crv2.order-1, x, crv2.knots);
-%! N = basisfun (s, x, crv.order-1, crv.knots);
-%! N2 = basisfun (s2, x, crv2.order-1, crv2.knots);
-%! c = numbasisfun (s, x, crv.order-1, crv.knots) + 1;
-%! c2 = numbasisfun (s2, x, crv2.order-1, crv2.knots) + 1;
-%! for ii = 1:numel(x)
-%! assert (abs(N2(ii,:) * C(c2(ii,:),c(ii,:)) - N(ii,:)) < 1e-14)
-%! end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/bspdegelev.m
--- a/extra/nurbs/inst/bspdegelev.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,296 +0,0 @@
-function [ic,ik] = bspdegelev(d,c,k,t)
-
-% BSPDEGELEV: Degree elevate a univariate B-Spline.
-%
-% Calling Sequence:
-%
-% [ic,ik] = bspdegelev(d,c,k,t)
-%
-% INPUT:
-%
-% d - Degree of the B-Spline.
-% c - Control points, matrix of size (dim,nc).
-% k - Knot sequence, row vector of size nk.
-% t - Raise the B-Spline degree t times.
-%
-% OUTPUT:
-%
-% ic - Control points of the new B-Spline.
-% ik - Knot vector of the new B-Spline.
-%
-% Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-[mc,nc] = size(c);
- %
- % int bspdegelev(int d, double *c, int mc, int nc, double *k, int nk,
- % int t, int *nh, double *ic, double *ik)
- % {
- % int row,col;
- %
- % int ierr = 0;
- % int i, j, q, s, m, ph, ph2, mpi, mh, r, a, b, cind, oldr, mul;
- % int n, lbz, rbz, save, tr, kj, first, kind, last, bet, ii;
- % double inv, ua, ub, numer, den, alf, gam;
- % double **bezalfs, **bpts, **ebpts, **Nextbpts, *alfs;
- %
- % double **ctrl = vec2mat(c, mc, nc);
-% ic = zeros(mc,nc*(t)); % double **ictrl = vec2mat(ic, mc, nc*(t+1));
- %
-n = nc - 1; % n = nc - 1;
- %
-bezalfs = zeros(d+1,d+t+1); % bezalfs = matrix(d+1,d+t+1);
-bpts = zeros(mc,d+1); % bpts = matrix(mc,d+1);
-ebpts = zeros(mc,d+t+1); % ebpts = matrix(mc,d+t+1);
-Nextbpts = zeros(mc,d+1); % Nextbpts = matrix(mc,d+1);
-alfs = zeros(d,1); % alfs = (double *) mxMalloc(d*sizeof(double));
- %
-m = n + d + 1; % m = n + d + 1;
-ph = d + t; % ph = d + t;
-ph2 = floor(ph / 2); % ph2 = ph / 2;
- %
- % // compute bezier degree elevation coefficeients
-bezalfs(1,1) = 1; % bezalfs[0][0] = bezalfs[ph][d] = 1.0;
-bezalfs(d+1,ph+1) = 1; %
-
-for i=1:ph2 % for (i = 1; i <= ph2; i++) {
- inv = 1/bincoeff(ph,i); % inv = 1.0 / bincoeff(ph,i);
- mpi = min(d,i); % mpi = min(d,i);
- %
- for j=max(0,i-t):mpi % for (j = max(0,i-t); j <= mpi; j++)
- bezalfs(j+1,i+1) = inv*bincoeff(d,j)*bincoeff(t,i-j); % bezalfs[i][j] = inv * bincoeff(d,j) * bincoeff(t,i-j);
- end
-end % }
- %
-for i=ph2+1:ph-1 % for (i = ph2+1; i <= ph-1; i++) {
- mpi = min(d,i); % mpi = min(d, i);
- for j=max(0,i-t):mpi % for (j = max(0,i-t); j <= mpi; j++)
- bezalfs(j+1,i+1) = bezalfs(d-j+1,ph-i+1); % bezalfs[i][j] = bezalfs[ph-i][d-j];
- end
-end % }
- %
-mh = ph; % mh = ph;
-kind = ph+1; % kind = ph+1;
-r = -1; % r = -1;
-a = d; % a = d;
-b = d+1; % b = d+1;
-cind = 1; % cind = 1;
-ua = k(1); % ua = k[0];
- %
-for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- ic(ii+1,1) = c(ii+1,1); % ictrl[0][ii] = ctrl[0][ii];
-end %
-for i=0:ph % for (i = 0; i <= ph; i++)
- ik(i+1) = ua; % ik[i] = ua;
-end %
- % // initialise first bezier seg
-for i=0:d % for (i = 0; i <= d; i++)
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- bpts(ii+1,i+1) = c(ii+1,i+1); % bpts[i][ii] = ctrl[i][ii];
- end
-end %
- % // big loop thru knot vector
-while b < m % while (b < m) {
- i = b; % i = b;
- while b < m && k(b+1) == k(b+2) % while (b < m && k[b] == k[b+1])
- b = b + 1; % b++;
- end %
- mul = b - i + 1; % mul = b - i + 1;
- mh = mh + mul + t; % mh += mul + t;
- ub = k(b+1); % ub = k[b];
- oldr = r; % oldr = r;
- r = d - mul; % r = d - mul;
- %
- % // insert knot u(b) r times
- if oldr > 0 % if (oldr > 0)
- lbz = floor((oldr+2)/2); % lbz = (oldr+2) / 2;
- else % else
- lbz = 1; % lbz = 1;
- end %
-
- if r > 0 % if (r > 0)
- rbz = ph - floor((r+1)/2); % rbz = ph - (r+1)/2;
- else % else
- rbz = ph; % rbz = ph;
- end %
-
- if r > 0 % if (r > 0) {
- % // insert knot to get bezier segment
- numer = ub - ua; % numer = ub - ua;
- for q=d:-1:mul+1 % for (q = d; q > mul; q--)
- alfs(q-mul) = numer / (k(a+q+1)-ua); % alfs[q-mul-1] = numer / (k[a+q]-ua);
- end
-
- for j=1:r % for (j = 1; j <= r; j++) {
- save = r - j; % save = r - j;
- s = mul + j; % s = mul + j;
- %
- for q=d:-1:s % for (q = d; q >= s; q--)
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- tmp1 = alfs(q-s+1)*bpts(ii+1,q+1);
- tmp2 = (1-alfs(q-s+1))*bpts(ii+1,q);
- bpts(ii+1,q+1) = tmp1 + tmp2; % bpts[q][ii] = alfs[q-s]*bpts[q][ii]+(1.0-alfs[q-s])*bpts[q-1][ii];
- end
- end %
-
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- Nextbpts(ii+1,save+1) = bpts(ii+1,d+1); % Nextbpts[save][ii] = bpts[d][ii];
- end
- end % }
- end % }
- % // end of insert knot
- %
- % // degree elevate bezier
- for i=lbz:ph % for (i = lbz; i <= ph; i++) {
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- ebpts(ii+1,i+1) = 0; % ebpts[i][ii] = 0.0;
- end
- mpi = min(d, i); % mpi = min(d, i);
- for j=max(0,i-t):mpi % for (j = max(0,i-t); j <= mpi; j++)
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- tmp1 = ebpts(ii+1,i+1);
- tmp2 = bezalfs(j+1,i+1)*bpts(ii+1,j+1);
- ebpts(ii+1,i+1) = tmp1 + tmp2; % ebpts[i][ii] = ebpts[i][ii] + bezalfs[i][j]*bpts[j][ii];
- end
- end
- end % }
- % // end of degree elevating bezier
- %
- if oldr > 1 % if (oldr > 1) {
- % // must remove knot u=k[a] oldr times
- first = kind - 2; % first = kind - 2;
- last = kind; % last = kind;
- den = ub - ua; % den = ub - ua;
- bet = floor((ub-ik(kind)) / den); % bet = (ub-ik[kind-1]) / den;
- %
- % // knot removal loop
- for tr=1:oldr-1 % for (tr = 1; tr < oldr; tr++) {
- i = first; % i = first;
- j = last; % j = last;
- kj = j - kind + 1; % kj = j - kind + 1;
- while j-i > tr % while (j - i > tr) {
- % // loop and compute the new control points
- % // for one removal step
- if i < cind % if (i < cind) {
- alf = (ub-ik(i+1))/(ua-ik(i+1)); % alf = (ub-ik[i])/(ua-ik[i]);
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- tmp1 = alf*ic(ii+1,i+1);
- tmp2 = (1-alf)*ic(ii+1,i);
- ic(ii+1,i+1) = tmp1 + tmp2; % ictrl[i][ii] = alf * ictrl[i][ii] + (1.0-alf) * ictrl[i-1][ii];
- end
- end % }
- if j >= lbz % if (j >= lbz) {
- if j-tr <= kind-ph+oldr % if (j-tr <= kind-ph+oldr) {
- gam = (ub-ik(j-tr+1)) / den; % gam = (ub-ik[j-tr]) / den;
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- tmp1 = gam*ebpts(ii+1,kj+1);
- tmp2 = (1-gam)*ebpts(ii+1,kj+2);
- ebpts(ii+1,kj+1) = tmp1 + tmp2; % ebpts[kj][ii] = gam*ebpts[kj][ii] + (1.0-gam)*ebpts[kj+1][ii];
- end % }
- else % else {
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- tmp1 = bet*ebpts(ii+1,kj+1);
- tmp2 = (1-bet)*ebpts(ii+1,kj+2);
- ebpts(ii+1,kj+1) = tmp1 + tmp2; % ebpts[kj][ii] = bet*ebpts[kj][ii] + (1.0-bet)*ebpts[kj+1][ii];
- end
- end % }
- end % }
- i = i + 1; % i++;
- j = j - 1; % j--;
- kj = kj - 1; % kj--;
- end % }
- %
- first = first - 1; % first--;
- last = last + 1; % last++;
- end % }
- end % }
- % // end of removing knot n=k[a]
- %
- % // load the knot ua
- if a ~= d % if (a != d)
- for i=0:ph-oldr-1 % for (i = 0; i < ph-oldr; i++) {
- ik(kind+1) = ua; % ik[kind] = ua;
- kind = kind + 1; % kind++;
- end
- end % }
- %
- % // load ctrl pts into ic
- for j=lbz:rbz % for (j = lbz; j <= rbz; j++) {
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- ic(ii+1,cind+1) = ebpts(ii+1,j+1); % ictrl[cind][ii] = ebpts[j][ii];
- end
- cind = cind + 1; % cind++;
- end % }
- %
- if b < m % if (b < m) {
- % // setup for next pass thru loop
- for j=0:r-1 % for (j = 0; j < r; j++)
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- bpts(ii+1,j+1) = Nextbpts(ii+1,j+1); % bpts[j][ii] = Nextbpts[j][ii];
- end
- end
- for j=r:d % for (j = r; j <= d; j++)
- for ii=0:mc-1 % for (ii = 0; ii < mc; ii++)
- bpts(ii+1,j+1) = c(ii+1,b-d+j+1); % bpts[j][ii] = ctrl[b-d+j][ii];
- end
- end
- a = b; % a = b;
- b = b+1; % b++;
- ua = ub; % ua = ub;
- % }
- else % else
- % // end knot
- for i=0:ph % for (i = 0; i <= ph; i++)
- ik(kind+i+1) = ub; % ik[kind+i] = ub;
- end
- end
-end % }
-% End big while loop % // end while loop
- %
- % *nh = mh - ph - 1;
- %
- % freevec2mat(ctrl);
- % freevec2mat(ictrl);
- % freematrix(bezalfs);
- % freematrix(bpts);
- % freematrix(ebpts);
- % freematrix(Nextbpts);
- % mxFree(alfs);
- %
- % return(ierr);
-end % }
-
-
-function b = bincoeff(n,k)
-% Computes the binomial coefficient.
-%
-% ( n ) n!
-% ( ) = --------
-% ( k ) k!(n-k)!
-%
-% b = bincoeff(n,k)
-%
-% Algorithm from 'Numerical Recipes in C, 2nd Edition' pg215.
-
- % double bincoeff(int n, int k)
- % {
-b = floor(0.5+exp(factln(n)-factln(k)-factln(n-k))); % return floor(0.5+exp(factln(n)-factln(k)-factln(n-k)));
-end % }
-
-function f = factln(n)
-% computes ln(n!)
-if n <= 1, f = 0; return, end
-f = gammaln(n+1); %log(factorial(n));
-end
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/bspderiv.m
--- a/extra/nurbs/inst/bspderiv.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,67 +0,0 @@
-function [dc,dk] = bspderiv(d,c,k)
-
-% BSPDERIV: B-Spline derivative.
-%
-% MATLAB SYNTAX:
-%
-% [dc,dk] = bspderiv(d,c,k)
-%
-% INPUT:
-%
-% d - degree of the B-Spline
-% c - control points double matrix(mc,nc)
-% k - knot sequence double vector(nk)
-%
-% OUTPUT:
-%
-% dc - control points of the derivative double matrix(mc,nc)
-% dk - knot sequence of the derivative double vector(nk)
-%
-% Modified version of Algorithm A3.3 from 'The NURBS BOOK' pg98.
-%
-% Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-[mc,nc] = size(c);
-nk = numel(k);
- %
- % int bspderiv(int d, double *c, int mc, int nc, double *k, int nk, double *dc,
- % double *dk)
- % {
- % int ierr = 0;
- % int i, j, tmp;
- %
- % // control points
- % double **ctrl = vec2mat(c,mc,nc);
- %
- % // control points of the derivative
-dc = zeros(mc,nc-1); % double **dctrl = vec2mat(dc,mc,nc-1);
- %
-for i=0:nc-2 % for (i = 0; i < nc-1; i++) {
- tmp = d / (k(i+d+2) - k(i+2)); % tmp = d / (k[i+d+1] - k[i+1]);
- for j=0:mc-1 % for (j = 0; j < mc; j++) {
- dc(j+1,i+1) = tmp*(c(j+1,i+2) - c(j+1,i+1)); % dctrl[i][j] = tmp * (ctrl[i+1][j] - ctrl[i][j]);
- end % }
-end % }
- %
-dk = zeros(1,nk-2); % j = 0;
-for i=1:nk-2 % for (i = 1; i < nk-1; i++)
- dk(i) = k(i+1); % dk[j++] = k[i];
-end %
- % freevec2mat(dctrl);
- % freevec2mat(ctrl);
- %
- % return ierr;
-end % }
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/bspeval.m
--- a/extra/nurbs/inst/bspeval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,72 +0,0 @@
-function p = bspeval(d,c,k,u)
-
-% BSPEVAL: Evaluate B-Spline at parametric points.
-%
-% Calling Sequence:
-%
-% p = bspeval(d,c,k,u)
-%
-% INPUT:
-%
-% d - Degree of the B-Spline.
-% c - Control Points, matrix of size (dim,nc).
-% k - Knot sequence, row vector of size nk.
-% u - Parametric evaluation points, row vector of size nu.
-%
-% OUTPUT:
-%
-% p - Evaluated points, matrix of size (dim,nu)
-%
-% Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton, 2010 C. de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-nu = numel(u);
-[mc,nc] = size(c);
- % int bspeval(int d, double *c, int mc, int nc, double *k, int nk, double *u,int nu, double *p){
- % int ierr = 0;
- % int i, s, tmp1, row, col;
- % double tmp2;
- %
- % // Construct the control points
- % double **ctrl = vec2mat(c,mc,nc);
- %
- % // Contruct the evaluated points
- % double **pnt = vec2mat(p,mc,nu);
- %
- % // space for the basis functions
-%N = zeros(d+1,1); % double *N = (double*) mxMalloc((d+1)*sizeof(double));
- %
- % // for each parametric point i
-%for col=1:nu % for (col = 0; col < nu; col++) {
- % // find the span of u[col]
- s = findspan(nc-1, d, u(:), k); % s = findspan(nc-1, d, u[col], k);
- N = basisfun(s,u(:),d,k); % basisfun(s, u[col], d, k, N);
- %
- tmp1 = s - d + 1; % tmp1 = s - d;
- %for row=1:mc % for (row = 0; row < mc; row++) {
- p = zeros (mc, nu); % tmp2 = 0.0;
- for i=0:d % for (i = 0; i <= d; i++)
- p = p + repmat (N(:,i+1)', mc, 1).*c(:,tmp1+i); % tmp2 += N[i] * ctrl[tmp1+i][row];
- end %
- %p(row,:) = tmp2; % pnt[col][row] = tmp2;
- %end % }
-%end % }
- %
- % mxFree(N);
- % freevec2mat(pnt);
- % freevec2mat(ctrl);
- %
- % return ierr;
-end % }
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/bspkntins.m
--- a/extra/nurbs/inst/bspkntins.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,112 +0,0 @@
-function [ic,ik] = bspkntins(d,c,k,u)
-
-% BSPKNTINS: Insert knots into a B-Spline
-%
-% Calling Sequence:
-%
-% [ic,ik] = bspkntins(d,c,k,u)
-%
-% INPUT:
-%
-% d - spline degree integer
-% c - control points double matrix(mc,nc)
-% k - knot sequence double vector(nk)
-% u - new knots double vector(nu)
-%
-% OUTPUT:
-%
-% ic - new control points double matrix(mc,nc+nu)
-% ik - new knot sequence double vector(nk+nu)
-%
-% Modified version of Algorithm A5.4 from 'The NURBS BOOK' pg164.
-%
-% Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton, 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-[mc,nc] = size(c);
-u = sort(u);
-nu = numel(u);
-nk = numel(k);
- %
- % int bspkntins(int d, double *c, int mc, int nc, double *k, int nk,
- % double *u, int nu, double *ic, double *ik)
- % {
- % int ierr = 0;
- % int a, b, r, l, i, j, m, n, s, q, ind;
- % double alfa;
- %
- % double **ctrl = vec2mat(c, mc, nc);
-ic = zeros(mc,nc+nu); % double **ictrl = vec2mat(ic, mc, nc+nu);
-ik = zeros(1,nk+nu);
- %
-n = size(c,2) - 1; % n = nc - 1;
-r = length(u) - 1; % r = nu - 1;
- %
-m = n + d + 1; % m = n + d + 1;
-a = findspan(n, d, u(1), k); % a = findspan(n, d, u[0], k);
-b = findspan(n, d, u(r+1), k); % b = findspan(n, d, u[r], k);
-b = b+1; % ++b;
- %
-for q=0:mc-1 % for (q = 0; q < mc; q++) {
- for j=0:a-d, ic(q+1,j+1) = c(q+1,j+1); end % for (j = 0; j <= a-d; j++) ictrl[j][q] = ctrl[j][q];
- for j=b-1:n, ic(q+1,j+r+2) = c(q+1,j+1); end % for (j = b-1; j <= n; j++) ictrl[j+r+1][q] = ctrl[j][q];
-end % }
-
-for j=0:a, ik(j+1) = k(j+1); end % for (j = 0; j <= a; j++) ik[j] = k[j];
-for j=b+d:m, ik(j+r+2) = k(j+1); end % for (j = b+d; j <= m; j++) ik[j+r+1] = k[j];
- %
-i = b + d - 1; % i = b + d - 1;
-s = b + d + r; % s = b + d + r;
-
-for j=r:-1:0 % for (j = r; j >= 0; j--) {
- while u(j+1) <= k(i+1) && i > a % while (u[j] <= k[i] && i > a) {
- for q=0:mc-1 % for (q = 0; q < mc; q++)
- ic(q+1,s-d) = c(q+1,i-d); % ictrl[s-d-1][q] = ctrl[i-d-1][q];
- end
- ik(s+1) = k(i+1); % ik[s] = k[i];
- s = s - 1; % --s;
- i = i - 1; % --i;
- end % }
-
- for q=0:mc-1 % for (q = 0; q < mc; q++)
- ic(q+1,s-d) = ic(q+1,s-d+1); % ictrl[s-d-1][q] = ictrl[s-d][q];
- end
-
- for l=1:d % for (l = 1; l <= d; l++) {
- ind = s - d + l; % ind = s - d + l;
- alfa = ik(s+l+1) - u(j+1); % alfa = ik[s+l] - u[j];
- if abs(alfa) == 0 % if (fabs(alfa) == 0.0)
- for q=0:mc-1 % for (q = 0; q < mc; q++)
- ic(q+1,ind) = ic(q+1,ind+1); % ictrl[ind-1][q] = ictrl[ind][q];
- end
- else % else {
- alfa = alfa/(ik(s+l+1) - k(i-d+l+1)); % alfa /= (ik[s+l] - k[i-d+l]);
- for q=0:mc-1 % for (q = 0; q < mc; q++)
- tmp = (1-alfa)*ic(q+1,ind+1);
- ic(q+1,ind) = alfa*ic(q+1,ind) + tmp; % ictrl[ind-1][q] = alfa*ictrl[ind-1][q]+(1.0-alfa)*ictrl[ind][q];
- end
- end % }
- end % }
- %
- ik(s+1) = u(j+1); % ik[s] = u[j];
- s = s - 1; % --s;
-end % }
- %
- % freevec2mat(ctrl);
- % freevec2mat(ictrl);
- %
- % return ierr;
-end % }
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/crvkntremove.m
--- a/extra/nurbs/inst/crvkntremove.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,173 +0,0 @@
-
-
-function [rcrv, t] = crvkntremove (crv, u, r, s, num, d)
-%
-% CRVKNTREMOVE: Remove one knot from the knot-vector of a NURBS curve.
-%
-% Calling Sequence:
-%
-% [rcrv, remflag] = crvkntremove (crv, u, r, s, num, d);
-%
-% INPUT:
-%
-% crv : NURBS curve, see nrbmak.
-%
-% u : knot to be removed.
-%
-% r : index of the knot to be removed.
-%
-% s : multiplicity of the knot to be removed.
-%
-% num : number of knot removals requested.
-%
-% d : curve deviation tolerance.
-%
-% OUTPUT:
-%
-% rcrv : new NURBS structure for the curve with knot u remuved.
-%
-% t : actual number of knot removals performed.
-%
-%
-%
-% DESCRIPTION:
-%
-% Remove knot u from the NURBS curve crv at most num times.
-% Check that the maximum deviation of the curve be less than d.
-% Based on algorithm A5.8 NURBS Book (pag183)
-%
-% SEE ALSO:
-%
-% nrbkntins
-%
-% Copyright (C) 2013 Jacopo Corno
-% Copyright (C) 2013 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- [U, Pw, t] = RemoveCurveKnot (crv.number, crv.order - 1, crv.knots, ...
- crv.coefs, u, r, s, num, d);
- rcrv = nrbmak (Pw, U);
-
-end
-
-%!test
-%! crv = nrbdegelev (nrbline (), 3);
-%! acrv = nrbkntins (crv, [.11 .11 .11]);
-%! [rcrv, t] = crvkntremove (acrv, .11, 8, 3, 3, 1e-10);
-%! assert (crv.knots, rcrv.knots, 1e-10);
-%! assert (t, 3);
-
-%!test
-%! crv = nrbcirc ();
-%! acrv = nrbkntins (crv, [.3 .3]);
-%! [rcrv, t] = crvkntremove (acrv, .3, 7, 2, 2, 1e-10);
-%! assert (crv.knots, rcrv.knots, 1e-10);
-%! assert (t, 2);
-
-function [U, Pw, t] = RemoveCurveKnot (n, p, U, Pw, u, r, s, num, d)
-% see algorithm A5.8 NURBS Book (pag183)
-
- w = min (Pw(4,:));
- Pmax = max (sqrt (sum (Pw.^2, 1)));
- TOL = d*w / (1 + Pmax);
-
- m = n + p + 1;
- ord = p + 1;
- fout = (2*r - s - p) / 2; % first control point out
- last = r - s;
- first = r - p;
-
- temp = zeros (4, 2*p + 1);
-
- for t = 0:num-1
- off = first - 1; % diff in index between temp and P
- temp(:,1) = Pw(:,off);
- temp(:,last+1-off+1) = Pw(:,last+1);
- i = first;
- j = last;
- ii = 1;
- jj = last - off;
- remflag = 0;
- while (j - i > t)
- % compute new control points for one removal step
- alfi = (u-U(i)) / (U(i+ord+t)-U(i));
- alfj = (u-U(j-t)) / (U(j+ord)-U(j-t));
- temp(:,ii+1) = (Pw(:,i)-(1.0-alfi).*temp(:,ii-1+1))./alfi;
- temp(:,jj+1) = (Pw(:,j)-alfj.*temp(:,jj+1+1))./(1.0-alfj);
- i = i + 1;
- ii = ii + 1;
- j = j - 1;
- jj = jj - 1;
- end
- if (j - i <= t)
- % check if knot removable
- if (norm (temp(:,ii-1+1) - temp(:,jj+1+1)) <= TOL)
- remflag = 1;
- else
- alfi = (u-U(i)) / (U(i+ord+t)-U(i));
- if (norm (Pw(:,i) - (alfi.*temp(:,ii+t+1+1) + ...
- (1-alfi).*temp(:,ii-1+1))) <= TOL)
- remflag = 1;
- end%if
- end%if
- end%if
- if (remflag == 0)
- break; % cannot remove any more knots -> get out of for loop
- else
- % successful removal -> save new control points
- i = first;
- j = last;
- while (j - i > t)
- Pw(:,i) = temp(:,i-off+1);
- Pw(:,j) = temp(:,j-off+1);
- i = i + 1;
- j = j - 1;
- end
- end%if
- first = first - 1;
- last = last + 1;
- t = t + 1;
- end % end of for loop
-
- if (t == 0)
- return;
- end%if
-
- % shift knots
- for k = r+1:m
- U(k-t) = U(k);
- end
- U = U(1:end-t);
-
- j = floor(fout);
- i = j;
- for k = 1:t-1
- if (mod (k, 2) == 1)
- i = i+1;
- else
- j = j-1;
- end%if
- end
-
- % shift points
- for k = i+1:n
- Pw(:,j) = Pw(:,k);
- j = j+1;
- end
- Pw = Pw(:,1:end-t);
-
- return;
-end
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/curvederivcpts.m
--- a/extra/nurbs/inst/curvederivcpts.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,60 +0,0 @@
-function pk = curvederivcpts (n, p, U, P, d, r1, r2)
-% Compute control points of n-th derivatives of a B-spline curve.
-%
-% usage: pk = curvederivcpts (n, p, U, P, d)
-% pk = curvederivcpts (n, p, U, P, d, r1, r2)
-%
-% If r1, r2 are not given, all the control points are computed.
-%
-% INPUT:
-% n+1 = number of control points
-% p = degree of the spline
-% d = maximum derivative order (d<=p)
-% U = knots
-% P = control points
-% r1 = first control point to compute
-% r2 = auxiliary index for the last control point to compute
-% OUTPUT:
-% pk(k,i) = i-th control point of (k-1)-th derivative, r1 <= i <= r2-k
-%
-% Adaptation of algorithm A3.3 from the NURBS book, pg98.
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- if (nargin <= 5)
- r1 = 0;
- r2 = n;
- end
-
- r = r2 - r1;
- for i=0:r
- pk(1, i+1) = P(r1+i+1);
- end
-
- for k=1:d
- tmp = p - k + 1;
- for i=0:r-k
- pk (k+1, i+1) = tmp * (pk(k,i+2)-pk(k,i+1)) / ...
- (U(r1+i+p+2)-U(r1+i+k+1));
- end
- end
-end
-
-%!test
-%! line = nrbmak([0.0 1.5; 0.0 3.0],[0.0 0.0 1.0 1.0]);
-%! pk = curvederivcpts (line.number-1, line.order-1, line.knots,...
-%! line.coefs(1,:), 2);
-%! assert (pk, [0 3/2; 3/2 0], 100*eps);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/curvederiveval.m
--- a/extra/nurbs/inst/curvederiveval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,68 +0,0 @@
-function ck = curvederiveval (n, p, U, P, u, d)
-%
-% CURVEDERIVEVAL: Compute the derivatives of a B-spline curve.
-%
-% usage: ck = curvederiveval (n, p, U, P, u, d)
-%
-% INPUT:
-%
-% n+1 = number of control points
-% p = spline order
-% U = knots
-% P = control points
-% u = evaluation point
-% d = derivative order
-%
-% OUTPUT:
-%
-% ck (k+1) = curve differentiated k times
-%
-% Adaptation of algorithm A3.4 from the NURBS book, pg99
-%
-% Copyright (C) 2009 Carlo de Falco
-% Copyright (C) 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- ck = zeros (d+1, 1);
- du = min (d, p);
-
- span = findspan (n, p, u, U);
- N = zeros (p+1, p+1);
- for ip=0:p
- N(1:ip+1,ip+1) = basisfun (span, u, ip, U)';
- end
-
- pk = curvederivcpts (n, p, U, P, du, span-p, span);
-
- for k = 0:du
- for j = 0:p-k
- ck(k+1) = ck(k+1) + N(j+1,p-k+1)*pk(k+1,j+1);
- end
- end
-
-end
-
-%!test
-%! k = [0 0 0 1 1 1];
-%! coefs(:,1) = [0;0;0;1];
-%! coefs(:,2) = [1;0;1;1];
-%! coefs(:,3) = [1;1;1;1];
-%! crv = nrbmak (coefs, k);
-%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(1,:,:)), 0.5, 2);
-%! assert(ck, [0.75; 1; -2]);
-%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(2,:,:)), 0.5, 2);
-%! assert(ck, [0.25; 1; 2]);
-%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(3,:,:)), 0.5, 2);
-%! assert(ck, [0.75; 1; -2]);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/deg2rad.m
--- a/extra/nurbs/inst/deg2rad.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,44 +0,0 @@
-function rad = deg2rad(deg)
-
-% DEG2RAD: Convert degrees to radians.
-%
-% Calling Sequence:
-%
-% rad = deg2rad(deg);
-%
-% INPUT:
-%
-% deg : Angle in degrees.
-%
-% OUTPUT:
-%
-% rad : Angle in radians.
-%
-% Description:
-%
-% Convenient utility function for converting degrees to radians, which are
-% often the required angular units for functions in the NURBS toolbox.
-%
-% Examples:
-%
-% // Convert 35 degrees to radians
-% rad = deg2rad(35);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-rad = pi*deg/180.0;
-
-end
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/findspan.m
--- a/extra/nurbs/inst/findspan.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,61 +0,0 @@
-function s = findspan(n,p,u,U)
-% FINDSPAN Find the span of a B-Spline knot vector at a parametric point
-%
-% Calling Sequence:
-%
-% s = findspan(n,p,u,U)
-%
-% INPUT:
-%
-% n - number of control points - 1
-% p - spline degree
-% u - parametric point
-% U - knot sequence
-%
-% OUTPUT:
-%
-% s - knot span index
-%
-% Modification of Algorithm A2.1 from 'The NURBS BOOK' pg68
-%
-% Copyright (C) 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (max(u(:))>U(end) || min(u(:))= U,1,'last')-1;
-end
-
-end
-
-%!test
-%! n = 3;
-%! U = [0 0 0 1/2 1 1 1];
-%! p = 2;
-%! u = linspace(0, 1, 10);
-%! s = findspan (n, p, u, U);
-%! assert (s, [2*ones(1, 5) 3*ones(1, 5)]);
-
-%!test
-%! p = 2; m = 7; n = m - p - 1;
-%! U = [zeros(1,p) linspace(0,1,m+1-2*p) ones(1,p)];
-%! u = [ 0 0.11880 0.55118 0.93141 0.40068 0.35492 0.44392 0.88360 0.35414 0.92186 0.83085 1];
-%! s = [2 2 3 4 3 3 3 4 3 4 4 4];
-%! assert (findspan (n, p, u, U), s, 1e-10);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/kntbrkdegmult.m
--- a/extra/nurbs/inst/kntbrkdegmult.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,122 +0,0 @@
-% KNTBRKDEGMULT: Construct an open knot vector by giving the sequence of
-% knots, the degree and the multiplicity.
-%
-% knots = kntbrkdegreg (breaks, degree)
-% knots = kntbrkdegreg (breaks, degree, mult)
-%
-% INPUT:
-%
-% breaks: sequence of knots.
-% degree: polynomial degree of the splines associated to the knot vector.
-% mult: multiplicity of the knots.
-%
-% OUTPUT:
-%
-% knots: knot vector.
-%
-% If MULT has as many entries as BREAKS, or as the number of interior
-% knots, a different multiplicity will be assigned to each knot. If
-% MULT is not present, it will be taken equal to 1.
-%
-% Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-function knots = kntbrkdegmult (breaks, degree, mult)
-
- if (iscell (breaks))
- if (nargin == 2)
- mult = 1;
- end
-
- if (numel(breaks)~=numel(degree) || numel(breaks)~=numel(mult))
- error('kntbrkdegmult: degree and multiplicity must have the same length as the number of knot vectors')
- end
-
- degree = num2cell (degree);
-
- if (~iscell (mult))
- mult = num2cell (mult);
- end
-
- knots = cellfun (@do_kntbrkdegmult, breaks, degree, mult, 'uniformoutput', false);
-
- else
-
- if (nargin == 2)
- mult = 1;
- end
-
- knots = do_kntbrkdegmult (breaks, degree, mult);
- end
-end
-
-
-function knots = do_kntbrkdegmult (breaks, degree, mult)
-
-if (numel (breaks) < 2)
- error ('kntbrkdegmult: the knots sequence should contain at least two points')
-end
-
-if (numel (mult) == 1)
- mults = [degree+1, mult(ones (1, numel (breaks) - 2)), degree+1];
-elseif (numel (mult) == numel (breaks))
- mults = [degree+1 mult(2:end-1) degree+1];
-elseif (numel (mult) == numel (breaks) - 2)
- mults = [degree+1 mult degree+1];
-else
- error('kntbrkdegmult: the length of mult should be equal to one or the number of knots')
-end
-
-if (any (mults > degree+1))
- warning ('kntbrkdegmult: some knots have higher multiplicity than the degree+1')
-end
-
-breaks = sort (breaks);
-
-lm = numel (mults);
-sm = sum (mults);
-
-mm = zeros (1,sm);
-mm (cumsum ([1 reshape(mults (1:end-1), 1, lm-1)])) = ones (1,lm);
-knots = breaks (cumsum (mm));
-
-end
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! knots = kntbrkdegmult (breaks, degree);
-%! assert (knots, [0 0 0 0 1 2 3 4 4 4 4])
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! mult = 2;
-%! knots = kntbrkdegmult (breaks, degree, mult);
-%! assert (knots, [0 0 0 0 1 1 2 2 3 3 4 4 4 4])
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! mult = [1 2 3];
-%! knots = kntbrkdegmult (breaks, degree, mult);
-%! assert (knots, [0 0 0 0 1 2 2 3 3 3 4 4 4 4])
-
-%!test
-%! breaks = {[0 1 2 3 4] [0 1 2 3]};
-%! degree = [3 2];
-%! mult = {[1 2 3] 2};
-%! knots = kntbrkdegmult (breaks, degree, mult);
-%! assert (knots, {[0 0 0 0 1 2 2 3 3 3 4 4 4 4] [0 0 0 1 1 2 2 3 3 3]})
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/kntbrkdegreg.m
--- a/extra/nurbs/inst/kntbrkdegreg.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,117 +0,0 @@
-% KNTBRKDEGREG: Construct an open knot vector by giving the sequence of
-% knots, the degree and the regularity.
-%
-% knots = kntbrkdegreg (breaks, degree)
-% knots = kntbrkdegreg (breaks, degree, regularity)
-%
-% INPUT:
-%
-% breaks: sequence of knots.
-% degree: polynomial degree of the splines associated to the knot vector.
-% regularity: splines regularity.
-%
-% OUTPUT:
-%
-% knots: knot vector.
-%
-% If REGULARITY has as many entries as BREAKS, or as the number of interior
-% knots, a different regularity will be assigned to each knot. If
-% REGULARITY is not present, it will be taken equal to DEGREE-1.
-%
-% Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-function knots = kntbrkdegreg (breaks, degree, reg)
-
-if (iscell (breaks))
- if (nargin == 2)
- reg = degree - 1;
- end
-
- if (numel(breaks)~=numel(degree) || numel(breaks)~=numel(reg))
- error('kntbrkdegreg: degree and regularity must have the same length as the number of knot vectors')
- end
-
- degree = num2cell (degree);
-
- if (~iscell (reg))
- reg = num2cell (reg);
- end
-
- knots = cellfun (@do_kntbrkdegreg, breaks, degree, reg, 'uniformoutput', false);
-else
-
- if (nargin == 2)
- reg = degree - 1;
- end
-
- knots = do_kntbrkdegreg (breaks, degree, reg);
-end
-
-end
-
-function knots = do_kntbrkdegreg (breaks, degree, reg)
-
-if (numel (breaks) < 2)
- error ('kntbrkdegreg: the knots sequence should contain at least two points')
-end
-
-if (numel (reg) == 1)
- mults = [-1, (degree (ones (1, numel (breaks) - 2)) - reg), -1];
-elseif (numel (reg) == numel (breaks))
- mults = degree - reg;
-elseif (numel (reg) == numel (breaks) - 2)
- mults = [-1 degree-reg -1];
-else
- error('kntbrkdegreg: the length of mult should be equal to one or the number of knots')
-end
-
-if (any (reg < -1))
- warning ('kntbrkdegreg: for some knots the regularity is lower than -1')
-elseif (any (reg > degree-1))
- error('kntbrkdegreg: the regularity should be lower than the degree')
-end
-
-knots = kntbrkdegmult (breaks, degree, mults);
-
-end
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! knots = kntbrkdegreg (breaks, degree);
-%! assert (knots, [0 0 0 0 1 2 3 4 4 4 4])
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! reg = 1;
-%! knots = kntbrkdegreg (breaks, degree, reg);
-%! assert (knots, [0 0 0 0 1 1 2 2 3 3 4 4 4 4])
-
-%!test
-%! breaks = [0 1 2 3 4];
-%! degree = 3;
-%! reg = [0 1 2];
-%! knots = kntbrkdegreg (breaks, degree, reg);
-%! assert (knots, [0 0 0 0 1 1 1 2 2 3 4 4 4 4])
-
-%!test
-%! breaks = {[0 1 2 3 4] [0 1 2 3]};
-%! degree = [3 2];
-%! reg = {[0 1 2] 0};
-%! knots = kntbrkdegreg (breaks, degree, reg);
-%! assert (knots, {[0 0 0 0 1 1 1 2 2 3 4 4 4 4] [0 0 0 1 1 2 2 3 3 3]})
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/kntrefine.m
--- a/extra/nurbs/inst/kntrefine.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,158 +0,0 @@
-% KNTREFINE: Refine a given knot vector by dividing each interval uniformly,
-% maintaining the continuity in previously existing knots.
-%
-% [rknots] = kntrefine (knots, n_sub, degree, regularity)
-% [rknots, zeta] = kntrefine (knots, n_sub, degree, regularity)
-% [rknots, zeta, new_knots] = kntrefine (knots, n_sub, degree, regularity)
-%
-% INPUT:
-%
-% knots: initial knot vector.
-% n_sub: number of new knots to be added in each interval.
-% degree: polynomial degree of the refined knot vector
-% regularity: maximum global regularity
-%
-% OUTPUT:
-%
-% rknots: refined knot vector
-% zeta: refined knot vector without repetitions
-% new_knots: new knots, to apply the knot insertion
-%
-% The regularity at the new inserted knots is the one given by the user.
-% At previously existing knots, the regularity is the minimum
-% between the previous regularity, and the one given by the user.
-% This ensures optimal convergence rates in the context of IGA.
-%
-% Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-function varargout = kntrefine (knots, n_sub, degree, regularity)
-
- if (iscell(knots))
- if (numel(n_sub)~=numel(degree) || numel(n_sub)~=numel(regularity) || ...
- numel(n_sub)~=numel(knots))
- error('kntrefine: n_sub, degree and regularity must have the same length as the number of knot vectors')
- end
- aux_knots = knots;
- else
- if (numel(n_sub)~=numel(degree) || numel(n_sub)~=numel(regularity) || ...
- numel(n_sub)~=1)
- error('kntrefine: n_sub, degree and regularity must have the same length as the number of knot vectors')
- end
- aux_knots = {knots};
- end
-
- if (nargout == 3)
- for idim = 1:numel(n_sub)
- if (degree(idim)+1 ~= sum (aux_knots{idim}==aux_knots{idim}(1)))
- error ('kntrefine: new_knots is only computed when the degree is maintained');
- end
- end
- for idim = 1:numel(n_sub)
- min_mult = degree(idim) - regularity(idim);
- z = unique (aux_knots{idim});
- nz = numel (z);
- deg = sum (aux_knots{idim} == z(1)) - 1;
- rknots{idim} = z(ones(1, degree(idim)+1));
- new_knots{idim} = [];
-
- for ik = 2:nz
- insk = linspace (z(ik-1), z(ik), n_sub(idim) + 2);
- insk = vec (repmat (insk(2:end-1), min_mult, 1))';
- old_mult = sum (aux_knots{idim} == z(ik));
- mult = max (min_mult, degree(idim) - deg + old_mult);
- rknots{idim} = [rknots{idim}, insk, z(ik*ones(1, mult))];
- new_knots{idim} = [new_knots{idim}, insk, z(ik*ones(1, mult-old_mult))];
- end
- zeta{idim} = unique (rknots{idim});
- end
- if (~iscell(knots))
- rknots = rknots{1};
- zeta = zeta{1};
- new_knots = new_knots{1};
- end
- varargout{1} = rknots;
- varargout{2} = zeta;
- varargout{3} = new_knots;
- else
- for idim = 1:numel(n_sub)
- min_mult = degree(idim) - regularity(idim);
- z = unique (aux_knots{idim});
- nz = numel (z);
- deg = sum (aux_knots{idim} == z(1)) - 1;
- rknots{idim} = z(ones(1, degree(idim)+1));
-
- for ik = 2:nz
- insk = linspace (z(ik-1), z(ik), n_sub(idim) + 2);
- insk = vec (repmat (insk(2:end-1), min_mult, 1))';
- old_mult = sum (aux_knots{idim} == z(ik));
- mult = max (min_mult, degree(idim) - deg + old_mult);
- rknots{idim} = [rknots{idim}, insk, z(ik*ones(1, mult))];
- end
- zeta{idim} = unique (rknots{idim});
- end
- if (~iscell(knots))
- rknots = rknots{1};
- zeta = zeta{1};
- end
- varargout{1} = rknots;
- if (nargout == 2)
- varargout{2} = zeta;
- end
- end
-end
-
-function v = vec (in)
- v = in(:);
-end
-
-%!shared nrbs
-%!test
-%! knots = {[0 0 1 1] [0 0 0 1 1 1]};
-%! coefs(1,:,:) = [1 sqrt(2)/2 0; 2 sqrt(2) 0];
-%! coefs(2,:,:) = [0 sqrt(2)/2 1; 0 sqrt(2) 2];
-%! coefs(4,:,:) = [1 sqrt(2)/2 1; 1 sqrt(2)/2 1];
-%! nrbs = nrbmak (coefs, knots);
-%! nrbs = nrbkntins (nrbs, {[] [0.5 0.6 0.6]});
-%! nrbs = nrbdegelev (nrbs, [0 1]);
-%! nrbs = nrbkntins (nrbs, {[] [0.4]});
-%! rknots = kntrefine (nrbs.knots, [1 1], [1 1], [0 0]);
-%! assert (rknots{1} == [0 0 0.5 1 1]);
-%! assert (rknots{2} == [0 0 0.2 0.4 0.45 0.5 0.55 0.6 0.8 1 1]);
-%!
-%!test
-%! rknots = kntrefine (nrbs.knots, [1 1], [3 3], [0 0]);
-%! assert (rknots{1}, [0 0 0 0 0.5 0.5 0.5 1 1 1 1]);
-%! assert (rknots{2}, [0 0 0 0 0.2 0.2 0.2 0.4 0.4 0.4 0.45 0.45 0.45 0.5 0.5 0.5 0.55 0.55 0.55 0.6 0.6 0.6 0.8 0.8 0.8 1 1 1 1]);
-%!
-%!test
-%! rknots = kntrefine (nrbs.knots, [1 1], [3 3], [2 2]);
-%! assert (rknots{1}, [0 0 0 0 0.5 1 1 1 1]);
-%! assert (rknots{2}, [0 0 0 0 0.2 0.4 0.45 0.5 0.5 0.55 0.6 0.6 0.6 0.8 1 1 1 1]);
-%!
-%!test
-%! rknots = kntrefine (nrbs.knots, [1 1], [4 4], [0 0]);
-%! assert (rknots{1}, [0 0 0 0 0 0.5 0.5 0.5 0.5 1 1 1 1 1]);
-%! assert (rknots{2}, [0 0 0 0 0 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.45 0.45 0.45 0.45 0.5 0.5 0.5 0.5 0.55 0.55 0.55 0.55 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 1 1 1 1 1]);
-%!
-%!test
-%! rknots = kntrefine (nrbs.knots, [1 1], [4 4], [3 3]);
-%! assert (rknots{1}, [0 0 0 0 0 0.5 1 1 1 1 1]);
-%! assert (rknots{2}, [0 0 0 0 0 0.2 0.4 0.4 0.45 0.5 0.5 0.5 0.55 0.6 0.6 0.6 0.6 0.8 1 1 1 1 1]);
-%!
-%!test
-%! knots = [0 0 0 0 0.4 0.5 0.5 0.6 0.6 0.6 1 1 1 1];
-%! rknots = kntrefine (knots, 1, 4, 3);
-%! assert (rknots, [0 0 0 0 0 0.2 0.4 0.4 0.45 0.5 0.5 0.5 0.55 0.6 0.6 0.6 0.6 0.8 1 1 1 1 1]);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/kntuniform.m
--- a/extra/nurbs/inst/kntuniform.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,52 +0,0 @@
-% KNTUNIFORM: generate uniform open knot vectors in the reference domain.
-%
-% [csi, zeta] = kntuniform (num, degree, regularity)
-%
-% INPUT:
-%
-% num: number of breaks (in each direction)
-% degree: polynomial degree (in each direction)
-% regularity: global regularity (in each direction)
-%
-% OUTPUT:
-%
-% csi: knots
-% zeta: breaks = knots without repetitions
-%
-% Copyright (C) 2009, 2010 Carlo de Falco
-% Copyright (C) 2011 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-function [csi, zeta] = kntuniform (num, degree, regularity)
-
- if (numel(num)~=numel(degree) || numel(num)~=numel(regularity))
- error('kntuniform: num, degree and regularity must have the same length')
- else
- for idim=1:numel(num)
- zeta{idim} = linspace (0, 1, num(idim));
- rep = degree(idim) - regularity(idim);
- if (rep > 0)
- csi{idim} = [zeros(1, degree(idim)+1-rep)...
- reshape(repmat(zeta{idim}, rep, 1), 1, []) ones(1, degree(idim)+1-rep)];
- else
- error ('kntuniform: regularity requested is too high')
- end
- end
- if (numel(num) == 1)
- csi = csi{1};
- zeta = zeta{1};
- end
- end
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrb2iges.m
--- a/extra/nurbs/inst/nrb2iges.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,303 +0,0 @@
-function nrb2iges (nurbs, filename)
-% NRB2IGES : Write a NURBS curve or surface to an IGES file.
-%
-% Calling Sequence:
-%
-% nrb2iges (nurbs, filename);
-%
-% INPUT:
-%
-% nurbs : NURBS curve or surface, see nrbmak.
-% filename : name of the output file.
-%
-% Description:
-%
-% The data of the nurbs structure is written in a file following the IGES
-% format. For a more in-depth explanation see, for example:
-% .
-%
-% Copyright (C) 2014 Jacopo Corno
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-%
-% This file is based on nurbs2iges.m, (C) 2006 Fu Qiang, originally
-% released under the MIT license.
-
- dt = datestr (now, 'yyyy.mm.dd');
-
- dim = numel (nurbs(1).order);
-
- % START SECTION
- S{1} = '';
- S{2} = 'IGES obtained from Nurbs toolbox.';
- S{3} = 'See .';
- S{4} = '';
-
- % GLOBAL SECTION
- G{1} = '1H,'; % Parameter Deliminator Character
- G{2} = '1H;'; % Record Delimiter Character
- G{3} = HString ('Nurbs toolbox'); % Product ID from Sender
- G{4} = HString (filename); % File Name
- G{5} = HString ('Octave Nurbs'); % System ID
- G{6} = HString ('nrb2iges'); % Pre-processor Version
- G{7} = '32'; % Number of Bits for Integers (No. of bits present in the integer representation of the sending system)
- G{8} = '75'; % Single Precision Magnitude (Maximum power of 10 which may be represented as a single precision floating point number from the sending system)
- G{9} = '6'; % Single Precision Significance (No. of significant digits of a single precision floating point number on the sending system)
- G{10}= '75'; % Double Precision Magnitude (Maximum power of 10 which may be represented as a double precision floating point number from the sending system)
- G{11}= '15'; % Double Precision Significance (No. of significant digits of a double precision floating point number on the sending system)
- G{12}= HString('Nurbs from Octave'); % Product ID for Receiver
- G{13}= '1.0'; % Model Space Scale
- G{14}= '6'; % Unit Flag (6 = metres)
- G{15}= HString('M'); % Units (metres = "M")
- G{16}= '1000'; % Maximum Number of Line Weights
- G{17}= '1.0'; % Size of Maximum Line Width
- G{18}= HString(dt); % Date and Time of file generation
- G{19}= '0.000001'; % Minimum User-intended Resolution
- G{20}= '10000.0'; % Approximate Maximum Coordinate
- G{21}= HString('Jacopo Corno'); % Name of Author
- G{22}= HString('GSCE - TU Darmstadt'); % Author's Organization
- G{23}= '3'; % IGES Version Number (3 = IGES version 2.0)
- G{24}= '0'; % Drafting Standard Code (0 = no standard)
-
- % Convert section array to lines (maximum lenght 72)
- SectionG = make_section (G, 72);
-
- % DIRECTORY ENTRY SECTION
- % Each directory entry consists of two, 80 character, fixed formatted lines
- D = [];
- for ii = 1:length (nurbs)
- switch (dim)
- case 1 % NURBS curve
- D(ii).type = 126;
- case 2 % NURBS surface
- D(ii).type = 128;
- otherwise
- error ('Only curves and surfaces can be saved in IGES format.')
- end
- D(ii).id = 2*ii - 1; % odd counter (see Parameter data section)
- D(ii).p_start = 0;
- D(ii).p_count = 0;
- end
-
- % PARAMETER DATA SECTION
- % The structure is a free formatted data entry from columns 1 to 64.
- % Each line of free formatted data consists of the entity type number
- % followed by the parameter data describing the entity.
- % Columns 65 to 72 are reserved for a parameter data index which is an
- % odd number counter, right justified in the field, which begins at the
- % number 1 and progresses in odd increments for each entity entered.
- % Column 73 is reserved for the letter ‘P’ to indicate the data element
- % belongs to the parameter data section.
- % Columns 74 to 80 are reserved for the sequence number. Each line of
- % data corresponds to the entity type as specified in the global section.
- SectionP = {};
- for ii = 1:length (nurbs)
- P = make_section_array (nurbs(ii)); % finish one entity
- % Convert section array to lines
- SP = make_section (P, 64);
- D(ii).p_count = length (SP);
- if (ii == 1)
- D(ii).p_start = 1;
- else
- D(ii).p_start = D(ii-1).p_start + D(ii-1).p_count;
- end
- SectionP{ii} = SP;
- end
-
- % SAVE
- fid = fopen (filename, 'w');
-
- % Save Start Section
- for ii = 1:length (S)
- fprintf (fid, '%-72sS%7d\n', S{ii}, ii);
- end
-
- % Save Global Section
- for ii = 1:length (SectionG)
- fprintf (fid, '%-72sG%7d\n', SectionG{ii}, ii);
- end
-
- % Save Directory Entry Section
- for i = 1:length (D)
- fprintf (fid, '%8d%8d%8d%8d%8d%8d%8d%8d%8dD%7d\n', ...
- D(i).type, D(i).p_start, 0, 0 ,0, 0, 0, 0, 0, i*2-1);
- fprintf (fid, '%8d%8d%8d%8d%8d%8s%8s%8s%8dD%7d\n', ...
- D(i).type, 0, 0, D(i).p_count, 0, ' ', ' ', ' ', 0, i*2);
- end
-
- % Save Parameter Data Section
- lines_p = 0;
- for jj = 1:length (D)
- sec = SectionP{jj};
- for ii = 1:length (sec)
- lines_p = lines_p + 1;
- fprintf (fid, '%-64s %7dP%7d\n', sec{ii}, D(jj).id, lines_p);
- end
- end
-
- % Save Terminate Section
- sec_t = sprintf ('%7dS%7dG%7dD%7dP%7d', length (S), length(SectionG), 2*length(D), lines_p);
- fprintf (fid, '%-72sT%7d\n', sec_t, 1);
-
- fclose(fid);
-
-end
-
-function P = make_section_array (nurbs)
- dim = numel (nurbs.order);
-
- % in IGES the control points are stored in the format [x, y, z, w]
- % instead of [w*x, w*y, w*z, w]
- for idim = 1:3
- nurbs.coefs(idim,:) = nurbs.coefs(idim,:) ./ nurbs.coefs(4,:);
- end
-
- P = {};
- switch dim
- case 1
- % Rational B-Spline Curve Entity
- cp = nurbs.coefs;
- deg = nurbs.order - 1;
- knots = nurbs.knots;
- uspan = [0 1];
- isplanar = ~any(cp(3,:));
- P{1} = '126'; % NURBS curve
- P{2} = int2str (size (cp, 2) - 1); % Number of control points
- P{3} = int2str (deg); % Degree
- P{4} = int2str (isplanar); % Curve on xy plane
- P{5} = '0';
- P{6} = '0';
- P{7} = '0';
- index = 8;
- for ii = 1:length (knots)
- P{index} = sprintf ('%f', knots(ii));
- index = index + 1;
- end
- for ii = 1:size (cp, 2)
- P{index} = sprintf ('%f', cp(4,ii));
- index = index + 1;
- end
- for ii = 1:size (cp, 2)
- P{index} = sprintf ('%f', cp(1,ii));
- index = index + 1;
- P{index} = sprintf ('%f', cp(2,ii));
- index = index + 1;
- P{index} = sprintf ('%f', cp(3,ii));
- index = index + 1;
- end
- P{index} = sprintf ('%f', uspan(1));
- index = index +1;
- P{index} = sprintf ('%f', uspan(2));
- index = index +1;
- P{index} = '0.0';
- index = index +1;
- P{index} = '0.0';
- index = index +1;
- if isplanar
- P{index} = '1.0';
- else
- P{index} = '0.0';
- end
- index = index + 1;
- P{index} = '0';
- index = index + 1;
- P{index} = '0';
- case 2
- % Rational B-Spline Surface Entity
- cp = nurbs.coefs;
- degU = nurbs.order(1) - 1;
- degV = nurbs.order(2) - 1;
- knotsU = nurbs.knots{1};
- knotsV = nurbs.knots{2};
- uspan = [0 1];
- vspan = [0 1];
- P{1} = '128'; % NURBS surface
- P{2} = int2str (size (cp, 2) - 1); % Number of control points in U
- P{3} = int2str (size (cp, 3) - 1); % Number of control points in V
- P{4} = int2str (degU); % Degree in U
- P{5} = int2str (degV); % Degree in V
- P{6} = '0';
- P{7} = '0';
- P{8} = '0';
- P{9} = '0';
- P{10} = '0';
- index = 11;
- for ii = 1:length (knotsU)
- P{index} = sprintf ('%f', knotsU(ii));
- index = index + 1;
- end
- for ii = 1:length (knotsV)
- P{index} = sprintf ('%f', knotsV(ii));
- index = index + 1;
- end
- for jj = 1:size (cp, 3)
- for ii = 1:size (cp, 2)
- P{index} = sprintf ('%f', cp(4,ii,jj));
- index = index + 1;
- end
- end
- for jj = 1:size (cp, 3)
- for ii = 1:size (cp, 2)
- P{index} = sprintf ('%f',cp(1,ii,jj));
- index = index + 1;
- P{index} = sprintf ('%f',cp(2,ii,jj));
- index = index + 1;
- P{index} = sprintf ('%f',cp(3,ii,jj));
- index = index + 1;
- end
- end
- P{index} = sprintf('%f',uspan(1));
- index = index +1;
- P{index} = sprintf('%f',uspan(2));
- index = index +1;
- P{index} = sprintf('%f',vspan(1));
- index = index +1;
- P{index} = sprintf('%f',vspan(2));
- index = index +1;
- P{index} = '0';
- index = index + 1;
- P{index} = '0';
- otherwise
-
- end
-end
-
-function hs = HString (str)
-% HString : Convert the string STR to the Hollerith format.
-
- hs = sprintf ('%dH%s', length(str), str);
-end
-
-function sec = make_section (fields, linewidth)
- sec = {};
- index = 1;
- line = '';
- num = length (fields);
- for i = 1:num
- if (i < num)
- newitem = [fields{i} ','];
- else
- newitem = [fields{i} ';'];
- end
- len = length (line) + length (newitem);
- if ( len > linewidth )
- % new line
- sec{index} = line;
- index = index + 1;
- line = '';
- end
- line = [line newitem];
- end
- sec{index} = line;
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrb4surf.m
--- a/extra/nurbs/inst/nrb4surf.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,74 +0,0 @@
-function srf = nrb4surf(p11,p12,p21,p22)
-%
-% NRB4SURF: Constructs a NURBS bilinear surface.
-%
-% Calling Sequence:
-%
-% srf = nrb4surf(p11,p12,p21,p22)
-%
-% INPUT:
-%
-% p11 : Cartesian coordinate of the lhs bottom corner point.
-%
-% p12 : Cartesian coordinate of the rhs bottom corner point.
-%
-% p21 : Cartesian coordinate of the lhs top corner point.
-%
-% p22 : Cartesian coordinate of the rhs top corner point.
-%
-% OUTPUT:
-%
-% srf : NURBS bilinear surface, see nrbmak.
-%
-% Description:
-%
-% Constructs a bilinear surface defined by four coordinates.
-%
-% The position of the corner points
-%
-% ^ V direction
-% |
-% ----------------
-% |p21 p22|
-% | |
-% | SRF |
-% | |
-% |p11 p12|
-% -------------------> U direction
-%
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin ~= 4
- error('Four corner points must be defined');
-end
-
-coefs = cat (1, zeros (3,2,2), ones (1,2,2));
-coefs(1:length(p11),1,1) = p11(:);
-coefs(1:length(p12),2,1) = p12(:);
-coefs(1:length(p21),1,2) = p21(:);
-coefs(1:length(p22),2,2) = p22(:);
-
-knots = {[0 0 1 1] [0 0 1 1]};
-srf = nrbmak(coefs, knots);
-
-end
-
-%!demo
-%! srf = nrb4surf([0.0 0.0 0.5],[1.0 0.0 -0.5],[0.0 1.0 -0.5],[1.0 1.0 0.5]);
-%! nrbplot(srf,[10,10]);
-%! title('Construction of a bilinear surface.');
-%! hold off
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbbasisfun.m
--- a/extra/nurbs/inst/nrbbasisfun.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,140 +0,0 @@
-function [B, id] = nrbbasisfun (points, nrb)
-
-% NRBBASISFUN: Basis functions for NURBS
-%
-% Calling Sequence:
-%
-% B = nrbbasisfun (u, crv)
-% B = nrbbasisfun ({u, v}, srf)
-% [B, N] = nrbbasisfun ({u, v}, srf)
-% [B, N] = nrbbasisfun (pts, srf)
-%
-% INPUT:
-%
-% u - parametric coordinates along u direction
-% v - parametric coordinates along v direction
-% pts - array of scattered points in parametric domain, array size: (2,num_points)
-% crv - NURBS curve
-% srf - NURBS surface
-%
-% If the parametric coordinates are given in a cell-array, the values
-% are computed in a tensor product set of points
-%
-% OUTPUT:
-%
-% B - Value of the basis functions at the points
-% size(B)=[numel(u),(p+1)] for curves
-% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
-%
-% N - Indices of the basis functions that are nonvanishing at each
-% point. size(N) == size(B)
-%
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- if ( (nargin<2) ...
- || (nargout>2) ...
- || (~isstruct(nrb)) ...
- || (iscell(points) && ~iscell(nrb.knots)) ...
- || (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=2)) ...
- )
- error('Incorrect input arguments in nrbbasisfun');
- end
-
- if (~iscell(nrb.knots)) %% NURBS curve
-
- [B, id] = nrb_crv_basisfun__ (points, nrb);
-
- elseif size(nrb.knots,2) == 2 %% NURBS surface
- if (iscell(points))
- [v, u] = meshgrid(points{2}, points{1});
- p = [u(:), v(:)]';
- else
- p = points;
- end
-
- [B, id] = nrb_srf_basisfun__ (p, nrb);
-
- else %% NURBS volume
- error('The function nrbbasisfun is not yet ready for volumes')
- end
-end
-
-%!demo
-%! U = [0 0 0 0 1 1 1 1];
-%! x = [0 1/3 2/3 1] ;
-%! y = [0 0 0 0];
-%! w = [1 1 1 1];
-%! nrb = nrbmak ([x;y;y;w], U);
-%! u = linspace(0, 1, 30);
-%! B = nrbbasisfun (u, nrb);
-%! xplot = sum(bsxfun(@(x,y) x.*y, B, x),2);
-%! plot(xplot, B)
-%! title('Cubic Bernstein polynomials')
-%! hold off
-
-%!test
-%! U = [0 0 0 0 1 1 1 1];
-%! x = [0 1/3 2/3 1] ;
-%! y = [0 0 0 0];
-%! w = rand(1,4);
-%! nrb = nrbmak ([x;y;y;w], U);
-%! u = linspace(0, 1, 30);
-%! B = nrbbasisfun (u, nrb);
-%! xplot = sum(bsxfun(@(x,y) x.*y, B, x),2);
-%!
-%! yy = y; yy(1) = 1;
-%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
-%! aux = nrbeval(nrb2,u);
-%! %figure, plot(xplot, B(:,1), aux(1,:).', w(1)*aux(2,:).')
-%! assert(B(:,1), w(1)*aux(2,:).', 1e-6)
-%!
-%! yy = y; yy(2) = 1;
-%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
-%! aux = nrbeval(nrb2, u);
-%! %figure, plot(xplot, B(:,2), aux(1,:).', w(2)*aux(2,:).')
-%! assert(B(:,2), w(2)*aux(2,:).', 1e-6)
-%!
-%! yy = y; yy(3) = 1;
-%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
-%! aux = nrbeval(nrb2,u);
-%! %figure, plot(xplot, B(:,3), aux(1,:).', w(3)*aux(2,:).')
-%! assert(B(:,3), w(3)*aux(2,:).', 1e-6)
-%!
-%! yy = y; yy(4) = 1;
-%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
-%! aux = nrbeval(nrb2,u);
-%! %figure, plot(xplot, B(:,4), aux(1,:).', w(4)*aux(2,:).')
-%! assert(B(:,4), w(4)*aux(2,:).', 1e-6)
-
-%!test
-%! p = 2; q = 3; m = 4; n = 5;
-%! Lx = 1; Ly = 1;
-%! nrb = nrb4surf ([0 0], [1 0], [0 1], [1 1]);
-%! nrb = nrbdegelev (nrb, [p-1, q-1]);
-%! aux1 = linspace(0,1,m); aux2 = linspace(0,1,n);
-%! nrb = nrbkntins (nrb, {aux1(2:end-1), aux2(2:end-1)});
-%! u = rand (1, 30); v = rand (1, 10);
-%! u = u - min (u); u = u / max (u);
-%! v = v - min (v); v = v / max (v);
-%! [B, N] = nrbbasisfun ({u, v}, nrb);
-%! assert (sum(B, 2), ones(300, 1), 1e-6)
-%! assert (all (all (B<=1)), true)
-%! assert (all (all (B>=0)), true)
-%! assert (all (all (N>0)), true)
-%! assert (all (all (N <= prod (nrb.number))), true)
-%! assert (max (max (N)),prod (nrb.number))
-%! assert (min (min (N)),1)
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbbasisfunder.m
--- a/extra/nurbs/inst/nrbbasisfunder.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,127 +0,0 @@
-function varargout = nrbbasisfunder (points, nrb)
-
-% NRBBASISFUNDER: NURBS basis functions derivatives
-%
-% Calling Sequence:
-%
-% Bu = nrbbasisfunder (u, crv)
-% [Bu, N] = nrbbasisfunder (u, crv)
-% [Bu, Bv] = nrbbasisfunder ({u, v}, srf)
-% [Bu, Bv, N] = nrbbasisfunder ({u, v}, srf)
-% [Bu, Bv, N] = nrbbasisfunder (pts, srf)
-%
-% INPUT:
-%
-% u - parametric coordinates along u direction
-% v - parametric coordinates along v direction
-% pts - array of scattered points in parametric domain, array size: (2,num_points)
-% crv - NURBS curve
-% srf - NURBS surface
-%
-% If the parametric coordinates are given in a cell-array, the values
-% are computed in a tensor product set of points
-%
-% OUTPUT:
-%
-% Bu - Basis functions derivatives WRT direction u
-% size(Bu)=[numel(u),(p+1)] for curves
-% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
-%
-% Bv - Basis functions derivatives WRT direction v
-% size(Bv)=[numel(v),(p+1)] for curves
-% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
-%
-% N - Indices of the basis functions that are nonvanishing at each
-% point. size(N) == size(B)
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-
- if ( (nargin<2) ...
- || (nargout>3) ...
- || (~isstruct(nrb)) ...
- || (iscell(points) && ~iscell(nrb.knots)) ...
- || (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=2)) ...
- || (~iscell(nrb.knots) && (nargout>2)) ...
- )
- error('Incorrect input arguments in nrbbasisfun');
- end
-
- if (~iscell(nrb.knots)) %% NURBS curve
-
- [varargout{1}, varargout{2}] = nrb_crv_basisfun_der__ (points, nrb);
-
- elseif size(nrb.knots,2) == 2 %% NURBS surface
-
- if (iscell(points))
- [v, u] = meshgrid(points{2}, points{1});
- p = [u(:), v(:)]';
- else
- p = points;
- end
-
- [varargout{1}, varargout{2}, varargout{3}] = nrb_srf_basisfun_der__ (p, nrb);
-
- else %% NURBS volume
- error('The function nrbbasisfunder is not yet ready for volumes')
- end
-end
-
-%!demo
-%! U = [0 0 0 0 1 1 1 1];
-%! x = [0 1/3 2/3 1] ;
-%! y = [0 0 0 0];
-%! w = [1 1 1 1];
-%! nrb = nrbmak ([x;y;y;w], U);
-%! u = linspace(0, 1, 30);
-%! [Bu, id] = nrbbasisfunder (u, nrb);
-%! plot(u, Bu)
-%! title('Derivatives of the cubic Bernstein polynomials')
-%! hold off
-
-%!test
-%! U = [0 0 0 0 1 1 1 1];
-%! x = [0 1/3 2/3 1] ;
-%! y = [0 0 0 0];
-%! w = rand(1,4);
-%! nrb = nrbmak ([x;y;y;w], U);
-%! u = linspace(0, 1, 30);
-%! [Bu, id] = nrbbasisfunder (u, nrb);
-%! #plot(u, Bu)
-%! assert (sum(Bu, 2), zeros(numel(u), 1), 1e-10),
-
-%!test
-%! U = [0 0 0 0 1/2 1 1 1 1];
-%! x = [0 1/4 1/2 3/4 1] ;
-%! y = [0 0 0 0 0];
-%! w = rand(1,5);
-%! nrb = nrbmak ([x;y;y;w], U);
-%! u = linspace(0, 1, 300);
-%! [Bu, id] = nrbbasisfunder (u, nrb);
-%! assert (sum(Bu, 2), zeros(numel(u), 1), 1e-10)
-
-%!test
-%! p = 2; q = 3; m = 4; n = 5;
-%! Lx = 1; Ly = 1;
-%! nrb = nrb4surf ([0 0], [1 0], [0 1], [1 1]);
-%! nrb = nrbdegelev (nrb, [p-1, q-1]);
-%! aux1 = linspace(0,1,m); aux2 = linspace(0,1,n);
-%! nrb = nrbkntins (nrb, {aux1(2:end-1), aux2(2:end-1)});
-%! nrb.coefs (4,:,:) = nrb.coefs(4,:,:) + rand (size (nrb.coefs (4,:,:)));
-%! [Bu, Bv, N] = nrbbasisfunder ({rand(1, 20), rand(1, 20)}, nrb);
-%! #plot3(squeeze(u(1,:,:)), squeeze(u(2,:,:)), reshape(Bu(:,10), 20, 20),'o')
-%! assert (sum (Bu, 2), zeros(20^2, 1), 1e-10)
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbcirc.m
--- a/extra/nurbs/inst/nrbcirc.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,123 +0,0 @@
-function curve = nrbcirc(radius,center,sang,eang)
-%
-% NRBCIRC: Construct a circular arc.
-%
-% Calling Sequence:
-%
-% crv = nrbcirc()
-% crv = nrbcirc(radius)
-% crv = nrbcirc(radius,center)
-% crv = nrbcirc(radius,center,sang,eang)
-%
-% INPUT:
-%
-% radius : Radius of the circle, default 1.0
-%
-% center : Center of the circle, default (0,0,0)
-%
-% sang : Start angle, default 0 radians (0 degrees)
-%
-% eang : End angle, default 2*pi radians (360 degrees)
-%
-% OUTPUT:
-%
-% crv : NURBS curve for a circular arc.
-%
-% Description:
-%
-% Constructs NURBS data structure for a circular arc in the x-y plane. If
-% no rhs arguments are supplied a unit circle with center (0.0,0.0) is
-% constructed.
-%
-% Angles are defined as positive in the anti-clockwise direction.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 1
- radius = 1;
-end
-
-if nargin < 2
- center = [];
-end
-
-if nargin < 4
- sang = 0;
- eang = 2*pi;
-end
-
-sweep = eang - sang; % sweep angle of arc
-if sweep < 0
- sweep = 2*pi + sweep;
-end
-
-if abs(sweep) <= pi/2
- narcs = 1; % number of arc segments
- knots = [0 0 0 1 1 1];
-elseif abs(sweep) <= pi
- narcs = 2;
- knots = [0 0 0 0.5 0.5 1 1 1];
-elseif abs(sweep) <= 3*pi/2
- narcs = 3;
- knots = [0 0 0 1/3 1/3 2/3 2/3 1 1 1];
-else
- narcs = 4;
- knots = [0 0 0 0.25 0.25 0.5 0.5 0.75 0.75 1 1 1];
-end
-
-dsweep = sweep/(2*narcs); % arc segment sweep angle/2
-
-% determine middle control point and weight
-wm = cos(dsweep);
-x = radius*wm;
-y = radius*sin(dsweep);
-xm = x+y*tan(dsweep);
-
-% arc segment control points
-ctrlpt = [ x wm*xm x; % w*x - coordinate
- -y 0 y; % w*y - coordinate
- 0 0 0; % w*z - coordinate
- 1 wm 1]; % w - coordinate
-
-% build up complete arc from rotated segments
-coefs = zeros(4,2*narcs+1); % nurbs control points of arc
-xx = vecrotz(sang + dsweep);
-coefs(:,1:3) = xx*ctrlpt; % rotate to start angle
-xx = vecrotz(2*dsweep);
-for n = 2:narcs
- m = 2*n+[0 1];
- coefs(:,m) = xx*coefs(:,m-2);
-end
-
-% vectrans arc if necessary
-if ~isempty(center)
- xx = vectrans(center);
- coefs = xx*coefs;
-end
-
-curve = nrbmak(coefs,knots);
-
-end
-
-%!demo
-%! for r = 1:9
-%! crv = nrbcirc(r,[],deg2rad(45),deg2rad(315));
-%! nrbplot(crv,50);
-%! hold on;
-%! end
-%! hold off;
-%! axis equal;
-%! title('NURBS construction of several 2D arcs.');
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbcoons.m
--- a/extra/nurbs/inst/nrbcoons.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,190 +0,0 @@
-function srf = nrbcoons(u1, u2, v1, v2)
-%
-% NRBCOONS: Construction of a Coons patch.
-%
-% Calling Sequence:
-%
-% srf = nrbcoons(ucrv1, ucrv2, vcrv1, vcrv2)
-%
-% INPUT:
-%
-% ucrv1 : NURBS curve defining the bottom U direction boundary of
-% the constructed NURBS surface.
-%
-% ucrv2 : NURBS curve defining the top U direction boundary of
-% the constructed NURBS surface.
-%
-% vcrv1 : NURBS curve defining the bottom V direction boundary of
-% the constructed NURBS surface.
-%
-% vcrv2 : NURBS curve defining the top V direction boundary of
-% the constructed NURBS surface.
-%
-% OUTPUT:
-%
-% srf : Coons NURBS surface patch.
-%
-% Description:
-%
-% Construction of a bilinearly blended Coons surface patch from four NURBS
-% curves that define the boundary.
-%
-% The orientation of the four NURBS boundary curves.
-%
-% ^ V direction
-% |
-% | ucrv2
-% ------->--------
-% | |
-% | |
-% vcrv1 ^ Surface ^ vcrv2
-% | |
-% | |
-% ------->-----------> U direction
-% ucrv1
-%
-%
-% Examples:
-%
-% // Define four NURBS curves and construct a Coons surface patch.
-% pnts = [ 0.0 3.0 4.5 6.5 8.0 10.0;
-% 0.0 0.0 0.0 0.0 0.0 0.0;
-% 2.0 2.0 7.0 4.0 7.0 9.0];
-% crv1 = nrbmak(pnts, [0 0 0 1/3 0.5 2/3 1 1 1]);
-%
-% pnts= [ 0.0 3.0 5.0 8.0 10.0;
-% 10.0 10.0 10.0 10.0 10.0;
-% 3.0 5.0 8.0 6.0 10.0];
-% crv2 = nrbmak(pnts, [0 0 0 1/3 2/3 1 1 1]);
-%
-% pnts= [ 0.0 0.0 0.0 0.0;
-% 0.0 3.0 8.0 10.0;
-% 2.0 0.0 5.0 3.0];
-% crv3 = nrbmak(pnts, [0 0 0 0.5 1 1 1]);
-%
-% pnts= [ 10.0 10.0 10.0 10.0 10.0;
-% 0.0 3.0 5.0 8.0 10.0;
-% 9.0 7.0 7.0 10.0 10.0];
-% crv4 = nrbmak(pnts, [0 0 0 0.25 0.75 1 1 1]);
-%
-% srf = nrbcoons(crv1, crv2, crv3, crv4);
-% nrbplot(srf,[20 20],220,45);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin ~= 4
- error('Incorrect number of input arguments');
-end
-
-if (max (abs (nrbeval (u1, u1.knots(1)) - nrbeval (v1, v1.knots(1)))) > 1e-10 || ...
- max (abs (nrbeval (u1, u1.knots(end)) - nrbeval (v2, v2.knots(1)))) > 1e-10 || ...
- max (abs (nrbeval (u2, u2.knots(1)) - nrbeval (v1, v1.knots(end)))) > 1e-10 || ...
- max (abs (nrbeval (u2, u2.knots(end)) - nrbeval (v2, v2.knots(end)))) > 1e-10)
- error ('The four curves do not define a closed boundary')
-end
-
-
-
-r1 = nrbruled(u1, u2);
-r2 = nrbtransp(nrbruled(v1, v2));
-t = nrb4surf(u1.coefs(:,1), u1.coefs(:,end), u2.coefs(:,1), u2.coefs(:,end));
-
-% raise all surfaces to a common degree
-du = max([r1.order(1), r2.order(1), t.order(1)]);
-dv = max([r1.order(2), r2.order(2), t.order(2)]);
-r1 = nrbdegelev(r1, [du - r1.order(1), dv - r1.order(2)]);
-r2 = nrbdegelev(r2, [du - r2.order(1), dv - r2.order(2)]);
-t = nrbdegelev(t, [du - t.order(1), dv - t.order(2)]);
-
-% merge the knot vectors, to obtain a common knot vector
-
-% U knots
-k1 = r1.knots{1};
-k2 = r2.knots{1};
-k3 = t.knots{1};
-k = unique([k1 k2 k3]);
-n = length(k);
-kua = [];
-kub = [];
-kuc = [];
-for i = 1:n
- i1 = length(find(k1 == k(i)));
- i2 = length(find(k2 == k(i)));
- i3 = length(find(k3 == k(i)));
- m = max([i1, i2, i3]);
- kua = [kua k(i)*ones(1,m-i1)];
- kub = [kub k(i)*ones(1,m-i2)];
- kuc = [kuc k(i)*ones(1,m-i3)];
-end
-
-% V knots
-k1 = r1.knots{2};
-k2 = r2.knots{2};
-k3 = t.knots{2};
-k = unique([k1 k2 k3]);
-n = length(k);
-kva = [];
-kvb = [];
-kvc = [];
-for i = 1:n
- i1 = length(find(k1 == k(i)));
- i2 = length(find(k2 == k(i)));
- i3 = length(find(k3 == k(i)));
- m = max([i1, i2, i3]);
- kva = [kva k(i)*ones(1,m-i1)];
- kvb = [kvb k(i)*ones(1,m-i2)];
- kvc = [kvc k(i)*ones(1,m-i3)];
-end
-
-r1 = nrbkntins(r1, {kua, kva});
-r2 = nrbkntins(r2, {kub, kvb});
-t = nrbkntins(t, {kuc, kvc});
-
-% combine coefficient to construct Coons surface
-coefs(1,:,:) = r1.coefs(1,:,:) + r2.coefs(1,:,:) - t.coefs(1,:,:);
-coefs(2,:,:) = r1.coefs(2,:,:) + r2.coefs(2,:,:) - t.coefs(2,:,:);
-coefs(3,:,:) = r1.coefs(3,:,:) + r2.coefs(3,:,:) - t.coefs(3,:,:);
-coefs(4,:,:) = r1.coefs(4,:,:) + r2.coefs(4,:,:) - t.coefs(4,:,:);
-srf = nrbmak(coefs, r1.knots);
-
-end
-
-%!demo
-%! pnts = [ 0.0 3.0 4.5 6.5 8.0 10.0;
-%! 0.0 0.0 0.0 0.0 0.0 0.0;
-%! 2.0 2.0 7.0 4.0 7.0 9.0];
-%! crv1 = nrbmak(pnts, [0 0 0 1/3 0.5 2/3 1 1 1]);
-%!
-%! pnts= [ 0.0 3.0 5.0 8.0 10.0;
-%! 10.0 10.0 10.0 10.0 10.0;
-%! 3.0 5.0 8.0 6.0 10.0];
-%! crv2 = nrbmak(pnts, [0 0 0 1/3 2/3 1 1 1]);
-%!
-%! pnts= [ 0.0 0.0 0.0 0.0;
-%! 0.0 3.0 8.0 10.0;
-%! 2.0 0.0 5.0 3.0];
-%! crv3 = nrbmak(pnts, [0 0 0 0.5 1 1 1]);
-%!
-%! pnts= [ 10.0 10.0 10.0 10.0 10.0;
-%! 0.0 3.0 5.0 8.0 10.0;
-%! 9.0 7.0 7.0 10.0 10.0];
-%! crv4 = nrbmak(pnts, [0 0 0 0.25 0.75 1 1 1]);
-%!
-%! srf = nrbcoons(crv1, crv2, crv3, crv4);
-%!
-%! nrbplot(srf,[20 20]);
-%! title('Construction of a bilinearly blended Coons surface.');
-%! hold off
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbcrvderiveval.m
--- a/extra/nurbs/inst/nrbcrvderiveval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,89 +0,0 @@
-% NRBCRVDERIVEVAL: Evaluate n-th order derivatives of a NURBS curve.
-%
-% usage: skl = nrbcrvderiveval (crv, u, d)
-%
-% INPUT:
-%
-% crv : NURBS curve structure, see nrbmak
-%
-% u : parametric coordinate of the points where we compute the derivatives
-%
-% d : number of partial derivatives to compute
-%
-%
-% OUTPUT:
-%
-% ck (i, j, l) = i-th component derived j-1 times at the l-th point.
-%
-% Adaptation of algorithm A4.2 from the NURBS book, pg127
-%
-% Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-function ck = nrbcrvderiveval (crv, u, d)
- ck = arrayfun (@(x) nrbcrvderiveval__ (crv, x, d), u, 'UniformOutput', false);
- ck = cat (3, ck{:});
-end
-
-function ck = nrbcrvderiveval__ (crv, u, d)
-
- persistent nc;
- if isempty (nc)
- nc = [0 0 0 0 0;
- 1 0 0 0 0;
- 2 1 0 0 0;
- 3 3 1 0 0;
- 4 6 4 1 0];
- end
-
- ck = zeros (3, d+1);
- wders = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(4, :)), u, d);
-
- for idim = 1:3
-
- Aders = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(idim, :)), u, d);
-
- ck(idim, 1) = Aders(1) / wders(1);
- for k = 1:d
- ck(idim, k+1) = (Aders(k+1) - sum (nc(k+1, 1:k) .* wders(2:k+1).' .* squeeze (ck(idim, k:-1:1)))) / wders(1);
- end
-
- end
-
-end
-
-
-%!test
-%! knots = [0 0 0 1 1 1];
-%! coefs(:,1) = [0; 0; 0; 1];
-%! coefs(:,2) = [1; 0; 1; 1];
-%! coefs(:,3) = [1; 1; 1; 2];
-%! crv = nrbmak (coefs, knots);
-%! u = linspace (0, 1, 100);
-%! ck = nrbcrvderiveval (crv, u, 2);
-%! w = @(x) 1 + x.^2;
-%! dw = @(x) 2*x;
-%! F1 = @(x) (2*x - x.^2)./w(x);
-%! F2 = @(x) x.^2./w(x);
-%! F3 = @(x) (2*x - x.^2)./w(x);
-%! dF1 = @(x) (2 - 2*x)./w(x) - 2*(2*x - x.^2).*x./w(x).^2;
-%! dF2 = @(x) 2*x./w(x) - 2*x.^3./w(x).^2;
-%! dF3 = @(x) (2 - 2*x)./w(x) - 2*(2*x - x.^2).*x./w(x).^2;
-%! d2F1 = @(x) -2./w(x) - 2*x.*(2-2*x)./w(x).^2 - (8*x-6*x.^2)./w(x).^2 + 8*x.^2.*(2*x-x.^2)./w(x).^3;
-%! d2F2 = @(x) 2./w(x) - 4*x.^2./w(x).^2 - 6*x.^2./w(x).^2 + 8*x.^4./w(x).^3;
-%! d2F3 = @(x) -2./w(x) - 2*x.*(2-2*x)./w(x).^2 - (8*x-6*x.^2)./w(x).^2 + 8*x.^2.*(2*x-x.^2)./w(x).^3;
-%! assert ([F1(u); F2(u); F3(u)], squeeze(ck(:, 1, :)), 1e2*eps);
-%! assert ([dF1(u); dF2(u); dF3(u)], squeeze(ck(:, 2, :)), 1e2*eps);
-%! assert ([d2F1(u); d2F2(u); d2F3(u)], squeeze(ck(:, 3, :)), 1e2*eps);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbctrlplot.m
--- a/extra/nurbs/inst/nrbctrlplot.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,131 +0,0 @@
-function nrbctrlplot (nurbs)
-
-% NRBCTRLPLOT: Plot a NURBS entity along with its control points.
-%
-% Calling Sequence:
-%
-% nrbctrlplot (nurbs)
-%
-% INPUT:
-%
-% nurbs: NURBS curve, surface or volume, see nrbmak.
-%
-% Example:
-%
-% Plot the test curve and test surface with their control polygon and
-% control net, respectively
-%
-% nrbctrlplot(nrbtestcrv)
-% nrbctrlplot(nrbtestsrf)
-%
-% See also:
-%
-% nrbkntplot
-%
-% Copyright (C) 2011, 2012 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin < 1)
- error ('nrbctrlplot: Need a NURBS to plot!');
-end
-
-% Default values
-light='on';
-cmap='summer';
-
-colormap (cmap);
-
-hold_flag = ishold;
-
-if (iscell (nurbs.knots))
- if (size (nurbs.knots,2) == 3)
- nsub = 100;
- nrbplot (nurbs, [nsub nsub nsub], 'light', light, 'colormap', cmap);
- hold on
-% Plot the control points
- coefs = bsxfun (@rdivide, nurbs.coefs(1:3,:,:,:), nurbs.coefs(4,:,:,:));
- coefs = reshape (coefs, 3, []);
- plot3 (coefs(1,:), coefs(2,:), coefs(3,:), 'r.','MarkerSize',20);
-% Plot the control net
- for ii = 1:size (nurbs.coefs, 2)
- for jj = 1:size (nurbs.coefs, 3)
- coefs = reshape (nurbs.coefs(1:3,ii,jj,:), 3, []);
- weights = reshape (nurbs.coefs(4,ii,jj,:), 1, []);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- end
- for kk = 1:size (nurbs.coefs, 4)
- coefs = reshape (nurbs.coefs(1:3,ii,:,kk), 3, []);
- weights = reshape (nurbs.coefs(4,ii,:,kk), 1, []);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- end
- end
- for jj = 1:size (nurbs.coefs, 3)
- for kk = 1:size (nurbs.coefs, 4)
- coefs = reshape (nurbs.coefs(1:3,:,jj,kk), 3, []);
- weights = reshape (nurbs.coefs(4,:,jj,kk), 1, []);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- end
- end
-
- elseif (size (nurbs.knots,2) == 2) % plot a NURBS surface
-
- nsub = 100;
- nrbplot (nurbs, [nsub nsub], 'light', light, 'colormap', cmap);
- hold on
-
-% And plot the control net
- for ii = 1:size (nurbs.coefs, 2)
- coefs = reshape (nurbs.coefs(1:3,ii,:), 3, []);
- weights = reshape (nurbs.coefs(4,ii,:), 1, []);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'r.','MarkerSize',20)
- end
- for jj = 1:size (nurbs.coefs, 3)
- coefs = reshape (nurbs.coefs(1:3,:,jj), 3, []);
- weights = reshape (nurbs.coefs(4,:,jj), 1, []);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'r.','MarkerSize',20)
- end
- end
-else % plot a NURBS curve
- nsub = 1000;
- nrbplot (nurbs, nsub);
- hold on
-
-% And plot the control polygon
- coefs = nurbs.coefs(1:3,:);
- weights = nurbs.coefs(4,:);
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'k--')
- plot3 (coefs(1,:)./weights, coefs(2,:)./weights, coefs(3,:)./weights,'r.','MarkerSize',20)
-end
-
-if (~hold_flag)
- hold off
-end
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! nrbctrlplot(crv)
-%! title('Test curve')
-%! hold off
-
-%!demo
-%! srf = nrbtestsrf;
-%! nrbctrlplot(srf)
-%! title('Test surface')
-%! hold off
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbcylind.m
--- a/extra/nurbs/inst/nrbcylind.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,74 +0,0 @@
-function surf = nrbcylind(height,radius,center,sang,eang)
-%
-% NRBCYLIND: Construct a cylinder or cylindrical patch.
-%
-% Calling Sequence:
-%
-% srf = nrbcylind()
-% srf = nrbcylind(height)
-% srf = nrbcylind(height,radius)
-% srf = nrbcylind(height,radius,center)
-% srf = nrbcylind(height,radius,center,sang,eang)
-%
-% INPUT:
-%
-% height : Height of the cylinder along the axis, default 1.0
-%
-% radius : Radius of the cylinder, default 1.0
-%
-% center : Center of the cylinder, default (0,0,0)
-%
-% sang : Start angle relative to the origin, default 0.
-%
-% eang : End angle relative to the origin, default 2*pi.
-%
-% OUTPUT:
-%
-% srf : cylindrical surface patch
-%
-% Description:
-%
-% Construct a cylinder or cylindrical patch by extruding a circular arc.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 1
- height = 1;
-end
-
-if nargin < 2
- radius = 1;
-end
-
-if nargin < 3
- center = [];
-end
-
-if nargin < 5
- sang = 0;
- eang = 2*pi;
-end
-
-surf = nrbextrude(nrbcirc(radius,center,sang,eang),[0.0 0.0 height]);
-
-end
-
-%!demo
-%! srf = nrbcylind(3,1,[],deg2rad(270),deg2rad(180));
-%! nrbplot(srf,[20,20]);
-%! axis equal;
-%! title('Cylinderical section by extrusion of a circular arc.');
-%! hold off
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbdegelev.m
--- a/extra/nurbs/inst/nrbdegelev.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,173 +0,0 @@
-function inurbs = nrbdegelev(nurbs, ntimes)
-%
-% NRBDEGELEV: Elevate the degree of the NURBS curve, surface or volume.
-%
-% Calling Sequence:
-%
-% ecrv = nrbdegelev(crv,utimes);
-% esrf = nrbdegelev(srf,[utimes,vtimes]);
-% evol = nrbdegelev(vol,[utimes,vtimes,wtimes]);
-%
-% INPUT:
-%
-% crv : NURBS curve, see nrbmak.
-%
-% srf : NURBS surface, see nrbmak.
-%
-% vol : NURBS volume, see nrbmak.
-%
-% utimes : Increase the degree along U direction utimes.
-%
-% vtimes : Increase the degree along V direction vtimes.
-%
-% wtimes : Increase the degree along W direction vtimes.
-%
-% OUTPUT:
-%
-% ecrv : new NURBS structure for a curve with degree elevated.
-%
-% esrf : new NURBS structure for a surface with degree elevated.
-%
-% evol : new NURBS structure for a volume with degree elevated.
-%
-%
-% Description:
-%
-% Degree elevates the NURBS curve or surface. This function uses the
-% B-Spline function bspdegelev, which interface to an internal 'C'
-% routine.
-%
-% Examples:
-%
-% Increase the NURBS surface twice along the V direction.
-% esrf = nrbdegelev(srf, [0, 2]);
-%
-% See also:
-%
-% bspdegelev
-%
-% Copyright (C) 2000 Mark Spink, 2010 Rafel Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 2
- error('Input argument must include the NURBS and degree increment.');
-end
-
-if ~isstruct(nurbs)
- error('NURBS representation is not structure!');
-end
-
-if ~strcmp(nurbs.form,'B-NURBS')
- error('Not a recognised NURBS representation');
-end
-
-degree = nurbs.order-1;
-
-if iscell(nurbs.knots)
- if size(nurbs.knots,2) == 3
- % NURBS represents a volume
- [dim,num1,num2,num3] = size(nurbs.coefs);
-
- % Degree elevate along the w direction
- if ntimes(3) == 0
- coefs = nurbs.coefs;
- knots{3} = nurbs.knots{3};
- else
- coefs = reshape(nurbs.coefs,4*num1*num2,num3);
- [coefs,knots{3}] = bspdegelev(degree(3),coefs,nurbs.knots{3},ntimes(3));
- num3 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num2 num3]);
- end
-
- % Degree elevate along the v direction
- if ntimes(2) == 0
- knots{2} = nurbs.knots{2};
- else
- coefs = permute(coefs,[1 2 4 3]);
- coefs = reshape(coefs,4*num1*num3,num2);
- [coefs,knots{2}] = bspdegelev(degree(2),coefs,nurbs.knots{2},ntimes(2));
- num2 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num3 num2]);
- coefs = permute(coefs,[1 2 4 3]);
- end
-
- % Degree elevate along the u direction
- if ntimes(1) == 0
- knots{1} = nurbs.knots{1};
- else
- coefs = permute(coefs,[1 3 4 2]);
- coefs = reshape(coefs,4*num2*num3,num1);
- [coefs,knots{1}] = bspdegelev(degree(1),coefs,nurbs.knots{1},ntimes(1));
- coefs = reshape(coefs,[4 num2 num3 size(coefs,2)]);
- coefs = permute(coefs,[1 4 2 3]);
- end
-
- elseif size(nurbs.knots,2) == 2
- % NURBS represents a surface
- [dim,num1,num2] = size(nurbs.coefs);
-
- % Degree elevate along the v direction
- if ntimes(2) == 0
- coefs = nurbs.coefs;
- knots{2} = nurbs.knots{2};
- else
- coefs = reshape(nurbs.coefs,4*num1,num2);
- [coefs,knots{2}] = bspdegelev(degree(2),coefs,nurbs.knots{2},ntimes(2));
- num2 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num2]);
- end
-
- % Degree elevate along the u direction
- if ntimes(1) == 0
- knots{1} = nurbs.knots{1};
- else
- coefs = permute(coefs,[1 3 2]);
- coefs = reshape(coefs,4*num2,num1);
- [coefs,knots{1}] = bspdegelev(degree(1),coefs,nurbs.knots{1},ntimes(1));
- coefs = reshape(coefs,[4 num2 size(coefs,2)]);
- coefs = permute(coefs,[1 3 2]);
- end
- end
-else
-
- % NURBS represents a curve
- if isempty(ntimes)
- coefs = nurbs.coefs;
- knots = nurbs.knots;
- else
- [coefs,knots] = bspdegelev(degree,nurbs.coefs,nurbs.knots,ntimes);
- end
-
-end
-
-% construct new NURBS
-inurbs = nrbmak(coefs,knots);
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! plot(crv.coefs(1,:),crv.coefs(2,:),'bo')
-%! title('Degree elevation along test curve: curve and control polygons.');
-%! hold on;
-%! plot(crv.coefs(1,:),crv.coefs(2,:),'b--');
-%! nrbplot(crv,48);
-%!
-%! icrv = nrbdegelev(crv, 1);
-%!
-%! plot(icrv.coefs(1,:),icrv.coefs(2,:),'ro')
-%! plot(icrv.coefs(1,:),icrv.coefs(2,:),'r--');
-%!
-%! hold off;
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbderiv.m
--- a/extra/nurbs/inst/nrbderiv.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,513 +0,0 @@
-function varargout = nrbderiv (nurbs)
-%
-% NRBDERIV: Construct the first and second derivative representation of a
-% NURBS curve, surface or volume.
-%
-% Calling Sequence:
-%
-% ders = nrbderiv (nrb);
-% [ders, ders2] = nrbderiv (nrb);
-%
-% INPUT:
-%
-% nrb : NURBS data structure, see nrbmak.
-%
-% OUTPUT:
-%
-% ders: A data structure that represents the first
-% derivatives of a NURBS curve, surface or volume.
-% ders2: A data structure that represents the second
-% derivatives of a NURBS curve, surface or volume.
-%
-% Description:
-%
-% The derivatives of a B-Spline are themselves a B-Spline of lower degree,
-% giving an efficient means of evaluating multiple derivatives. However,
-% although the same approach can be applied to NURBS, the situation for
-% NURBS is more complex. We have followed in this function the same idea
-% that was already used for the first derivative in the function nrbderiv.
-% The second derivative data structure can be evaluated later with the
-% function nrbdeval.
-%
-% See also:
-%
-% nrbdeval
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Carlo de Falco
-% Copyright (C) 2010, 2011 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (~isstruct(nurbs))
- error('NURBS representation is not structure!');
-end
-
-if (~strcmp(nurbs.form,'B-NURBS'))
- error('Not a recognised NURBS representation');
-end
-
-% We raise the degree to avoid errors in the computation of the second
-% derivative
-if (iscell (nurbs.knots))
- ndim = size(nurbs.knots, 2);
-else
- ndim = 1;
-end
-
-if (nargout == 2)
- degelev = max (2*ones(1, ndim) - (nurbs.order-1), 0);
- nurbs = nrbdegelev (nurbs, degelev);
-end
-
-degree = nurbs.order - 1;
-
-if (ndim == 3)
-% NURBS structure represents a volume
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
- num3 = nurbs.number(3);
-
-% taking derivatives along the u direction
- dknots = nurbs.knots;
- dcoefs = permute (nurbs.coefs,[1 3 4 2]);
- dcoefs = reshape (dcoefs,4*num2*num3,num1);
- [dcoefs,dknots{1}] = bspderiv (degree(1),dcoefs,nurbs.knots{1});
- dcoefs = permute (reshape (dcoefs,[4 num2 num3 size(dcoefs,2)]),[1 4 2 3]);
- dnurbs{1} = nrbmak (dcoefs, dknots);
-
- if (nargout == 2)
-% taking second derivative along the u direction (duu)
- dknots2 = dknots;
- dcoefs2 = permute (dcoefs, [1 3 4 2]);
- dcoefs2 = reshape (dcoefs2, 4*num2*num3, []);
- [dcoefs2, dknots2{1}] = bspderiv (degree(1)-1, dcoefs2, dknots{1});
- dcoefs2 = permute (reshape (dcoefs2, 4, num2, num3, []), [1 4 2 3]);
- dnurbs2{1,1} = nrbmak (dcoefs2, dknots2);
-
-% taking second derivative along the v direction (duv and dvu)
- dknots2 = dknots;
- dcoefs2 = permute (dcoefs,[1 2 4 3]);
- dcoefs2 = reshape (dcoefs2, 4*(num1-1)*num3, num2);
- [dcoefs2, dknots2{2}] = bspderiv (degree(2), dcoefs2, dknots{2});
- dcoefs2 = permute (reshape (dcoefs2, 4, num1-1, num3, []), [1 2 4 3]);
- dnurbs2{1,2} = nrbmak (dcoefs2, dknots2);
- dnurbs2{2,1} = dnurbs2{1,2};
-
-% taking second derivative along the w direction (duw and dwu)
- dknots2 = dknots;
- dcoefs2 = reshape (dcoefs, 4*(num1-1)*num2, num3);
- [dcoefs2, dknots2{3}] = bspderiv (degree(3), dcoefs2, dknots{3});
- dcoefs2 = reshape (dcoefs2, 4, num1-1, num2, []);
- dnurbs2{1,3} = nrbmak (dcoefs2, dknots2);
- dnurbs2{3,1} = dnurbs2{1,3};
- end
-
-% taking derivatives along the v direction
- dknots = nurbs.knots;
- dcoefs = permute (nurbs.coefs,[1 2 4 3]);
- dcoefs = reshape (dcoefs,4*num1*num3,num2);
- [dcoefs,dknots{2}] = bspderiv (degree(2),dcoefs,nurbs.knots{2});
- dcoefs = permute (reshape (dcoefs,[4 num1 num3 size(dcoefs,2)]),[1 2 4 3]);
- dnurbs{2} = nrbmak (dcoefs, dknots);
-
- if (nargout == 2)
-% taking second derivative along the v direction (dvv)
- dknots2 = dknots;
- dcoefs2 = permute (dcoefs,[1 2 4 3]);
- dcoefs2 = reshape (dcoefs2, 4*num1*num3, num2-1);
- [dcoefs2, dknots2{2}] = bspderiv (degree(2)-1, dcoefs2, dknots{2});
- dcoefs2 = permute (reshape (dcoefs2, 4, num1, num3, []), [1 2 4 3]);
- dnurbs2{2,2} = nrbmak (dcoefs2, dknots2);
-
-% taking second derivative along the w direction (dvw and dwv)
- dknots2 = dknots;
- dcoefs2 = reshape (dcoefs, 4*num1*(num2-1), num3);
- [dcoefs2, dknots2{3}] = bspderiv (degree(3), dcoefs2, dknots{3});
- dcoefs2 = reshape (dcoefs2, 4, num1, num2-1, []);
- dnurbs2{2,3} = nrbmak (dcoefs2, dknots2);
- dnurbs2{3,2} = dnurbs2{2,3};
- end
-
-% taking derivatives along the w direction
- dknots = nurbs.knots;
- dcoefs = reshape (nurbs.coefs,4*num1*num2,num3);
- [dcoefs,dknots{3}] = bspderiv (degree(3),dcoefs,nurbs.knots{3});
- dcoefs = reshape (dcoefs,[4 num1 num2 size(dcoefs,2)]);
- dnurbs{3} = nrbmak (dcoefs, dknots);
-
- if (nargout == 2)
-% taking second derivative along the w direction (dww)
- dknots2 = dknots;
- dcoefs2 = reshape (dcoefs, 4*num1*num2, num3-1);
- [dcoefs2, dknots2{3}] = bspderiv (degree(3)-1, dcoefs2, dknots{3});
- dcoefs2 = reshape (dcoefs2, 4, num1, num2, []);
- dnurbs2{3,3} = nrbmak (dcoefs2, dknots2);
- end
-
-elseif (ndim == 2)
-% NURBS structure represents a surface
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
-
-% taking first derivative along the u direction
- dknots = nurbs.knots;
- dcoefs = permute (nurbs.coefs,[1 3 2]);
- dcoefs = reshape (dcoefs,4*num2,num1);
- [dcoefs,dknots{1}] = bspderiv (degree(1),dcoefs,nurbs.knots{1});
- dcoefs = permute (reshape (dcoefs,[4 num2 size(dcoefs,2)]),[1 3 2]);
- dnurbs{1} = nrbmak (dcoefs, dknots);
-
- if (nargout == 2)
-% taking second derivative along the u direction (duu)
- dknots2 = dknots;
- dcoefs2 = permute (dcoefs, [1 3 2]);
- dcoefs2 = reshape (dcoefs2, 4*num2, []);
- [dcoefs2, dknots2{1}] = bspderiv (degree(1)-1, dcoefs2, dknots{1});
- dcoefs2 = permute (reshape (dcoefs2, 4, num2, []), [1 3 2]);
- dnurbs2{1,1} = nrbmak (dcoefs2, dknots2);
-
-% taking second derivative along the v direction (duv and dvu)
- dknots2 = dknots;
- dcoefs2 = reshape (dcoefs, 4*(num1-1), num2);
- [dcoefs2, dknots2{2}] = bspderiv (degree(2), dcoefs2, dknots{2});
- dcoefs2 = reshape (dcoefs2, 4, num1-1, []);
- dnurbs2{1,2} = nrbmak (dcoefs2, dknots2);
- dnurbs2{2,1} = dnurbs2{1,2};
- end
-
-% taking first derivative along the v direction
- dknots = nurbs.knots;
- dcoefs = reshape (nurbs.coefs,4*num1,num2);
- [dcoefs,dknots{2}] = bspderiv (degree(2),dcoefs,nurbs.knots{2});
- dcoefs = reshape (dcoefs,[4 num1 size(dcoefs,2)]);
- dnurbs{2} = nrbmak (dcoefs, dknots);
-
- if (nargout == 2)
-% taking second derivative along the v direction (dvv)
- dknots2 = dknots;
- dcoefs2 = reshape (dcoefs, 4*num1, num2-1);
- [dcoefs2, dknots2{2}] = bspderiv (degree(2)-1, dcoefs2, dknots{2});
- dcoefs2 = reshape (dcoefs2, 4, num1, []);
- dnurbs2{2,2} = nrbmak (dcoefs2, dknots2);
- end
-
-else
- % NURBS structure represents a curve
- [dcoefs,dknots] = bspderiv (degree, nurbs.coefs, nurbs.knots);
- dnurbs = nrbmak (dcoefs, dknots);
- if (nargout == 2)
- [dcoefs2,dknots2] = bspderiv (degree-1, dcoefs, dknots);
- dnurbs2 = nrbmak (dcoefs2, dknots2);
- end
-end
-
-varargout{1} = dnurbs;
-if (nargout == 2)
- varargout{2} = dnurbs2;
-
- if (iscell (dnurbs2))
- dnurbs2 = [dnurbs2{:}];
- end
- if (any (arrayfun(@(x) any(isnan(x.coefs(:)) | isinf(x.coefs(:))), dnurbs2)))
- warning ('nrbderiv:SecondDerivative', ...
- ['The structure for the second derivative contains Inf and/or NaN coefficients, ' ...
- 'probably due to low continuity at repeated knots. This should not affect the ' ...
- 'computation of the second derivatives, except at those knots.'])
- end
-end
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! nrbplot(crv,48);
-%! title('First derivatives along a test curve.');
-%!
-%! tt = linspace(0.0,1.0,9);
-%!
-%! dcrv = nrbderiv(crv);
-%!
-%! [p1, dp] = nrbdeval(crv,dcrv,tt);
-%!
-%! p2 = vecnorm(dp);
-%!
-%! hold on;
-%! plot(p1(1,:),p1(2,:),'ro');
-%! h = quiver(p1(1,:),p1(2,:),p2(1,:),p2(2,:),0);
-%! set(h,'Color','black');
-%! hold off;
-
-%!demo
-%! srf = nrbtestsrf;
-%! p = nrbeval(srf,{linspace(0.0,1.0,20) linspace(0.0,1.0,20)});
-%! h = surf(squeeze(p(1,:,:)),squeeze(p(2,:,:)),squeeze(p(3,:,:)));
-%! set(h,'FaceColor','blue','EdgeColor','blue');
-%! title('First derivatives over a test surface.');
-%!
-%! npts = 5;
-%! tt = linspace(0.0,1.0,npts);
-%! dsrf = nrbderiv(srf);
-%!
-%! [p1, dp] = nrbdeval(srf, dsrf, {tt, tt});
-%!
-%! up2 = vecnorm(dp{1});
-%! vp2 = vecnorm(dp{2});
-%!
-%! hold on;
-%! plot3(p1(1,:),p1(2,:),p1(3,:),'ro');
-%! h1 = quiver3(p1(1,:),p1(2,:),p1(3,:),up2(1,:),up2(2,:),up2(3,:));
-%! h2 = quiver3(p1(1,:),p1(2,:),p1(3,:),vp2(1,:),vp2(2,:),vp2(3,:));
-%! set(h1,'Color','black');
-%! set(h2,'Color','black');
-%!
-%! hold off;
-
-%!test
-%! knots = [0 0 0 0.5 1 1 1];
-%! coefs(1,:) = [0 2 4 2];
-%! coefs(2,:) = [0 2 2 0];
-%! coefs(3,:) = [0 4 2 0];
-%! coefs(4,:) = [1 2 2 1];
-%! nrb = nrbmak (coefs, knots);
-%! [dnrb, dnrb2] = nrbderiv (nrb);
-%! x = linspace (0, 1, 10);
-%! [pnt, jac, hess] = nrbdeval (nrb, dnrb, dnrb2, x);
-%! w = -4*x.^2 + 4*x + 1;
-%! F = zeros (3,numel(x)); DF = zeros (3, numel(x)); D2F = zeros (3, numel(x));
-%! F(1,:) = (-4*x.*(x-2)./w) .* (x<0.5) + ((4*x - 5)./w + 3) .* (x>0.5);
-%! F(2,:) = (2-2./w);
-%! F(3,:) = (-4*x.*(5*x-4)./w) .* (x<0.5) + (-4*(x.^2 - 1)./w) .* (x>0.5);
-%! DF(1,:) = (8*(2*x.^2-x+1)./w.^2) .* (x<0.5) + (8*(2*x-3).*(x-1)./w.^2) .* (x>0.5);
-%! DF(2,:) = -8*(2*x-1)./w.^2;
-%! DF(3,:) = -(8*(2*x.^2+5*x-2)./w.^2) .* (x<0.5) - (8*(2*x.^2-3*x+2)./w.^2) .* (x>0.5);
-%! D2F(1,:) = 8*(16*x.^3-12*x.^2+24*x-9)./w.^3 .* (x<0.5) + 8*(16*x.^3-60*x.^2+72*x-29)./w.^3 .* (x>0.5);
-%! D2F(2,:) = -16*(12*x.^2-12*x+5)./w.^3;
-%! D2F(3,:) = -8*(16*x.^3+60*x.^2-48*x+21)./w.^3 .* (x<0.5) -8*(16*x.^3-36*x.^2+48*x-19)./w.^3 .* (x>0.5);
-%! assert (F, pnt, 1e3*eps)
-%! assert (DF, jac, 1e3*eps)
-%! assert (D2F, hess, 1e3*eps)
-
-%!test
-%! knots = {[0 0 0 1 1 1], [0 0 0 0.5 1 1 1]};
-%! coefs = ones (4,3,4);
-%! coefs(1,:,:) = reshape ([0 0 0 0; 1 1 1 1; 2 2 4 2], 1, 3, 4);
-%! coefs(2,:,:) = reshape ([0 1 2 3; 0 1 2 3; 0 1 4 3], 1, 3, 4);
-%! coefs(3,:,:) = reshape ([0 1 0 0; 0 0 0 0; 0 0 0 0], 1, 3, 4);
-%! coefs(4,:,:) = reshape ([1 1 1 1; 1 1 1 1; 1 1 2 1], 1, 3, 4);
-%! nrb = nrbmak (coefs, knots);
-%! [dnrb, dnrb2] = nrbderiv (nrb);
-%! X = linspace (0, 1, 4); Y = linspace (0, 1, 4);
-%! [pnt, jac, hess] = nrbdeval (nrb, dnrb, dnrb2, {X Y});
-%! [y, x] = meshgrid (X, Y);
-%! w = (2*x.^2.*y.^2 + 1) .* (y < 0.5) + (-6*x.^2.*y.^2 + 8*x.^2.*y - 2*x.^2 + 1) .* (y > 0.5);
-%! F = zeros ([3,size(x)]);
-%! F(1,:,:) = ((2*x - 2) ./w + 2) .* (y<0.5) + (2 + (2*x-2)./w) .* (y > 0.5);
-%! F(2,:,:) = (2 - (2*(y-1).^2)./w).*(y<0.5) + ...
-%! ((-12*x.^2.*y.^2 + 16*x.^2.*y - 4*x.^2 + 2*y.^2 + 1)./w).*(y>0.5);
-%! F(3,:,:) = (-2*y.*(3*y - 2).*(x - 1).^2./w) .* (y<0.5) + ...
-%! (2*(x - 1).^2.*(y - 1).^2./w) .* (y>0.5);
-%! dFdu = zeros ([3,size(x)]);
-%! dFdu(1,:,:) = (((8*x - 4*x.^2).*y.^2 + 2)./w.^2).*(y<0.5) + ...
-%! (((12*y.^2 - 16*y + 4).*x.^2 + (-24*y.^2 + 32*y - 8).*x + 2)./w.^2).*(y>0.5);
-%! dFdu(2,:,:) = (8*x.*y.^2.*(y - 1).^2./w.^2).*(y<0.5) + ...
-%! ((4*x.*(3*y - 1).*(2*y.^2 - 1).*(y - 1))./w.^2).*(y>0.5);
-%! dFdu(3,:,:) = (-4*y.*(2.*x.*y.^2 + 1).*(3*y - 2).*(x - 1)./w.^2).*(y<0.5) + ...
-%! ((-4*(x - 1).*(y - 1).^2.*(6*x.*y.^2 - 8*x.*y + 2*x - 1))./w.^2).*(y>0.5);
-%! dFdv = zeros ([3,size(x)]);
-%! dFdv(1,:,:) = (-8*x.^2.*y.*(x - 1)./w.^2).*(y<0.5) + ...
-%! (8*x.^2.*(3*y - 2).*(x - 1)./w.^2).*(y>0.5);
-%! dFdv(2,:,:) = (-4*(2*y.*x.^2 + 1).*(y - 1)./w.^2).*(y<0.5) + ...
-%! (((16*y.^2 - 20*y + 8).*x.^2 + 4*y)./w.^2).*(y>0.5);
-%! dFdv(3,:,:) = (-4*(x - 1).^2.*(2*x.^2.*y.^2 + 3*y - 1)./w.^2).*(y<0.5) + ...
-%! (4*(x - 1).^2.*(y - 1).*(2*x.^2 - 2*x.^2.*y + 1)./w.^2).*(y>0.5);
-%! d2Fduu = zeros ([3, size(x)]);
-%! d2Fduu(1,:,:) = (-((48*x.^2 - 16*x.^3).*y.^4 + (24*x - 8).*y.^2)./w.^3).*(y<0.5) + ...
-%! (((32*(3*y - 1).*(x - 1).*(y - 1))-(8*(3*y - 1).*(x - 3).*(y - 1).*w))./w.^3).*(y>0.5);
-%! d2Fduu(2,:,:) = (-(8*y.^2.*(6*x.^2.*y.^2 - 1).*(y - 1).^2)./w.^3).*(y<0.5) + ...
-%! ((4*(3*y - 1).*(2*y.^2 - 1).*(y - 1).*(18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 + 1))./w.^3).*(y>0.5);
-%! d2Fduu(3,:,:) = ((4*y.*(3*y - 2).*(8*x.^3.*y.^4 - 12*x.^2.*y.^4 + 6*x.^2.*y.^2 - 12*x.*y.^2 + 2*y.^2 - 1))./w.^3).*(y<0.5) + ...
-%! ((4*(y - 1).^2.*(6*y.^2 - 8*y + 3) - 4*x.^3.*(y - 1).^2.*(72*y.^4 - 192*y.^3 + 176*y.^2 - 64*y + 8) + 4*x.^2.*(y - 1).^2.*(108*y.^4 - 288*y.^3 + 282*y.^2 - 120*y + 18) - 4*x.*(y - 1).^2.*(36*y.^2 - 48*y + 12))./w.^3) .* (y>0.5);
-%! d2Fdvv = zeros ([3, size(x)]);
-%! d2Fdvv(1,:,:) = (8*x.^2.*(6*x.^2.*y.^2 - 1).*(x - 1)./w.^3) .* (y<0.5) + ...
-%! (8*x.^2.*(x - 1).*(54*x.^2.*y.^2 - 72*x.^2.*y + 26*x.^2 + 3)./w.^3) .* (y>0.5);
-%! d2Fdvv(2,:,:) = (-((48*y.^2 - 32*y.^3).*x.^4 + (- 24*y.^2 + 48*y - 8).*x.^2 + 4)./w.^3) .*(y<0.5) + ...
-%! (((192*y.^3 - 360*y.^2 + 288*y - 88).*x.^4 + (72*y.^2 - 28).*x.^2 + 4)./w.^3) .* (y>0.5);
-%! d2Fdvv(3,:,:) = (4*(x - 1).^2.*(8*x.^4.*y.^3 + 18*x.^2.*y.^2 - 12*x.^2.*y - 3))./w.^3 .* (y<0.5) + ...
-%! ((4*(x - 1).^2.*(24*x.^4 + 18*x.^2 + 1) + 4*y.^2.*(72*x.^4 + 18*x.^2).*(x - 1).^2 - 96*x.^4.*y.^3.*(x - 1).^2 - 4*y.*(72*x.^4 + 36*x.^2).*(x - 1).^2)./w.^3) .* (y>0.5);
-%! d2Fduv = zeros ([3, size(x)]);
-%! d2Fduv(1,:,:) = (-(y.^3.*(32*x.^3 - 16*x.^4) - y.*(16*x - 24*x.^2))./w.^3) .* (y<0.5) + ...
-%! (-(-8*(3*y - 2).*(6*y.^2 - 8*y + 2).*x.^4 + 8*(3*y - 2).*(12*y.^2 - 16*y + 4).*x.^3 + (48 - 72*y).*x.^2 + (48*y - 32).*x)./w.^3) .* (y>0.5);
-%! d2Fduv(2,:,:) = (16*x.*y.*(y - 1).*(2*x.^2.*y.^2 + 2*y - 1)./w.^3) .* (y<0.5) + ...
-%! (-(8*x.*(4*y.^2 - 5*y + 2))./w.^2 + (16*x.*(3*y - 2).*(2*y.^2 - 1))./w.^3) .* (y>0.5);
-%! d2Fduv(3,:,:) = (-(8*(x - 1).*(4*x.^3.*y.^4 - 6*x.^2.*y.^3 + 6*x.^2.*y.^2 + 12*x.*y.^3 - 6*x.*y.^2 + 3*y - 1))./w.^3) .* (y<0.5) + ...
-%! ((8*(x - 1).*(y - 1).*(12*x.^3.*y.^3 - 28*x.^3.*y.^2 + 20*x.^3.*y - 4*x.^3 + 6*x.^2.*y.^2 - 12*x.^2.*y + 6*x.^2 - 12*x.*y.^2 + 18*x.*y - 6*x + 1))./w.^3) .* (y>0.5);
-%! assert (F, pnt, 1e3*eps)
-%! assert (dFdu, jac{1}, 1e3*eps)
-%! assert (dFdv, jac{2}, 1e3*eps)
-%! assert (d2Fduu, hess{1,1}, 1e3*eps)
-%! assert (d2Fduv, hess{1,2}, 1e3*eps)
-%! assert (d2Fduv, hess{2,1}, 1e3*eps)
-%! assert (d2Fdvv, hess{2,2}, 1e3*eps)
-
-%!test
-%! knots = {[0 0 0 1 1 1], [0 0 0 0.5 1 1 1]};
-%! coefs = ones (4,3,4);
-%! coefs(1,:,:) = reshape ([0 0 0 0; 1 1 1 1; 2 2 4 2], 1, 3, 4);
-%! coefs(2,:,:) = reshape ([0 1 2 3; 0 1 2 3; 0 1 4 3], 1, 3, 4);
-%! coefs(3,:,:) = reshape ([0 1 0 0; 0 0 0 0; 0 0 0 0], 1, 3, 4);
-%! coefs(4,:,:) = reshape ([1 1 1 1; 1 1 1 1; 1 1 2 1], 1, 3, 4);
-%! nrb = nrbmak (coefs, knots);
-%! nrb = nrbdegelev (nrbextrude (nrb, [0.4 0.6 2]), [0 0 1]);
-%! nrb.coefs(4,2,3,3) = 1.5;
-%! [dnrb, dnrb2] = nrbderiv (nrb);
-%! X = linspace (0, 1, 4); Y = linspace (0, 1, 4); Z = linspace (0, 1, 4);
-%! [pnt, jac, hess] = nrbdeval (nrb, dnrb, dnrb2, {X Y Z});
-%! [y, x, z] = meshgrid (X, Y, Z);
-%! w = (-2*x.^2.*y.^2.*z.^2 + 2*x.^2.*y.^2 + 2*x.*y.^2.*z.^2 + 1) .* (y < 0.5) + ...
-%! (6*x.^2.*y.^2.*z.^2 - 6*x.^2.*y.^2 - 8*x.^2.*y.*z.^2 + 8*x.^2.*y + 2*x.^2.*z.^2 - 2*x.^2 - 6*x.*y.^2.*z.^2 + 8*x.*y.*z.^2 - 2*x.*z.^2 + 1) .* (y > 0.5);
-%! F = zeros ([3,size(x)]);
-%! F(1,:,:,:) = ((10*x + 20*x.^2.*y.^2 + z.*(4*x.^2.*y.^2 + 2))./(5*w)) .* (y<0.5) + ...
-%! (60*x.^2.*y.^2 - 10*x + z.*(12*x.^2.*y.^2 - 16*x.^2.*y + 4*x.^2 - 2) - 80*x.^2.*y + 20*x.^2)./(-5*w) .* (y > 0.5);
-%! F(2,:,:,:) = ((20*y + 20*x.^2.*y.^2 + z.*(6*x.^2.*y.^2 + 3) - 10*y.^2)./(5*w)).*(y<0.5) + ...
-%! ((60*x.^2.*y.^2 + z.*(18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 - 3) - 80*x.^2.*y + 20*x.^2 - 10*y.^2 - 5)./(-5*w)).*(y>0.5);
-%! F(3,:,:,:) = ((4*y - 6*x.^2.*y.^2 + z.*(4*x.^2.*y.^2 + 2) - 8*x.*y + 12*x.*y.^2 + 4*x.^2.*y - 6*y.^2)./w) .* (y<0.5) + ...
-%! ((2*z - 4*y - 4*x + 2*x.^2.*y.^2 + 8*x.*y - 4*x.*y.^2 - 4*x.^2.*y - 4*x.^2.*z + 2*x.^2 + 2*y.^2 + 16*x.^2.*y.*z - 12*x.^2.*y.^2.*z + 2)./w) .* (y>0.5);
-%! dFdu = zeros ([3,size(x)]);
-%! dFdu(1,:,:,:) = ((x.*((8*y.^2.*z.^3)/5 + 8*y.^2) - (4*y.^2.*z.^3)/5 + x.^2.*(z.^2.*(8*y.^4 + 4*y.^2) + (8*y.^4.*z.^3)/5 - 4*y.^2) + 2)./w.^2).*(y<0.5) + ...
-%! ((z.^3.*(x.^2.*((72*y.^4)/5 - (192*y.^3)/5 + (176*y.^2)/5 - (64*y)/5 + 8/5) - (16*y)/5 - x.*((24*y.^2)/5 - (32*y)/5 + 8/5) + (12*y.^2)/5 + 4/5) - x.*(24*y.^2 - 32*y + 8) + x.^2.*(12*y.^2 - 16*y + 4) + x.^2.*z.^2.*(72*y.^4 - 192*y.^3 + 164*y.^2 - 48*y + 4) + 2)./w.^2).*(y>0.5);
-%! dFdu(2,:,:,:) = ((z.^2.*(8*x.^2.*y.^4 - y.^2.*(8*y - 4*y.^2) + (2*x.*y.^2.*(40*y - 20*y.^2))/5) + z.^3.*((12*x.^2.*y.^4)/5 + (12*x.*y.^2)/5 - (6*y.^2)/5) + (2*x.*y.^2.*(20*y.^2 - 40*y + 20))/5)./w.^2).*(y<0.5) + ...
-%! (((2*(3*y.^2 - 4*y + 1).*(18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 - 6*x + 3).*z.^3)/5 + (2*(3*y.^2 - 4*y + 1).*(60*x.^2.*y.^2 - 80*x.^2.*y + 20*x.^2 - 20*x.*y.^2 - 10*x + 10*y.^2 + 5).*z.^2)/5 - (2*(10*x - 20*x.*y.^2).*(3*y.^2 - 4*y + 1))/5)./w.^2).*(y>0.5);
-%! dFdu(3,:,:,:) = ((4*y.*(3*y - 2) + z.^3.*(8*x.^2.*y.^4 + 8*x.*y.^2 - 4*y.^2) - z.^2.*(4*y.*(2*y.^2 - 3*y.^3).*x.^2 - 4*y.*(4*y.^2 - 6*y.^3).*x + 4*y.*(2*y.^2 - 3*y.^3)) + 4*x.^2.*y.*(4*y.^2 - 6*y.^3) - 4*x.*y.*(- 6*y.^3 + 4*y.^2 + 3*y - 2)) ./w.^2).*(y<0.5) + ...
-%! ((z.^2.*(4*(y - 1).*(3*y.^3 - 7*y.^2 + 5*y - 1).*x.^2 - 4*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2).*x + 4*(y - 1).*(3*y.^3 - 7*y.^2 + 5*y - 1)) - 4*(y - 1).^2 + z.^3.*(4*(y - 1).*(18*y.^3 - 30*y.^2 + 14*y - 2).*x.^2 - 4*(6*y - 2).*(y - 1).*x + 4*(3*y - 1).*(y - 1)) + 4*x.*(y - 1).*(6*y.^3 - 14*y.^2 + 11*y - 3) - 4*x.^2.*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2))./w.^2) .* (y > 0.5);
-%! dFdv = zeros ([3,size(x)]);
-%! dFdv(1,:,:,:) = ((8*x.*y.*(x - 1).*(z.^3 + 5*x.*z.^2 - 5*x))/5./w.^2).*(y<0.5) + ...
-%! (-(8*x.*(3*y - 2).*(x - 1).*(z.^3 + 5*x.*z.^2 - 5*x))/5./w.^2).*(y>0.5);
-%! dFdv(2,:,:,:) = (-((8*x.*z.^2 - x.^2.*(8*z.^2 - 8)).*y.^2 + ((12*x.*z.^3)/5 - x.^2.*((12*z.^3)/5 + 8) + 4).*y - 4)./w.^2).*(y<0.5) + ...
-%! ((4*y + z.^3.*(x.*((36*y)/5 - 24/5) - x.^2.*((36*y)/5 - 24/5)) + z.^2.*(x.*(16*y.^2 + 4*y - 8) - x.^2.*(16*y.^2 + 4*y - 8)) + x.^2.*(16*y.^2 - 20*y + 8))./w.^2).*(y>0.5);
-%! dFdv(3,:,:,:) = ((4*(x - 1).^2 - y.*(4*(3*x - 3).*(x - 1) - 8*x.*z.^3.*(x - 1)) + y.^2.*(4*(x - 1).*(2*x.^3 - 4*x.^2 + 2*x).*z.^2 + 4*(2*x.^2 - 2*x.^3).*(x - 1)))./w.^2).*(y<0.5) + ...
-%! ((y.^2.*(4*(x - 1).*(2*x.^3 - 4*x.^2 + 2*x).*z.^2 + 4*(2*x.^2 - 2*x.^3).*(x - 1)) - 4*(x - 1).*(2*x.^3 - 2*x.^2 + x - 1) - y.*(24*x.*(x - 1).*z.^3 + 4*(x - 1).*(4*x.^3 - 8*x.^2 + 4*x).*z.^2 - 4*(x - 1).*(4*x.^3 - 4*x.^2 + x - 1)) + 16*x.*z.^3.*(x - 1) + 4*z.^2.*(x - 1).*(2*x.^3 - 4*x.^2 + 2*x))./w.^2).*(y>0.5);
-%! dFdw = zeros ([3,size(x)]);
-%! dFdw(1,:,:,:) = ((4*x.^2.*y.^2 + 2)./(- 10*x.^2.*y.^2.*z.^2 + 10*x.^2.*y.^2 + 10*x.*y.^2.*z.^2 + 5) - ((20*x.*y.^2.*z - 20*x.^2.*y.^2.*z).*(10*x + 20*x.^2.*y.^2 + z.*(4*x.^2.*y.^2 + 2)))./(5*w).^2).*(y<0.5) + ...
-%! ((12*x.^2.*y.^2 - 16*x.^2.*y + 4*x.^2 - 2)./(- 30*x.^2.*y.^2.*z.^2 + 30*x.^2.*y.^2 + 40*x.^2.*y.*z.^2 - 40*x.^2.*y - 10*x.^2.*z.^2 + 10*x.^2 + 30*x.*y.^2.*z.^2 - 40*x.*y.*z.^2 + 10*x.*z.^2 - 5) - ((60*x.^2.*y.^2 - 10*x + z.*(12*x.^2.*y.^2 - 16*x.^2.*y + 4*x.^2 - 2) - 80*x.^2.*y + 20*x.^2).*(- 60*z.*x.^2.*y.^2 + 80*z.*x.^2.*y - 20*z.*x.^2 + 60*z.*x.*y.^2 - 80*z.*x.*y + 20*z.*x))./(5*w).^2).*(y>0.5);
-%! dFdw(2,:,:,:) = ((6*x.^2.*y.^2 + 3)./(- 10*x.^2.*y.^2.*z.^2 + 10*x.^2.*y.^2 + 10*x.*y.^2.*z.^2 + 5) - ((20*x.*y.^2.*z - 20*x.^2.*y.^2.*z).*(20*y + 20*x.^2.*y.^2 + z.*(6*x.^2.*y.^2 + 3) - 10*y.^2))./(5*w).^2).*(y<0.5) + ...
-%! ((18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 - 3)./(- 30*x.^2.*y.^2.*z.^2 + 30*x.^2.*y.^2 + 40*x.^2.*y.*z.^2 - 40*x.^2.*y - 10*x.^2.*z.^2 + 10*x.^2 + 30*x.*y.^2.*z.^2 - 40*x.*y.*z.^2 + 10*x.*z.^2 - 5) - ((- 60*z.*x.^2.*y.^2 + 80*z.*x.^2.*y - 20*z.*x.^2 + 60*z.*x.*y.^2 - 80*z.*x.*y + 20*z.*x).*(60*x.^2.*y.^2 + z.*(18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 - 3) - 80*x.^2.*y + 20*x.^2 - 10*y.^2 - 5))./(5*w).^2).*(y>0.5);
-%! dFdw(3,:,:,:) = ((4*x.^2.*y.^2 + 2)./(2*x.^2.*y.^2 - z.^2.*(2*x.^2.*y.^2 - 2*x.*y.^2) + 1) + (2*z.*(2*x.^2.*y.^2 - 2*x.*y.^2).*(4*y - 6*x.^2.*y.^2 + z.*(4*x.^2.*y.^2 + 2) - 8*x.*y + 12*x.*y.^2 + 4*x.^2.*y - 6*y.^2))./w.^2).*(y<0.5) + ...
-%! ((12*x.^2.*y.^2 - 16*x.^2.*y + 4*x.^2 - 2)./(6*x.^2.*y.^2 + z.^2.*(- 6*x.^2.*y.^2 + 8*x.^2.*y - 2*x.^2 + 6*x.*y.^2 - 8*x.*y + 2*x) - 8*x.^2.*y + 2*x.^2 - 1) + (2*z.*(- 6*x.^2.*y.^2 + 8*x.^2.*y - 2*x.^2 + 6*x.*y.^2 - 8*x.*y + 2*x).*(2*z - 4*y - 4*x + 2*x.^2.*y.^2 + 8*x.*y - 4*x.*y.^2 - 4*x.^2.*y - 4*x.^2.*z + 2*x.^2 + 2*y.^2 + 16*x.^2.*y.*z - 12*x.^2.*y.^2.*z + 2))./w.^2).*(y>0.5);
-%! d2Fduu = zeros ([3, size(x)]);
-%! d2Fduu(1,:,:,:) = (((8*y.^2.*z.^3)/5 + 2*x.*(z.^2.*(8*y.^4 + 4*y.^2) + (8*y.^4.*z.^3)/5 - 4*y.^2) + 8*y.^2)./w.^2 - (2*(2*y.^2.*z.^2 + 4*x.*y.^2 - 4*x.*y.^2.*z.^2).*(x.*((8*y.^2.*z.^3)/5 + 8*y.^2) - (4*y.^2.*z.^3)/5 + x.^2.*(z.^2.*(8*y.^4 + 4*y.^2) + (8*y.^4.*z.^3)/5 - 4*y.^2) + 2))./w.^3).*(y<0.5) + ...
-%! ((32*y + 2*x.*(12*y.^2 - 16*y + 4) + z.^3.*((32*y)/5 + 2*x.*((72*y.^4)/5 - (192*y.^3)/5 + (176*y.^2)/5 - (64*y)/5 + 8/5) - (24*y.^2)/5 - 8/5) - 24*y.^2 + 2*x.*z.^2.*(72*y.^4 - 192*y.^3 + 164*y.^2 - 48*y + 4) - 8)./w.^2 - (2*(z.^3.*(x.^2.*((72*y.^4)/5 - (192*y.^3)/5 + (176*y.^2)/5 - (64*y)/5 + 8/5) - (16*y)/5 - x.*((24*y.^2)/5 - (32*y)/5 + 8/5) + (12*y.^2)/5 + 4/5) - x.*(24*y.^2 - 32*y + 8) + x.^2.*(12*y.^2 - 16*y + 4) + x.^2.*z.^2.*(72*y.^4 - 192*y.^3 + 164*y.^2 - 48*y + 4) + 2).*(4*x + 6*y.^2.*z.^2 - 16*x.*y + 12*x.*y.^2 - 4*x.*z.^2 - 8*y.*z.^2 + 2*z.^2 + 16*x.*y.*z.^2 - 12*x.*y.^2.*z.^2))./(-w).^3).*(y>0.5);
-%! d2Fduu(2,:,:,:) = ((z.^3.*((24*x.*y.^4)/5 + (12*y.^2)/5) + (2*y.^2.*(20*y.^2 - 40*y + 20))/5 + z.^2.*((2*y.^2.*(40*y - 20*y.^2))/5 + 16*x.*y.^4))./w.^2 - (2*(z.^2.*(8*x.^2.*y.^4 - y.^2.*(8*y - 4*y.^2) + (2*x.*y.^2.*(40*y - 20*y.^2))/5) + z.^3.*((12*x.^2.*y.^4)/5 + (12*x.*y.^2)/5 - (6*y.^2)/5) + (2*x.*y.^2.*(20*y.^2 - 40*y + 20))/5).*(2*y.^2.*z.^2 + 4*x.*y.^2 - 4*x.*y.^2.*z.^2))./w.^3).*(y<0.5) + ...
-%! (((2*(3*y.^2 - 4*y + 1).*(36*x.*y.^2 - 48*x.*y + 12*x - 6).*z.^3)/5 - (2*(3*y.^2 - 4*y + 1).*(160*x.*y - 40*x - 120*x.*y.^2 + 20*y.^2 + 10).*z.^2)/5 + (2*(20*y.^2 - 10).*(3*y.^2 - 4*y + 1))/5)./w.^2 - (2*((2*(3*y.^2 - 4*y + 1).*(18*x.^2.*y.^2 - 24*x.^2.*y + 6*x.^2 - 6*x + 3).*z.^3)/5 + (2*(3*y.^2 - 4*y + 1).*(60*x.^2.*y.^2 - 80*x.^2.*y + 20*x.^2 - 20*x.*y.^2 - 10*x + 10*y.^2 + 5).*z.^2)/5 - (2*(10*x - 20*x.*y.^2).*(3*y.^2 - 4*y + 1))/5).*(4*x + 6*y.^2.*z.^2 - 16*x.*y + 12*x.*y.^2 - 4*x.*z.^2 - 8*y.*z.^2 + 2*z.^2 + 16*x.*y.*z.^2 - 12*x.*y.^2.*z.^2))./(-w).^3).*(y>0.5);
-%! d2Fduu(3,:,:,:) = (((16*x.*y.^4 + 8*y.^2).*z.^3 + (4*y.*(4*y.^2 - 6*y.^3) - 8*x.*y.*(2*y.^2 - 3*y.^3)).*z.^2 - 4*y.*(- 6*y.^3 + 4*y.^2 + 3*y - 2) + 8*x.*y.*(4*y.^2 - 6*y.^3))./w.^2 - (2*(2*y.^2.*z.^2 + 4*x.*y.^2 - 4*x.*y.^2.*z.^2).*(4*y.*(3*y - 2) + z.^3.*(8*x.^2.*y.^4 + 8*x.*y.^2 - 4*y.^2) - z.^2.*(4*y.*(2*y.^2 - 3*y.^3).*x.^2 - 4*y.*(4*y.^2 - 6*y.^3).*x + 4*y.*(2*y.^2 - 3*y.^3)) + 4*x.^2.*y.*(4*y.^2 - 6*y.^3) - 4*x.*y.*(- 6*y.^3 + 4*y.^2 + 3*y - 2)))./w.^3).*(y<0.5) + ...
-%! (-((4*(6*y - 2).*(y - 1) - 8*x.*(y - 1).*(18*y.^3 - 30*y.^2 + 14*y - 2)).*z.^3 + (4*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2) - 8*x.*(y - 1).*(3*y.^3 - 7*y.^2 + 5*y - 1)).*z.^2 - 4*(y - 1).*(6*y.^3 - 14*y.^2 + 11*y - 3) + 8*x.*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2))./w.^2 - (2*(z.^2.*(4*(y - 1).*(3*y.^3 - 7*y.^2 + 5*y - 1).*x.^2 - 4*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2).*x + 4*(y - 1).*(3*y.^3 - 7*y.^2 + 5*y - 1)) - 4*(y - 1).^2 + z.^3.*(4*(y - 1).*(18*y.^3 - 30*y.^2 + 14*y - 2).*x.^2 - 4*(6*y - 2).*(y - 1).*x + 4*(3*y - 1).*(y - 1)) + 4*x.*(y - 1).*(6*y.^3 - 14*y.^2 + 11*y - 3) - 4*x.^2.*(y - 1).*(6*y.^3 - 14*y.^2 + 10*y - 2)).*(4*x + 6*y.^2.*z.^2 - 16*x.*y + 12*x.*y.^2 - 4*x.*z.^2 - 8*y.*z.^2 + 2*z.^2 + 16*x.*y.*z.^2 - 12*x.*y.^2.*z.^2))./(-w).^3) .* (y>0.5);
-%! d2Fduv = zeros ([3, size(x)]);
-%! d2Fduv(1,:,:,:) = ((((8.*x.^2.*(6.*z.^3 - 6.*z.^5))/5 + (8.*x.^4.*(10.*z.^4 - 20.*z.^2 + 10))/5 - (8.*x.^3.*(- 4.*z.^5 + 10.*z.^4 + 4.*z.^3 - 30.*z.^2 + 20))/5 + (16.*x.*z.^5)/5).*y.^3 + ((8.*x.*(2.*z.^3 - 10.*z.^2 + 10))/5 + (8.*x.^2.*(15.*z.^2 - 15))/5 - (8.*z.^3)/5).*y)./w.^3) .* (y<0.5) + ...
-%! (-(x.^4.*((8.*(3.*y - 2).*(30.*y.^2 - 40.*y + 10).*z.^4)/5 - (8.*(3.*y - 2).*(60.*y.^2 - 80.*y + 20).*z.^2)/5 + (8.*(3.*y - 2).*(30.*y.^2 - 40.*y + 10))/5) - x.^3.*(- (8.*(3.*y - 2).*(12.*y.^2 - 16.*y + 4).*z.^5)/5 + (8.*(3.*y - 2).*(30.*y.^2 - 40.*y + 10).*z.^4)/5 + (8.*(3.*y - 2).*(12.*y.^2 - 16.*y + 4).*z.^3)/5 - (8.*(3.*y - 2).*(90.*y.^2 - 120.*y + 30).*z.^2)/5 + (8.*(3.*y - 2).*(60.*y.^2 - 80.*y + 20))/5) + z.^3.*((24.*y)/5 - 16/5) - x.^2.*((8.*(3.*y - 2).*(18.*y.^2 - 24.*y + 6).*z.^5)/5 - (8.*(3.*y - 2).*(18.*y.^2 - 24.*y + 6).*z.^3)/5 + (72.*y - 48).*z.^2 - 72.*y + 48) + x.*((8.*(3.*y - 2).*(6.*y.^2 - 8.*y + 2).*z.^5)/5 + (32/5 - (48.*y)/5).*z.^3 + (48.*y - 32).*z.^2 - 48.*y + 32))./(-w).^3) .* (y>0.5);
-%! d2Fduv(2,:,:,:) = ((((4.*x.^2.*(60.*z.^2 - 60.*z.^4))/5 + (4.*x.^3.*(40.*z.^4 - 80.*z.^2 + 40))/5 + 16.*x.*z.^4).*y.^4 + ((4.*x.^2.*(18.*z.^3 - 18.*z.^5))/5 + (4.*x.^3.*(12.*z.^5 - 12.*z.^3 + 40.*z.^2 - 40))/5 + (4.*x.*(6.*z.^5 - 40.*z.^2 + 40))/5 + 16.*z.^2).*y.^3 + ((4.*x.*(60.*z.^2 - 60))/5 - 24.*z.^2).*y.^2 + ((4.*x.*(6.*z.^3 + 20))/5 - (12.*z.^3)/5).*y)./w.^3) .* (y<0.5) + ...
-%! ((z.^3.*(((432.*y.^3)/5 - (864.*y.^2)/5 + (528.*y)/5 - 96/5).*x.^3 + (- (648.*y.^3)/5 + (1296.*y.^2)/5 - (792.*y)/5 + 144/5).*x.^2 + ((72.*y)/5 - 48/5).*x - (36.*y)/5 + 24/5) - x.^3.*(192.*y.^4 - 496.*y.^3 + 480.*y.^2 - 208.*y + 32) + z.^4.*((- 192.*y.^4 + 208.*y.^3 + 96.*y.^2 - 144.*y + 32).*x.^3 + (288.*y.^4 - 312.*y.^3 - 144.*y.^2 + 216.*y - 48).*x.^2 + (- 96.*y.^4 + 104.*y.^3 + 48.*y.^2 - 72.*y + 16).*x) + x.*(- 96.*y.^3 + 96.*y.^2 + 8.*y - 16) + z.^2.*(x.^2.*(- 288.*y.^4 + 312.*y.^3 + 144.*y.^2 - 216.*y + 48) - 20.*y - x.^3.*(- 384.*y.^4 + 704.*y.^3 - 384.*y.^2 + 64.*y) + x.*(96.*y.^3 - 96.*y.^2 + 40.*y - 16) + 48.*y.^2 - 48.*y.^3 + 8) - z.^5.*(((432.*y.^3)/5 - (864.*y.^2)/5 + (528.*y)/5 - 96/5).*x.^3 + (- (648.*y.^3)/5 + (1296.*y.^2)/5 - (792.*y)/5 + 144/5).*x.^2 + ((216.*y.^3)/5 - (432.*y.^2)/5 + (264.*y)/5 - 48/5).*x))./(-w).^3) .* (y>0.5);
-%! d2Fduv(3,:,:,:) = (((x.^2.*(48.*z.^2 - 48.*z.^4) - x.^4.*(16.*z.^4 - 48.*z.^2 + 32) + x.^3.*(48.*z.^4 - 96.*z.^2 + 32) + 16.*x.*z.^4).*y.^4 + (x.^2.*(- 48.*z.^5 + 48.*z.^3 + 144.*z.^2 - 144) - x.^3.*(- 32.*z.^5 + 32.*z.^3 + 48.*z.^2 - 48) + x.*(16.*z.^5 - 144.*z.^2 + 96) + 48.*z.^2).*y.^3 + (x.*(96.*z.^2 - 48) + x.^3.*(48.*z.^2 - 48) - x.^2.*(120.*z.^2 - 96) - 24.*z.^2).*y.^2 + (x.*(16.*z.^3 - 24) - 8.*z.^3 + 24).*y + 8.*x - 8)./w.^3) .* (y<0.5) + ...
-%! ((8.*y - x.^4.*(96.*y.^4 - 320.*y.^3 + 384.*y.^2 - 192.*y + 32) + x.^3.*(96.*y.^4 - 368.*y.^3 + 528.*y.^2 - 336.*y + 80) + z.^3.*((288.*y.^3 - 576.*y.^2 + 352.*y - 64).*x.^3 + (- 432.*y.^3 + 864.*y.^2 - 528.*y + 96).*x.^2 + (48.*y - 32).*x - 24.*y + 16) - x.*(96.*y.^3 - 240.*y.^2 + 200.*y - 56) - z.^4.*((48.*y.^4 - 160.*y.^3 + 192.*y.^2 - 96.*y + 16).*x.^4 + (- 144.*y.^4 + 480.*y.^3 - 576.*y.^2 + 288.*y - 48).*x.^3 + (144.*y.^4 - 480.*y.^3 + 576.*y.^2 - 288.*y + 48).*x.^2 + (- 48.*y.^4 + 160.*y.^3 - 192.*y.^2 + 96.*y - 16).*x) + z.^2.*(x.^4.*(144.*y.^4 - 480.*y.^3 + 576.*y.^2 - 288.*y + 48) - 96.*y + x.^2.*(144.*y.^4 - 624.*y.^3 + 984.*y.^2 - 672.*y + 168) - x.^3.*(288.*y.^4 - 1008.*y.^3 + 1296.*y.^2 - 720.*y + 144) + x.*(144.*y.^3 - 384.*y.^2 + 336.*y - 96) + 120.*y.^2 - 48.*y.^3 + 24) - z.^5.*((288.*y.^3 - 576.*y.^2 + 352.*y - 64).*x.^3 + (- 432.*y.^3 + 864.*y.^2 - 528.*y + 96).*x.^2 + (144.*y.^3 - 288.*y.^2 + 176.*y - 32).*x) + x.^2.*(144.*y.^3 - 384.*y.^2 + 336.*y - 96) - 8)./(-w).^3) .* (y>0.5);
-%! d2Fduw = zeros ([3, size(x)]);
-%! d2Fduw(1,:,:,:) = ((x.^2.*((24.*y.^4.*z.^2)/5 + 2.*z.*(8.*y.^4 + 4.*y.^2)) - (12.*y.^2.*z.^2)/5 + (24.*x.*y.^2.*z.^2)/5)./w.^2 - (2.*(4.*x.*y.^2.*z - 4.*x.^2.*y.^2.*z).*(x.*((8.*y.^2.*z.^3)/5 + 8.*y.^2) - (4.*y.^2.*z.^3)/5 + x.^2.*(z.^2.*(8.*y.^4 + 4.*y.^2) + (8.*y.^4.*z.^3)/5 - 4.*y.^2) + 2))./w.^3) .* (y<0.5) + ...
-%! (-((- (4.*(3.*y - 1).*(y - 1).*(36.*y.^4 - 96.*y.^3 + 88.*y.^2 - 32.*y + 4).*x.^4)/5 + (4.*(3.*y - 1).*(y - 1).*(36.*y.^4 - 96.*y.^3 + 100.*y.^2 - 48.*y + 8).*x.^3)/5 - (4.*(3.*y - 1).*(y - 1).*(18.*y.^2 - 24.*y + 6).*x.^2)/5 + (4.*(3.*y - 1).*(y - 1).*(6.*y.^2 - 8.*y + 2).*x)/5).*z.^4 + ((4.*x.^3.*(3.*y - 1).*(y - 1).*(360.*y.^4 - 960.*y.^3 + 820.*y.^2 - 240.*y + 20))/5 - (4.*x.^4.*(3.*y - 1).*(y - 1).*(360.*y.^4 - 960.*y.^3 + 820.*y.^2 - 240.*y + 20))/5).*z.^3 + (- (4.*(3.*y - 1).*(y - 1).*(108.*y.^4 - 288.*y.^3 + 264.*y.^2 - 96.*y + 12).*x.^4)/5 + (4.*(3.*y - 1).*(y - 1).*(36.*y.^2 - 48.*y + 12).*x.^3)/5 - (24.*(3.*y - 1).*(y - 1).*x)/5 + (12.*(3.*y - 1).*(y - 1))/5).*z.^2 + (- (4.*(3.*y - 1).*(y - 1).*(360.*y.^4 - 960.*y.^3 + 940.*y.^2 - 400.*y + 60).*x.^4)/5 + (4.*(3.*y - 1).*(y - 1).*(360.*y.^2 - 480.*y + 120).*x.^3)/5 - (4.*(3.*y - 1).*(y - 1).*(180.*y.^2 - 240.*y + 90).*x.^2)/5 + 16.*(3.*y - 1).*(y - 1).*x).*z)./(-w).^3) .* (y>0.5);
-%! d2Fduw(2,:,:,:) = ((2.*z.*(8.*x.^2.*y.^4 - y.^2.*(8.*y - 4.*y.^2) + (2.*x.*y.^2.*(40.*y - 20.*y.^2))/5) + 3.*z.^2.*((12.*x.^2.*y.^4)/5 + (12.*x.*y.^2)/5 - (6.*y.^2)/5))./w.^2 - (2.*(4.*x.*y.^2.*z - 4.*x.^2.*y.^2.*z).*(z.^2.*(8.*x.^2.*y.^4 - y.^2.*(8.*y - 4.*y.^2) + (2.*x.*y.^2.*(40.*y - 20.*y.^2))/5) + z.^3.*((12.*x.^2.*y.^4)/5 + (12.*x.*y.^2)/5 - (6.*y.^2)/5) + (2.*x.*y.^2.*(20.*y.^2 - 40.*y + 20))/5))./w.^3) .* (y<0.5) + ...
-%! (((6.*(3.*y.^2 - 4.*y + 1).*(18.*x.^2.*y.^2 - 24.*x.^2.*y + 6.*x.^2 - 6.*x + 3).*z.^2)/5 + (4.*(3.*y.^2 - 4.*y + 1).*(60.*x.^2.*y.^2 - 80.*x.^2.*y + 20.*x.^2 - 20.*x.*y.^2 - 10.*x + 10.*y.^2 + 5).*z)/5)./w.^2 - (2.*((2.*(3.*y.^2 - 4.*y + 1).*(18.*x.^2.*y.^2 - 24.*x.^2.*y + 6.*x.^2 - 6.*x + 3).*z.^3)/5 + (2.*(3.*y.^2 - 4.*y + 1).*(60.*x.^2.*y.^2 - 80.*x.^2.*y + 20.*x.^2 - 20.*x.*y.^2 - 10.*x + 10.*y.^2 + 5).*z.^2)/5 - (2.*(10.*x - 20.*x.*y.^2).*(3.*y.^2 - 4.*y + 1))/5).*(- 12.*z.*x.^2.*y.^2 + 16.*z.*x.^2.*y - 4.*z.*x.^2 + 12.*z.*x.*y.^2 - 16.*z.*x.*y + 4.*z.*x))./(-w).^3) .* (y>0.5);
-%! d2Fduw(3,:,:,:) = (- (2.*z.*(4.*y.*(2.*y.^2 - 3.*y.^3).*x.^2 - 4.*y.*(4.*y.^2 - 6.*y.^3).*x + 4.*y.*(2.*y.^2 - 3.*y.^3)) - 3.*z.^2.*(8.*x.^2.*y.^4 + 8.*x.*y.^2 - 4.*y.^2))./w.^2 - (2.*(4.*x.*y.^2.*z - 4.*x.^2.*y.^2.*z).*(4.*y.*(3.*y - 2) + z.^3.*(8.*x.^2.*y.^4 + 8.*x.*y.^2 - 4.*y.^2) - z.^2.*(4.*y.*(2.*y.^2 - 3.*y.^3).*x.^2 - 4.*y.*(4.*y.^2 - 6.*y.^3).*x + 4.*y.*(2.*y.^2 - 3.*y.^3)) + 4.*x.^2.*y.*(4.*y.^2 - 6.*y.^3) - 4.*x.*y.*(- 6.*y.^3 + 4.*y.^2 + 3.*y - 2)))./w.^3) .* (y<0.5) + ...
-%! ((2.*z.*(4.*(y - 1).*(3.*y.^3 - 7.*y.^2 + 5.*y - 1).*x.^2 - 4.*(y - 1).*(6.*y.^3 - 14.*y.^2 + 10.*y - 2).*x + 4.*(y - 1).*(3.*y.^3 - 7.*y.^2 + 5.*y - 1)) + 3.*z.^2.*(4.*(y - 1).*(18.*y.^3 - 30.*y.^2 + 14.*y - 2).*x.^2 - 4.*(6.*y - 2).*(y - 1).*x + 4.*(3.*y - 1).*(y - 1)))./w.^2 - (2.*(z.^2.*(4.*(y - 1).*(3.*y.^3 - 7.*y.^2 + 5.*y - 1).*x.^2 - 4.*(y - 1).*(6.*y.^3 - 14.*y.^2 + 10.*y - 2).*x + 4.*(y - 1).*(3.*y.^3 - 7.*y.^2 + 5.*y - 1)) - 4.*(y - 1).^2 + z.^3.*(4.*(y - 1).*(18.*y.^3 - 30.*y.^2 + 14.*y - 2).*x.^2 - 4.*(6.*y - 2).*(y - 1).*x + 4.*(3.*y - 1).*(y - 1)) + 4.*x.*(y - 1).*(6.*y.^3 - 14.*y.^2 + 11.*y - 3) - 4.*x.^2.*(y - 1).*(6.*y.^3 - 14.*y.^2 + 10.*y - 2)).*(- 12.*z.*x.^2.*y.^2 + 16.*z.*x.^2.*y - 4.*z.*x.^2 + 12.*z.*x.*y.^2 - 16.*z.*x.*y + 4.*z.*x))./(-w).^3) .* (y>0.5);
-%! d2Fdvv = zeros ([3, size(x)]);
-%! d2Fdvv(1,:,:,:) = (-(8.*x.*(x - 1).*(z.^3 + 5.*x.*z.^2 - 5.*x).*(- 6.*x.^2.*y.^2.*z.^2 + 6.*x.^2.*y.^2 + 6.*x.*y.^2.*z.^2 - 1))/5./w.^3) .* (y<0.5) + ...
-%! ((8.*x.*(x - 1).*(z.^3 + 5.*x.*z.^2 - 5.*x).*(- 54.*x.^2.*y.^2.*z.^2 + 54.*x.^2.*y.^2 + 72.*x.^2.*y.*z.^2 - 72.*x.^2.*y - 26.*x.^2.*z.^2 + 26.*x.^2 + 54.*x.*y.^2.*z.^2 - 72.*x.*y.*z.^2 + 26.*x.*z.^2 + 3))/5./(-w).^3) .* (y>0.5);
-%! d2Fdvv(2,:,:,:) = ((2.*((8.*x.*z.^2 - x.^2.*(8.*z.^2 - 8)).*y.^2 + ((12.*x.*z.^3)/5 - x.^2.*((12.*z.^3)/5 + 8) + 4).*y - 4).*(- 4.*y.*x.^2.*z.^2 + 4.*y.*x.^2 + 4.*y.*x.*z.^2))./w.^3 - ((12.*x.*z.^3)/5 + 2.*y.*(8.*x.*z.^2 - x.^2.*(8.*z.^2 - 8)) - x.^2.*((12.*z.^3)/5 + 8) + 4)./w.^2) .* (y<0.5) + ...
-%! ((z.^2.*(x.*(32.*y + 4) - x.^2.*(32.*y + 4)) + x.^2.*(32.*y - 20) + z.^3.*((36.*x)/5 - (36.*x.^2)/5) + 4)./w.^2 - (2.*(4.*y + z.^3.*(x.*((36.*y)/5 - 24/5) - x.^2.*((36.*y)/5 - 24/5)) + z.^2.*(x.*(16.*y.^2 + 4.*y - 8) - x.^2.*(16.*y.^2 + 4.*y - 8)) + x.^2.*(16.*y.^2 - 20.*y + 8)).*(8.*x.^2.*z.^2 + 12.*x.^2.*y - 8.*x.*z.^2 - 8.*x.^2 + 12.*x.*y.*z.^2 - 12.*x.^2.*y.*z.^2))./(-w).^3) .* (y>0.5);
-%! d2Fdvv(3,:,:,:) = ((2.*y.*(4.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x).*z.^2 + 4.*(2.*x.^2 - 2.*x.^3).*(x - 1)) - 4.*(3.*x - 3).*(x - 1) + 8.*x.*z.^3.*(x - 1))./w.^2 - (2.*(4.*(x - 1).^2 - y.*(4.*(3.*x - 3).*(x - 1) - 8.*x.*z.^3.*(x - 1)) + y.^2.*(4.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x).*z.^2 + 4.*(2.*x.^2 - 2.*x.^3).*(x - 1))).*(- 4.*y.*x.^2.*z.^2 + 4.*y.*x.^2 + 4.*y.*x.*z.^2))./w.^3) .* (y<0.5) + ...
-%! ((4.*(x - 1).*(4.*x.^3 - 4.*x.^2 + x - 1) + 2.*y.*(4.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x).*z.^2 + 4.*(2.*x.^2 - 2.*x.^3).*(x - 1)) - 24.*x.*z.^3.*(x - 1) - 4.*z.^2.*(x - 1).*(4.*x.^3 - 8.*x.^2 + 4.*x))./w.^2 - (2.*(y.^2.*(4.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x).*z.^2 + 4.*(2.*x.^2 - 2.*x.^3).*(x - 1)) - 4.*(x - 1).*(2.*x.^3 - 2.*x.^2 + x - 1) - y.*(24.*x.*(x - 1).*z.^3 + 4.*(x - 1).*(4.*x.^3 - 8.*x.^2 + 4.*x).*z.^2 - 4.*(x - 1).*(4.*x.^3 - 4.*x.^2 + x - 1)) + 16.*x.*z.^3.*(x - 1) + 4.*z.^2.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x)).*(8.*x.^2.*z.^2 + 12.*x.^2.*y - 8.*x.*z.^2 - 8.*x.^2 + 12.*x.*y.*z.^2 - 12.*x.^2.*y.*z.^2))./(-w).^3) .* (y>0.5);
-%! d2Fdvw = zeros ([3, size(x)]);
-%! d2Fdvw(1,:,:,:) = (((8.*x.*z.*(x - 1).*(20.*x.^3.*z.^2 - 20.*x.^3 + 2.*x.^2.*z.^3 - 20.*x.^2.*z.^2 + 6.*x.^2.*z + 40.*x.^2 - 2.*x.*z.^3).*y.^3)/5 + (8.*x.*z.*(10.*x + 3.*z).*(x - 1).*y)/5)./w.^3) .* (y<0.5) + ...
-%! (((8.*x.*(3.*y - 2).*(x - 1).*(- 6.*x.^2.*y.^2 + 8.*x.^2.*y - 2.*x.^2 + 6.*x.*y.^2 - 8.*x.*y + 2.*x).*z.^4)/5 + (8.*x.*(3.*y - 2).*(x - 1).*(- 60.*x.^3.*y.^2 + 80.*x.^3.*y - 20.*x.^3 + 60.*x.^2.*y.^2 - 80.*x.^2.*y + 20.*x.^2).*z.^3)/5 - (8.*x.*(3.*y - 2).*(x - 1).*(18.*x.^2.*y.^2 - 24.*x.^2.*y + 6.*x.^2 - 3).*z.^2)/5 + (8.*x.*(3.*y - 2).*(x - 1).*(60.*x.^3.*y.^2 - 80.*x.^3.*y + 20.*x.^3 - 120.*x.^2.*y.^2 + 160.*x.^2.*y - 40.*x.^2 + 10.*x).*z)/5)./(-w).^3) .* (y>0.5);
-%! d2Fdvw(2,:,:,:) = ((4.*x.*y.*z.*(x - 1).*(40.*x.^2.*y.^3.*z.^2 - 40.*x.^2.*y.^3 + 6.*x.^2.*y.^2.*z.^3 + 18.*x.^2.*y.^2.*z + 80.*x.^2.*y.^2 - 40.*x.*y.^3.*z.^2 - 6.*x.*y.^2.*z.^3 - 40.*y.^2 + 60.*y + 9.*z))/5./w.^3) .* (y<0.5) + ...
-%! (-((4.*x.*(x - 1).*(54.*x.^2.*y.^3 - 108.*x.^2.*y.^2 + 66.*x.^2.*y - 12.*x.^2 - 54.*x.*y.^3 + 108.*x.*y.^2 - 66.*x.*y + 12.*x).*z.^4)/5 + (4.*x.*(x - 1).*(240.*x.^2.*y.^4 - 260.*x.^2.*y.^3 - 120.*x.^2.*y.^2 + 180.*x.^2.*y - 40.*x.^2 - 240.*x.*y.^4 + 260.*x.*y.^3 + 120.*x.*y.^2 - 180.*x.*y + 40.*x).*z.^3)/5 - (4.*x.*(x - 1).*(- 162.*x.^2.*y.^3 + 324.*x.^2.*y.^2 - 198.*x.^2.*y + 36.*x.^2 + 27.*y - 18).*z.^2)/5 - (4.*x.*(x - 1).*(240.*x.^2.*y.^4 - 980.*x.^2.*y.^3 + 1320.*x.^2.*y.^2 - 700.*x.^2.*y + 120.*x.^2 + 120.*y.^3 - 120.*y.^2 + 50.*y - 20).*z)/5)./(-w).^3) .* (y>0.5);
-%! d2Fdvw(3,:,:,:) = (-(y.^3.*(8.*x.*z.*(x - 1).*(12.*x.^2 - 24.*x + 12) - 48.*x.^3.*z.^2.*(x - 1) + 8.*x.*z.^4.*(2.*x - 2.*x.^2).*(x - 1)) + y.^4.*(8.*x.*(x - 1).*(- 4.*x.^4 + 12.*x.^3 - 12.*x.^2 + 4.*x).*z.^3 + 8.*x.*(x - 1).*(4.*x.^4 - 8.*x.^3 + 4.*x.^2).*z) - 24.*x.*y.*z.^2.*(x - 1) - 8.*x.*y.^2.*z.*(x - 1).*(6.*x.^2 - 12.*x + 6))./w.^3) .* (y<0.5) + ...
-%! ((8.*z.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x) - y.*(72.*x.*(x - 1).*z.^2 + 8.*(x - 1).*(4.*x.^3 - 8.*x.^2 + 4.*x).*z) + 48.*x.*z.^2.*(x - 1) + 8.*y.^2.*z.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x))./w.^2 - (2.*(y.^2.*(4.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x).*z.^2 + 4.*(2.*x.^2 - 2.*x.^3).*(x - 1)) - 4.*(x - 1).*(2.*x.^3 - 2.*x.^2 + x - 1) - y.*(24.*x.*(x - 1).*z.^3 + 4.*(x - 1).*(4.*x.^3 - 8.*x.^2 + 4.*x).*z.^2 - 4.*(x - 1).*(4.*x.^3 - 4.*x.^2 + x - 1)) + 16.*x.*z.^3.*(x - 1) + 4.*z.^2.*(x - 1).*(2.*x.^3 - 4.*x.^2 + 2.*x)).*(- 12.*z.*x.^2.*y.^2 + 16.*z.*x.^2.*y - 4.*z.*x.^2 + 12.*z.*x.*y.^2 - 16.*z.*x.*y + 4.*z.*x))./(-w).^3) .* (y>0.5);
-%! d2Fdww = zeros ([3, size(x)]);
-%! d2Fdww(1,:,:,:) = ((32.*x.*y.^2.*(2.*x.^2.*y.^2 + 1).*(x - 1).*(5.*x + z + 10.*x.^2.*y.^2 + 2.*x.^2.*y.^2.*z))./(5.*w.^3) - (8.*x.*y.^2.*(x - 1).*(15.*x + z + 30.*x.^2.*y.^2 + 2.*x.^2.*y.^2.*z))/5./w.^2) .* (y<0.5) + ...
-%! (((8.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(36.*x.^4.*y.^4 - 96.*x.^4.*y.^3 + 88.*x.^4.*y.^2 - 32.*x.^4.*y + 4.*x.^4 - 36.*x.^3.*y.^4 + 96.*x.^3.*y.^3 - 88.*x.^3.*y.^2 + 32.*x.^3.*y - 4.*x.^3 - 6.*x.^2.*y.^2 + 8.*x.^2.*y - 2.*x.^2 + 6.*x.*y.^2 - 8.*x.*y + 2.*x).*z.^3)/5 + (8.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(540.*x.^4.*y.^4 - 1440.*x.^4.*y.^3 + 1320.*x.^4.*y.^2 - 480.*x.^4.*y + 60.*x.^4 - 540.*x.^3.*y.^4 + 1440.*x.^3.*y.^3 - 1410.*x.^3.*y.^2 + 600.*x.^3.*y - 90.*x.^3 + 90.*x.^2.*y.^2 - 120.*x.^2.*y + 30.*x.^2).*z.^2)/5 + (8.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(108.*x.^4.*y.^4 - 288.*x.^4.*y.^3 + 264.*x.^4.*y.^2 - 96.*x.^4.*y + 12.*x.^4 - 36.*x.^2.*y.^2 + 48.*x.^2.*y - 12.*x.^2 + 3).*z)/5 + (8.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(180.*x.^4.*y.^4 - 480.*x.^4.*y.^3 + 440.*x.^4.*y.^2 - 160.*x.^4.*y + 20.*x.^4 - 30.*x.^3.*y.^2 + 40.*x.^3.*y - 10.*x.^3 - 30.*x.^2.*y.^2 + 40.*x.^2.*y - 10.*x.^2 + 5.*x))/5)./(-w).^3) .* (y>0.5);
-%! d2Fdww(2,:,:,:) = ((16.*x.*y.^2.*(2.*x.^2.*y.^2 + 1).*(x - 1).*(20.*y + 3.*z + 20.*x.^2.*y.^2 - 10.*y.^2 + 6.*x.^2.*y.^2.*z))./(5.*w.^3) - (12.*x.*y.^2.*(x - 1).*(20.*y + z + 20.*x.^2.*y.^2 - 10.*y.^2 + 2.*x.^2.*y.^2.*z))/5./w.^2) .* (y<0.5) + ...
-%! (((4.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(108.*x.^4.*y.^4 - 288.*x.^4.*y.^3 + 264.*x.^4.*y.^2 - 96.*x.^4.*y + 12.*x.^4 - 108.*x.^3.*y.^4 + 288.*x.^3.*y.^3 - 264.*x.^3.*y.^2 + 96.*x.^3.*y - 12.*x.^3 - 18.*x.^2.*y.^2 + 24.*x.^2.*y - 6.*x.^2 + 18.*x.*y.^2 - 24.*x.*y + 6.*x).*z.^3)/5 + (4.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(1080.*x.^4.*y.^4 - 2880.*x.^4.*y.^3 + 2640.*x.^4.*y.^2 - 960.*x.^4.*y + 120.*x.^4 - 1080.*x.^3.*y.^4 + 2880.*x.^3.*y.^3 - 2640.*x.^3.*y.^2 + 960.*x.^3.*y - 120.*x.^3 - 180.*x.^2.*y.^4 + 240.*x.^2.*y.^3 - 150.*x.^2.*y.^2 + 120.*x.^2.*y - 30.*x.^2 + 180.*x.*y.^4 - 240.*x.*y.^3 + 150.*x.*y.^2 - 120.*x.*y + 30.*x).*z.^2)/5 + (4.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(324.*x.^4.*y.^4 - 864.*x.^4.*y.^3 + 792.*x.^4.*y.^2 - 288.*x.^4.*y + 36.*x.^4 - 108.*x.^2.*y.^2 + 144.*x.^2.*y - 36.*x.^2 + 9).*z)/5 + (4.*x.*(3.*y - 1).*(x - 1).*(y - 1).*(360.*x.^4.*y.^4 - 960.*x.^4.*y.^3 + 880.*x.^4.*y.^2 - 320.*x.^4.*y + 40.*x.^4 - 60.*x.^2.*y.^4 + 80.*x.^2.*y.^3 - 110.*x.^2.*y.^2 + 120.*x.^2.*y - 30.*x.^2 + 10.*y.^2 + 5))/5)./(-w).^3) .* (y>0.5);
-%! d2Fdww(3,:,:,:) = ((32.*x.*y.^2.*(2.*x.^2.*y.^2 + 1).*(x - 1).*(2.*y + z - 3.*x.^2.*y.^2 - 4.*x.*y + 6.*x.*y.^2 + 2.*x.^2.*y - 3.*y.^2 + 2.*x.^2.*y.^2.*z))./w.^3 - (8.*x.*y.^2.*(x - 1).*(6.*y + z - 9.*x.^2.*y.^2 - 12.*x.*y + 18.*x.*y.^2 + 6.*x.^2.*y - 9.*y.^2 + 2.*x.^2.*y.^2.*z))./w.^2) .* (y<0.5) + ...
-%! ((2.*(- 6.*x.^2.*y.^2 + 8.*x.^2.*y - 2.*x.^2 + 6.*x.*y.^2 - 8.*x.*y + 2.*x).*(2.*z - 4.*y - 4.*x + 2.*x.^2.*y.^2 + 8.*x.*y - 4.*x.*y.^2 - 4.*x.^2.*y - 4.*x.^2.*z + 2.*x.^2 + 2.*y.^2 + 16.*x.^2.*y.*z - 12.*x.^2.*y.^2.*z + 2))./w.^2 - (8.*z.^2.*(- 6.*x.^2.*y.^2 + 8.*x.^2.*y - 2.*x.^2 + 6.*x.*y.^2 - 8.*x.*y + 2.*x).^2.*(2.*z - 4.*y - 4.*x + 2.*x.^2.*y.^2 + 8.*x.*y - 4.*x.*y.^2 - 4.*x.^2.*y - 4.*x.^2.*z + 2.*x.^2 + 2.*y.^2 + 16.*x.^2.*y.*z - 12.*x.^2.*y.^2.*z + 2))./(-w).^3 - (4.*z.*(12.*x.^2.*y.^2 - 16.*x.^2.*y + 4.*x.^2 - 2).*(- 6.*x.^2.*y.^2 + 8.*x.^2.*y - 2.*x.^2 + 6.*x.*y.^2 - 8.*x.*y + 2.*x))./w.^2) .* (y>0.5);
-%! assert (F, pnt, 1e3*eps)
-%! assert (dFdu, jac{1}, 1e3*eps)
-%! assert (dFdv, jac{2}, 1e3*eps)
-%! assert (dFdw, jac{3}, 1e3*eps)
-%! assert (d2Fduu, hess{1,1}, 1e3*eps)
-%! assert (d2Fduv, hess{1,2}, 1e3*eps)
-%! assert (d2Fduw, hess{1,3}, 1e3*eps)
-%! assert (d2Fduv, hess{2,1}, 1e3*eps)
-%! assert (d2Fdvv, hess{2,2}, 1e3*eps)
-%! assert (d2Fdvw, hess{2,3}, 1e3*eps)
-%! assert (d2Fduw, hess{3,1}, 1e3*eps)
-%! assert (d2Fdvw, hess{3,2}, 1e3*eps)
-%! assert (d2Fdww, hess{3,3}, 1e3*eps)
-
-
-
-%!test
-%! nrb = nrbextrude (nrb4surf ([0 0], [1 0], [0 1], [1 1]), [0 0 1]);
-%! nrb = nrbdegelev (nrb, [1 1 1]);
-%! nrb.coefs (4,2,2,2) = 1.1;
-%! [dnrb, dnrb2] = nrbderiv (nrb);
-%! X = linspace (0, 1, 24); Y = linspace (0, 1, 24); Z = linspace (0, 1, 24);
-%! [pnt, jac, hess] = nrbdeval (nrb, dnrb, dnrb2, {X Y Z});
-%! [y, x, z] = meshgrid (X, Y, Z);
-%! F = zeros ([3, size(x)]);
-%! F(1,:,:,:) = (5.*x)./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5);
-%! F(2,:,:,:) = (5.*y)./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5);
-%! F(3,:,:,:) = (5.*z)./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5);
-%! dFdu = zeros ([3, size(x)]);
-%! dFdu(1,:,:,:) = ((z.*(20.*y - 20.*y.^2) - z.^2.*(20.*y - 20.*y.^2)).*x.^2 + 25)./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^2;
-%! dFdu(2,:,:,:) = (y.^2.*(5.*z.*(8.*x - 4) - 5.*z.^2.*(8.*x - 4)) - y.^3.*(5.*z.*(8.*x - 4) - 5.*z.^2.*(8.*x - 4)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdu(3,:,:,:) = (z.^2.*(5.*y.*(8.*x - 4) - 5.*y.^2.*(8.*x - 4)) - z.^3.*(5.*y.*(8.*x - 4) - 5.*y.^2.*(8.*x - 4)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdv = zeros ([3, size(x)]);
-%! dFdv(1,:,:,:) = (x.^2.*(5.*z.*(8.*y - 4) - 5.*z.^2.*(8.*y - 4)) - x.^3.*(5.*z.*(8.*y - 4) - 5.*z.^2.*(8.*y - 4)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdv(2,:,:,:) = ((z.*(20.*x - 20.*x.^2) - z.^2.*(20.*x - 20.*x.^2)).*y.^2 + 25)./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^2;
-%! dFdv(3,:,:,:) = (z.^2.*(5.*x.*(8.*y - 4) - 5.*x.^2.*(8.*y - 4)) - z.^3.*(5.*x.*(8.*y - 4) - 5.*x.^2.*(8.*y - 4)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdw = zeros ([3, size(x)]);
-%! dFdw(1,:,:,:) = (x.^2.*(y.*(40.*z - 20) - y.^2.*(40.*z - 20)) - x.^3.*(y.*(40.*z - 20) - y.^2.*(40.*z - 20)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdw(2,:,:,:) = (y.^2.*(x.*(40.*z - 20) - x.^2.*(40.*z - 20)) - y.^3.*(x.*(40.*z - 20) - x.^2.*(40.*z - 20)))./((- 4.*x.^2.*y.^2 + 4.*x.^2.*y + 4.*x.*y.^2 - 4.*x.*y).*z.^2 + (4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y).*z + 5).^2;
-%! dFdw(3,:,:,:) = ((y.*(20.*x - 20.*x.^2) - y.^2.*(20.*x - 20.*x.^2)).*z.^2 + 25)./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^2;
-%! d2Fduu = zeros ([3, size(x)]);
-%! d2Fduu(1,:,:,:) = (40.*y.*z.*(y - 1).*(z - 1).*(4.*x.^3.*y.^2.*z.^2 - 4.*x.^3.*y.^2.*z - 4.*x.^3.*y.*z.^2 + 4.*x.^3.*y.*z + 15.*x - 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduu(2,:,:,:) = (40.*y.^2.*z.*(y - 1).*(z - 1).*(4.*y.^2.*z.^2 - 4.*y.^2.*z - 4.*y.*z.^2 + 4.*y.*z + 5) - 40.*x.*y.^2.*z.*(y - 1).*(z - 1).*(12.*y.^2.*z.^2 - 12.*y.^2.*z - 12.*y.*z.^2 + 12.*y.*z) + 40.*x.^2.*y.^2.*z.*(y - 1).*(z - 1).*(12.*y.^2.*z.^2 - 12.*y.^2.*z - 12.*y.*z.^2 + 12.*y.*z))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduu(3,:,:,:) = (40.*y.*z.^2.*(y - 1).*(z - 1).*(4.*y.^2.*z.^2 - 4.*y.^2.*z - 4.*y.*z.^2 + 4.*y.*z + 5) - 40.*x.*y.*z.^2.*(y - 1).*(z - 1).*(12.*y.^2.*z.^2 - 12.*y.^2.*z - 12.*y.*z.^2 + 12.*y.*z) + 40.*x.^2.*y.*z.^2.*(y - 1).*(z - 1).*(12.*y.^2.*z.^2 - 12.*y.^2.*z - 12.*y.*z.^2 + 12.*y.*z))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduv = zeros ([3, size(x)]);
-%! d2Fduv(1,:,:,:) = (20.*x.*z.*(2.*y - 1).*(z - 1).*(4.*x.^3.*y.^2.*z.^2 - 4.*x.^3.*y.^2.*z - 4.*x.^3.*y.*z.^2 + 4.*x.^3.*y.*z - 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 15.*x - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduv(2,:,:,:) = (20.*y.*z.*(2.*x - 1).*(z - 1).*(4.*x.^2.*y.^3.*z.^2 - 4.*x.^2.*y.^3.*z - 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z - 4.*x.*y.^3.*z.^2 + 4.*x.*y.^3.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z + 15.*y - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduv(3,:,:,:) = (20.*z.^2.*(2.*x - 1).*(2.*y - 1).*(z - 1).*(4.*x.^2.*y.^2.*z.^2 - 4.*x.^2.*y.^2.*z - 4.*x.^2.*y.*z.^2 + 4.*x.^2.*y.*z - 4.*x.*y.^2.*z.^2 + 4.*x.*y.^2.*z + 4.*x.*y.*z.^2 - 4.*x.*y.*z + 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduw = zeros ([3, size(x)]);
-%! d2Fduw(1,:,:,:) = (20.*x.*y.*(2.*z - 1).*(y - 1).*(4.*x.^3.*y.^2.*z.^2 - 4.*x.^3.*y.^2.*z - 4.*x.^3.*y.*z.^2 + 4.*x.^3.*y.*z - 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 15.*x - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduw(2,:,:,:) = (20.*y.^2.*(2.*x - 1).*(2.*z - 1).*(y - 1).*(4.*x.^2.*y.^2.*z.^2 - 4.*x.^2.*y.^2.*z - 4.*x.^2.*y.*z.^2 + 4.*x.^2.*y.*z - 4.*x.*y.^2.*z.^2 + 4.*x.*y.^2.*z + 4.*x.*y.*z.^2 - 4.*x.*y.*z + 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fduw(3,:,:,:) = (20.*y.*z.*(2.*x - 1).*(y - 1).*(4.*x.^2.*y.^2.*z.^3 - 4.*x.^2.*y.^2.*z.^2 - 4.*x.^2.*y.*z.^3 + 4.*x.^2.*y.*z.^2 - 4.*x.*y.^2.*z.^3 + 4.*x.*y.^2.*z.^2 + 4.*x.*y.*z.^3 - 4.*x.*y.*z.^2 + 15.*z - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvv = zeros ([3, size(x)]);
-%! d2Fdvv(1,:,:,:) = (40.*x.^2.*z.*(x - 1).*(z - 1).*(4.*x.^2.*z.^2 - 4.*x.^2.*z - 4.*x.*z.^2 + 4.*x.*z + 5) + 40.*x.^2.*y.^2.*z.*(x - 1).*(z - 1).*(12.*x.^2.*z.^2 - 12.*x.^2.*z - 12.*x.*z.^2 + 12.*x.*z) - 40.*x.^2.*y.*z.*(x - 1).*(z - 1).*(12.*x.^2.*z.^2 - 12.*x.^2.*z - 12.*x.*z.^2 + 12.*x.*z))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvv(2,:,:,:) = (40.*x.*z.*(x - 1).*(z - 1).*(4.*x.^2.*y.^3.*z.^2 - 4.*x.^2.*y.^3.*z - 4.*x.*y.^3.*z.^2 + 4.*x.*y.^3.*z + 15.*y - 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvv(3,:,:,:) = (40.*x.*z.^2.*(x - 1).*(z - 1).*(4.*x.^2.*z.^2 - 4.*x.^2.*z - 4.*x.*z.^2 + 4.*x.*z + 5) + 40.*x.*y.^2.*z.^2.*(x - 1).*(z - 1).*(12.*x.^2.*z.^2 - 12.*x.^2.*z - 12.*x.*z.^2 + 12.*x.*z) - 40.*x.*y.*z.^2.*(x - 1).*(z - 1).*(12.*x.^2.*z.^2 - 12.*x.^2.*z - 12.*x.*z.^2 + 12.*x.*z))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvw = zeros ([3, size(x)]);
-%! d2Fdvw(1,:,:,:) = (20.*x.^2.*(2.*y - 1).*(2.*z - 1).*(x - 1).*(4.*x.^2.*y.^2.*z.^2 - 4.*x.^2.*y.^2.*z - 4.*x.^2.*y.*z.^2 + 4.*x.^2.*y.*z - 4.*x.*y.^2.*z.^2 + 4.*x.*y.^2.*z + 4.*x.*y.*z.^2 - 4.*x.*y.*z + 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvw(2,:,:,:) = (20.*x.*y.*(2.*z - 1).*(x - 1).*(4.*x.^2.*y.^3.*z.^2 - 4.*x.^2.*y.^3.*z - 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z - 4.*x.*y.^3.*z.^2 + 4.*x.*y.^3.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z + 15.*y - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdvw(3,:,:,:) = (20.*x.*z.*(2.*y - 1).*(x - 1).*(4.*x.^2.*y.^2.*z.^3 - 4.*x.^2.*y.^2.*z.^2 - 4.*x.^2.*y.*z.^3 + 4.*x.^2.*y.*z.^2 - 4.*x.*y.^2.*z.^3 + 4.*x.*y.^2.*z.^2 + 4.*x.*y.*z.^3 - 4.*x.*y.*z.^2 + 15.*z - 10))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdww = zeros ([3, size(x)]);
-%! d2Fdww(1,:,:,:) = (40.*x.^2.*y.*(x - 1).*(y - 1).*(4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y + 5) + 40.*x.^2.*y.*z.^2.*(x - 1).*(y - 1).*(12.*x.^2.*y.^2 - 12.*x.^2.*y - 12.*x.*y.^2 + 12.*x.*y) - 40.*x.^2.*y.*z.*(x - 1).*(y - 1).*(12.*x.^2.*y.^2 - 12.*x.^2.*y - 12.*x.*y.^2 + 12.*x.*y))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdww(2,:,:,:) = (40.*x.*y.^2.*(x - 1).*(y - 1).*(4.*x.^2.*y.^2 - 4.*x.^2.*y - 4.*x.*y.^2 + 4.*x.*y + 5) + 40.*x.*y.^2.*z.^2.*(x - 1).*(y - 1).*(12.*x.^2.*y.^2 - 12.*x.^2.*y - 12.*x.*y.^2 + 12.*x.*y) - 40.*x.*y.^2.*z.*(x - 1).*(y - 1).*(12.*x.^2.*y.^2 - 12.*x.^2.*y - 12.*x.*y.^2 + 12.*x.*y))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
-%! d2Fdww(3,:,:,:) = (40.*x.*y.*(x - 1).*(y - 1).*(4.*x.^2.*y.^2.*z.^3 - 4.*x.^2.*y.*z.^3 - 4.*x.*y.^2.*z.^3 + 4.*x.*y.*z.^3 + 15.*z - 5))./(- 4.*x.^2.*y.^2.*z.^2 + 4.*x.^2.*y.^2.*z + 4.*x.^2.*y.*z.^2 - 4.*x.^2.*y.*z + 4.*x.*y.^2.*z.^2 - 4.*x.*y.^2.*z - 4.*x.*y.*z.^2 + 4.*x.*y.*z + 5).^3;
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbdeval.m
--- a/extra/nurbs/inst/nrbdeval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,278 +0,0 @@
-function varargout = nrbdeval (nurbs, dnurbs, varargin)
-
-% NRBDEVAL: Evaluation of the derivative and second derivatives of NURBS curve, surface or volume.
-%
-% [pnt, jac] = nrbdeval (crv, dcrv, tt)
-% [pnt, jac] = nrbdeval (srf, dsrf, {tu tv})
-% [pnt, jac] = nrbdeval (vol, dvol, {tu tv tw})
-% [pnt, jac, hess] = nrbdeval (crv, dcrv, dcrv2, tt)
-% [pnt, jac, hess] = nrbdeval (srf, dsrf, dsrf2, {tu tv})
-% [pnt, jac, hess] = nrbdeval (vol, dvol, {tu tv tw})
-%
-% INPUTS:
-%
-% crv, srf, vol - original NURBS curve, surface or volume.
-% dcrv, dsrf, dvol - NURBS derivative representation of crv, srf
-% or vol (see nrbderiv2)
-% dcrv2, dsrf2, dvol2 - NURBS second derivative representation of crv,
-% srf or vol (see nrbderiv2)
-% tt - parametric evaluation points
-% If the nurbs is a surface or a volume then tt is a cell
-% {tu, tv} or {tu, tv, tw} are the parametric coordinates
-%
-% OUTPUT:
-%
-% pnt - evaluated points.
-% jac - evaluated first derivatives (Jacobian).
-% hess - evaluated second derivatives (Hessian).
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Carlo de Falco
-% Copyright (C) 2010, 2011 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin == 3)
- tt = varargin{1};
-elseif (nargin == 4)
- dnurbs2 = varargin{1};
- tt = varargin{2};
-else
- error ('nrbrdeval: wrong number of input parameters')
-end
-
-if (~isstruct(nurbs))
- error('NURBS representation is not structure!');
-end
-
-if (~strcmp(nurbs.form,'B-NURBS'))
- error('Not a recognised NURBS representation');
-end
-
-[cp,cw] = nrbeval(nurbs, tt);
-
-if (iscell(nurbs.knots))
- if (size(nurbs.knots,2) == 3)
- % NURBS structure represents a volume
- temp = cw(ones(3,1),:,:,:);
- pnt = cp./temp;
-
- [cup,cuw] = nrbeval (dnurbs{1}, tt);
- tempu = cuw(ones(3,1),:,:,:);
- jac{1} = (cup-tempu.*pnt)./temp;
-
- [cvp,cvw] = nrbeval (dnurbs{2}, tt);
- tempv = cvw(ones(3,1),:,:,:);
- jac{2} = (cvp-tempv.*pnt)./temp;
-
- [cwp,cww] = nrbeval (dnurbs{3}, tt);
- tempw = cww(ones(3,1),:,:,:);
- jac{3} = (cwp-tempw.*pnt)./temp;
-
-% second derivatives
- if (nargout == 3)
- if (exist ('dnurbs2'))
- [cuup, cuuw] = nrbeval (dnurbs2{1,1}, tt);
- tempuu = cuuw(ones(3,1),:,:,:);
- hess{1,1} = (cuup - (2*cup.*tempu + cp.*tempuu)./temp + 2*cp.*tempu.^2./temp.^2)./temp;
- clear cuup cuuw tempuu
-
- [cvvp, cvvw] = nrbeval (dnurbs2{2,2}, tt);
- tempvv = cvvw(ones(3,1),:,:,:);
- hess{2,2} = (cvvp - (2*cvp.*tempv + cp.*tempvv)./temp + 2*cp.*tempv.^2./temp.^2)./temp;
- clear cvvp cvvw tempvv
-
- [cwwp, cwww] = nrbeval (dnurbs2{3,3}, tt);
- tempww = cwww(ones(3,1),:,:,:);
- hess{3,3} = (cwwp - (2*cwp.*tempw + cp.*tempww)./temp + 2*cp.*tempw.^2./temp.^2)./temp;
- clear cwwp cwww tempww
-
- [cuvp, cuvw] = nrbeval (dnurbs2{1,2}, tt);
- tempuv = cuvw(ones(3,1),:,:,:);
- hess{1,2} = (cuvp - (cup.*tempv + cvp.*tempu + cp.*tempuv)./temp + 2*cp.*tempu.*tempv./temp.^2)./temp;
- hess{2,1} = hess{1,2};
- clear cuvp cuvw tempuv
-
- [cuwp, cuww] = nrbeval (dnurbs2{1,3}, tt);
- tempuw = cuww(ones(3,1),:,:,:);
- hess{1,3} = (cuwp - (cup.*tempw + cwp.*tempu + cp.*tempuw)./temp + 2*cp.*tempu.*tempw./temp.^2)./temp;
- hess{3,1} = hess{1,3};
- clear cuwp cuww tempuw
-
- [cvwp, cvww] = nrbeval (dnurbs2{2,3}, tt);
- tempvw = cvww(ones(3,1),:,:,:);
- hess{2,3} = (cvwp - (cvp.*tempw + cwp.*tempv + cp.*tempvw)./temp + 2*cp.*tempv.*tempw./temp.^2)./temp;
- hess{3,2} = hess{2,3};
- clear cvwp cvww tempvw
- else
- warning ('nrbdeval: dnurbs2 missing. The second derivative is not computed');
- hess = [];
- end
- end
-
- elseif (size(nurbs.knots,2) == 2)
- % NURBS structure represents a surface
- temp = cw(ones(3,1),:,:);
- pnt = cp./temp;
-
- [cup,cuw] = nrbeval (dnurbs{1}, tt);
- tempu = cuw(ones(3,1),:,:);
- jac{1} = (cup-tempu.*pnt)./temp;
-
- [cvp,cvw] = nrbeval (dnurbs{2}, tt);
- tempv = cvw(ones(3,1),:,:);
- jac{2} = (cvp-tempv.*pnt)./temp;
-
-% second derivatives
- if (nargout == 3)
- if (exist ('dnurbs2'))
- [cuup, cuuw] = nrbeval (dnurbs2{1,1}, tt);
- tempuu = cuuw(ones(3,1),:,:);
- hess{1,1} = (cuup - (2*cup.*tempu + cp.*tempuu)./temp + 2*cp.*tempu.^2./temp.^2)./temp;
-
- [cvvp, cvvw] = nrbeval (dnurbs2{2,2}, tt);
- tempvv = cvvw(ones(3,1),:,:);
- hess{2,2} = (cvvp - (2*cvp.*tempv + cp.*tempvv)./temp + 2*cp.*tempv.^2./temp.^2)./temp;
-
- [cuvp, cuvw] = nrbeval (dnurbs2{1,2}, tt);
- tempuv = cuvw(ones(3,1),:,:);
- hess{1,2} = (cuvp - (cup.*tempv + cvp.*tempu + cp.*tempuv)./temp + 2*cp.*tempu.*tempv./temp.^2)./temp;
- hess{2,1} = hess{1,2};
- else
- warning ('nrbdeval: dnurbs2 missing. The second derivative is not computed');
- hess = [];
- end
- end
-
- end
-else
-
- % NURBS is a curve
- temp = cw(ones(3,1),:);
- pnt = cp./temp;
-
- % first derivative
- [cup,cuw] = nrbeval (dnurbs,tt);
- temp1 = cuw(ones(3,1),:);
- jac = (cup-temp1.*pnt)./temp;
- if (iscell (tt))
- jac = {jac};
- end
-
- % second derivative
- if (nargout == 3 && exist ('dnurbs2'))
- [cuup,cuuw] = nrbeval (dnurbs2, tt);
- temp2 = cuuw(ones(3,1),:);
- hess = (cuup - (2*cup.*temp1 + cp.*temp2)./temp + 2*cp.*temp1.^2./temp.^2)./temp;
- if (iscell (tt))
- hess = {hess};
- end
- end
-
-end
-
-varargout{1} = pnt;
-varargout{2} = jac;
-if (nargout == 3)
- varargout{3} = hess;
-end
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! nrbplot(crv,48);
-%! title('First derivatives along a test curve.');
-%!
-%! tt = linspace(0.0,1.0,9);
-%!
-%! dcrv = nrbderiv(crv);
-%!
-%! [p1, dp] = nrbdeval(crv,dcrv,tt);
-%!
-%! p2 = vecnorm(dp);
-%!
-%! hold on;
-%! plot(p1(1,:),p1(2,:),'ro');
-%! h = quiver(p1(1,:),p1(2,:),p2(1,:),p2(2,:),0);
-%! set(h,'Color','black');
-%! hold off;
-
-%!demo
-%! srf = nrbtestsrf;
-%! p = nrbeval(srf,{linspace(0.0,1.0,20) linspace(0.0,1.0,20)});
-%! h = surf(squeeze(p(1,:,:)),squeeze(p(2,:,:)),squeeze(p(3,:,:)));
-%! set(h,'FaceColor','blue','EdgeColor','blue');
-%! title('First derivatives over a test surface.');
-%!
-%! npts = 5;
-%! tt = linspace(0.0,1.0,npts);
-%! dsrf = nrbderiv(srf);
-%!
-%! [p1, dp] = nrbdeval(srf, dsrf, {tt, tt});
-%!
-%! up2 = vecnorm(dp{1});
-%! vp2 = vecnorm(dp{2});
-%!
-%! hold on;
-%! plot3(p1(1,:),p1(2,:),p1(3,:),'ro');
-%! h1 = quiver3(p1(1,:),p1(2,:),p1(3,:),up2(1,:),up2(2,:),up2(3,:));
-%! h2 = quiver3(p1(1,:),p1(2,:),p1(3,:),vp2(1,:),vp2(2,:),vp2(3,:));
-%! set(h1,'Color','black');
-%! set(h2,'Color','black');
-%!
-%! hold off;
-
-%!test
-%! knots{1} = [0 0 0 1 1 1];
-%! knots{2} = [0 0 0 .5 1 1 1];
-%! knots{3} = [0 0 0 0 1 1 1 1];
-%! cx = [0 0.5 1]; nx = length(cx);
-%! cy = [0 0.25 0.75 1]; ny = length(cy);
-%! cz = [0 1/3 2/3 1]; nz = length(cz);
-%! coefs(1,:,:,:) = repmat(reshape(cx,nx,1,1),[1 ny nz]);
-%! coefs(2,:,:,:) = repmat(reshape(cy,1,ny,1),[nx 1 nz]);
-%! coefs(3,:,:,:) = repmat(reshape(cz,1,1,nz),[nx ny 1]);
-%! coefs(4,:,:,:) = 1;
-%! nurbs = nrbmak(coefs, knots);
-%! x = rand(5,1); y = rand(5,1); z = rand(5,1);
-%! tt = [x y z]';
-%! ders = nrbderiv(nurbs);
-%! [points,jac] = nrbdeval(nurbs,ders,tt);
-%! assert(points,tt,1e-10)
-%! assert(jac{1}(1,:,:),ones(size(jac{1}(1,:,:))),1e-12)
-%! assert(jac{2}(2,:,:),ones(size(jac{2}(2,:,:))),1e-12)
-%! assert(jac{3}(3,:,:),ones(size(jac{3}(3,:,:))),1e-12)
-%!
-%!test
-%! knots{1} = [0 0 0 1 1 1];
-%! knots{2} = [0 0 0 0 1 1 1 1];
-%! knots{3} = [0 0 0 1 1 1];
-%! cx = [0 0 1]; nx = length(cx);
-%! cy = [0 0 0 1]; ny = length(cy);
-%! cz = [0 0.5 1]; nz = length(cz);
-%! coefs(1,:,:,:) = repmat(reshape(cx,nx,1,1),[1 ny nz]);
-%! coefs(2,:,:,:) = repmat(reshape(cy,1,ny,1),[nx 1 nz]);
-%! coefs(3,:,:,:) = repmat(reshape(cz,1,1,nz),[nx ny 1]);
-%! coefs(4,:,:,:) = 1;
-%! coefs = coefs([2 1 3 4],:,:,:);
-%! nurbs = nrbmak(coefs, knots);
-%! x = rand(5,1); y = rand(5,1); z = rand(5,1);
-%! tt = [x y z]';
-%! dnurbs = nrbderiv(nurbs);
-%! [points, jac] = nrbdeval(nurbs,dnurbs,tt);
-%! assert(points,[y.^3 x.^2 z]',1e-10);
-%! assert(jac{2}(1,:,:),3*y'.^2,1e-12)
-%! assert(jac{1}(2,:,:),2*x',1e-12)
-%! assert(jac{3}(3,:,:),ones(size(z')),1e-12)
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbeval.m
--- a/extra/nurbs/inst/nrbeval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,340 +0,0 @@
-function [p,w] = nrbeval(nurbs,tt)
-%
-% NRBEVAL: Evaluate a NURBS at parametric points.
-%
-% Calling Sequences:
-%
-% [p,w] = nrbeval(crv,ut)
-% [p,w] = nrbeval(srf,{ut,vt})
-% [p,w] = nrbeval(vol,{ut,vt,wt})
-% [p,w] = nrbeval(srf,pts)
-%
-% INPUT:
-%
-% crv : NURBS curve, see nrbmak.
-%
-% srf : NURBS surface, see nrbmak.
-%
-% vol : NURBS volume, see nrbmak.
-%
-% ut : Parametric evaluation points along U direction.
-%
-% vt : Parametric evaluation points along V direction.
-%
-% wt : Parametric evaluation points along W direction.
-%
-% pts : Array of scattered points in parametric domain
-%
-% OUTPUT:
-%
-% p : Evaluated points on the NURBS curve, surface or volume as
-% Cartesian coordinates (x,y,z). If w is included on the lhs argument
-% list the points are returned as homogeneous coordinates (wx,wy,wz).
-%
-% w : Weights of the homogeneous coordinates of the evaluated
-% points. Note inclusion of this argument changes the type
-% of coordinates returned in p (see above).
-%
-% Description:
-%
-% Evaluation of NURBS curves, surfaces or volume at parametric points along
-% the U, V and W directions. Either homogeneous coordinates are returned
-% if the weights are requested in the lhs arguments, or as Cartesian coordinates.
-% This function utilises the 'C' interface bspeval.
-%
-% Examples:
-%
-% Evaluate the NURBS circle at twenty points from 0.0 to 1.0
-%
-% nrb = nrbcirc;
-% ut = linspace(0.0,1.0,20);
-% p = nrbeval(nrb,ut);
-%
-% See also:
-%
-% bspeval
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Carlo de Falco
-% Copyright (C) 2010, 2011, 2015 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin < 2)
- error('Not enough input arguments');
-end
-
-foption = 1; % output format 3D cartesian coordinates
-if (nargout == 2)
- foption = 0; % output format 4D homogenous coordinates
-end
-
-if (~isstruct(nurbs))
- error('NURBS representation is not structure!');
-end
-
-if (~strcmp(nurbs.form,'B-NURBS'))
- error('Not a recognised NURBS representation');
-end
-
-if (iscell(nurbs.knots))
- if (size(nurbs.knots,2) == 3)
- %% NURBS structure represents a volume
-
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
- num3 = nurbs.number(3);
- degree = nurbs.order-1;
-
- if (iscell(tt))
- nt1 = numel (tt{1});
- nt2 = numel (tt{2});
- nt3 = numel (tt{3});
-
- %% evaluate along the w direction
- val = reshape (nurbs.coefs, 4*num1*num2, num3);
- val = bspeval (degree(3), val, nurbs.knots{3}, tt{3});
- val = reshape (val, [4 num1 num2 nt3]);
-
- %% Evaluate along the v direction
- val = permute (val, [1 2 4 3]);
- val = reshape (val, 4*num1*nt3, num2);
- val = bspeval (degree(2), val, nurbs.knots{2}, tt{2});
- val = reshape (val, [4 num1 nt3 nt2]);
- val = permute (val, [1 2 4 3]);
-
- %% Evaluate along the u direction
- val = permute (val, [1 3 4 2]);
- val = reshape (val, 4*nt2*nt3, num1);
- val = bspeval (degree(1), val, nurbs.knots{1}, tt{1});
- val = reshape (val, [4 nt2 nt3 nt1]);
- val = permute (val, [1 4 2 3]);
- pnts = val;
-
- p = pnts(1:3,:,:,:);
- w = pnts(4,:,:,:);
- if (foption)
- p = p./repmat(w,[3 1 1 1]);
- end
-
- else
-
- %% Evaluate at scattered points
- %% tt(1,:) represents the u direction
- %% tt(2,:) represents the v direction
- %% tt(3,:) represents the w direction
-
- st = size(tt);
- if (st(1) ~= 3 && st(2) == 3 && numel(st) == 2)
- tt = tt';
- st = size (tt);
- end
- nt = prod(st(2:end));
-
- tt = reshape (tt, [3, nt]);
-
- %% evaluate along the w direction
- val = reshape(nurbs.coefs,4*num1*num2,num3);
- val = bspeval(degree(3),val,nurbs.knots{3},tt(3,:));
- val = reshape(val,[4 num1 num2 nt]);
-
- %% evaluate along the v direction
- val2 = zeros(4*num1,nt);
- for v = 1:nt
- coefs = reshape(val(:,:,:,v),4*num1,num2);
- val2(:,v) = bspeval(degree(2),coefs,nurbs.knots{2},tt(2,v));
- end
- val2 = reshape(val2,[4 num1 nt]);
-
- %% evaluate along the u direction
- pnts = zeros(4,nt);
- for v = 1:nt
- coefs = reshape (val2(:,:,v), [4 num1]);
- pnts(:,v) = bspeval(degree(1),coefs,nurbs.knots{1},tt(1,v));
- end
-
- w = pnts(4,:);
- p = pnts(1:3,:);
- if (foption)
- p = p./repmat(w,[3, 1]);
- end
-
- if (numel(st) ~= 2)
- w = reshape (w, [st(2:end)]);
- p = reshape (p, [3, st(2:end)]);
- end
- end
-
- elseif (size(nurbs.knots,2) == 2)
- %% NURBS structure represents a surface
-
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
- degree = nurbs.order-1;
-
- if (iscell(tt))
- %% Evaluate over a [u,v] grid
- %% tt{1} represents the u direction
- %% tt{2} represents the v direction
-
- nt1 = length(tt{1});
- nt2 = length(tt{2});
-
- %% Evaluate along the v direction
- val = reshape(nurbs.coefs,4*num1,num2);
- val = bspeval(degree(2),val,nurbs.knots{2},tt{2});
- val = reshape(val,[4 num1 nt2]);
-
- %% Evaluate along the u direction
- val = permute(val,[1 3 2]);
- val = reshape(val,4*nt2,num1);
- val = bspeval(degree(1),val,nurbs.knots{1},tt{1});
- val = reshape(val,[4 nt2 nt1]);
- val = permute(val,[1 3 2]);
-
- w = val(4,:,:);
- p = val(1:3,:,:);
- if (foption)
- p = p./repmat(w,[3 1 1]);
- end
-
- else
-
- %% Evaluate at scattered points
- %% tt(1,:) represents the u direction
- %% tt(2,:) represents the v direction
-
- st = size(tt);
- if (st(1) ~= 2 && st(2) == 2 && numel(st) == 2)
- tt = tt';
- st = size (tt);
- end
- nt = prod(st(2:end));
-
- tt = reshape (tt, [2, nt]);
-
- val = reshape(nurbs.coefs,4*num1,num2);
- val = bspeval(degree(2),val,nurbs.knots{2},tt(2,:));
- val = reshape(val,[4 num1 nt]);
-
-
- %% evaluate along the u direction
- pnts = zeros(4,nt);
- for v = 1:nt
- coefs = reshape (val(:,:,v), [4 num1]);
- pnts(:,v) = bspeval(degree(1),coefs,nurbs.knots{1},tt(1,v));
- end
-
- w = pnts(4,:);
- p = pnts(1:3,:);
- if (foption)
- p = p./repmat(w,[3, 1]);
- end
-
- if (numel(st) ~= 2)
- w = reshape (w, [st(2:end)]);
- p = reshape (p, [3, st(2:end)]);
- end
-
- end
-
- end
-else
-
- %% NURBS structure represents a curve
- %% tt represent a vector of parametric points in the u direction
-
- if (iscell (tt) && numel (tt) == 1)
- tt = cell2mat (tt);
- end
-
- st = size (tt);
-
- val = bspeval(nurbs.order-1,nurbs.coefs,nurbs.knots,tt(:)');
-
- w = val(4,:);
- p = val(1:3,:);
- if foption
- p = p./repmat(w,3,1);
- end
-
- if (st(1) ~= 1 || numel(st) ~= 2)
- w = reshape (w, st);
- p = reshape (p, [3, st]);
- end
-
-end
-
-end
-
-%!demo
-%! srf = nrbtestsrf;
-%! p = nrbeval(srf,{linspace(0.0,1.0,20) linspace(0.0,1.0,20)});
-%! h = surf(squeeze(p(1,:,:)),squeeze(p(2,:,:)),squeeze(p(3,:,:)));
-%! title('Test surface.');
-%! hold off
-
-%!test
-%! knots{1} = [0 0 0 1 1 1];
-%! knots{2} = [0 0 0 .5 1 1 1];
-%! knots{3} = [0 0 0 0 1 1 1 1];
-%! cx = [0 0.5 1]; nx = length(cx);
-%! cy = [0 0.25 0.75 1]; ny = length(cy);
-%! cz = [0 1/3 2/3 1]; nz = length(cz);
-%! coefs(1,:,:,:) = repmat(reshape(cx,nx,1,1),[1 ny nz]);
-%! coefs(2,:,:,:) = repmat(reshape(cy,1,ny,1),[nx 1 nz]);
-%! coefs(3,:,:,:) = repmat(reshape(cz,1,1,nz),[nx ny 1]);
-%! coefs(4,:,:,:) = 1;
-%! nurbs = nrbmak(coefs, knots);
-%! x = rand(5,1); y = rand(5,1); z = rand(5,1);
-%! tt = [x y z]';
-%! points = nrbeval(nurbs,tt);
-%!
-%! assert(points,tt,1e-10)
-%!
-%!test
-%! knots{1} = [0 0 0 1 1 1];
-%! knots{2} = [0 0 0 0 1 1 1 1];
-%! knots{3} = [0 0 1 1];
-%! cx = [0 0 1]; nx = length(cx);
-%! cy = [0 0 0 1]; ny = length(cy);
-%! cz = [0 1]; nz = length(cz);
-%! coefs(1,:,:,:) = repmat(reshape(cx,nx,1,1),[1 ny nz]);
-%! coefs(2,:,:,:) = repmat(reshape(cy,1,ny,1),[nx 1 nz]);
-%! coefs(3,:,:,:) = repmat(reshape(cz,1,1,nz),[nx ny 1]);
-%! coefs(4,:,:,:) = 1;
-%! nurbs = nrbmak(coefs, knots);
-%! x = rand(5,1); y = rand(5,1); z = rand(5,1);
-%! tt = [x y z]';
-%! points = nrbeval(nurbs,tt);
-%! assert(points,[x.^2 y.^3 z]',1e-10);
-%!
-%!test
-%! knots{1} = [0 0 0 1 1 1];
-%! knots{2} = [0 0 0 0 1 1 1 1];
-%! knots{3} = [0 0 1 1];
-%! cx = [0 0 1]; nx = length(cx);
-%! cy = [0 0 0 1]; ny = length(cy);
-%! cz = [0 1]; nz = length(cz);
-%! coefs(1,:,:,:) = repmat(reshape(cx,nx,1,1),[1 ny nz]);
-%! coefs(2,:,:,:) = repmat(reshape(cy,1,ny,1),[nx 1 nz]);
-%! coefs(3,:,:,:) = repmat(reshape(cz,1,1,nz),[nx ny 1]);
-%! coefs(4,:,:,:) = 1;
-%! coefs = coefs([2 1 3 4],:,:,:);
-%! nurbs = nrbmak(coefs, knots);
-%! x = rand(5,1); y = rand(5,1); z = rand(5,1);
-%! tt = [x y z]';
-%! points = nrbeval(nurbs,tt);
-%! [y.^3 x.^2 z]';
-%! assert(points,[y.^3 x.^2 z]',1e-10);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbexport.m
--- a/extra/nurbs/inst/nrbexport.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,175 +0,0 @@
-function nrbexport (varargin)
-
-%
-% NRBEXPORT: export NURBS geometries to a format compatible with the one used in GeoPDEs.
-%
-% Calling Sequence:
-%
-% nrbexport (nurbs, filename);
-% nrbexport (nurbs, interfaces, boundaries, filename);
-% nrbexport (nurbs, interfaces, boundaries, subdomains, filename);
-% nrbexport (nurbs, filename, version);
-% nrbexport (nurbs, interfaces, boundaries, filename, version);
-% nrbexport (nurbs, interfaces, boundaries, subdomains, filename, version);
-%
-% INPUT:
-%
-% nurbs : NURBS curve, surface or volume, see nrbmak.
-% interfaces: interface information for GeoPDEs (see nrbmultipatch)
-% boundaries: boundary information for GeoPDEs (see nrbmultipatch)
-% filename : name of the output file.
-% version : either '-V0.7' or '-V2.1', to select the file format
-%
-%
-% Description:
-%
-% The data of the nurbs structure is written in the file, in a format
-% that can be read by GeoPDEs. By default, the file is saved in the
-% format used by GeoPDEs 2.1. For the format of GeoPDEs 2.0 use the
-% option '-v0.7'. Earlier versions of GeoPDEs are not supported.
-%
-% Copyright (C) 2011, 2014, 2015 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (strcmpi (varargin{end}, '-v0.7'))
- version = '0.7';
-else
- version = '2.1';
-end
-
-if (nargin == 2 || nargin == 3)
- nurbs = varargin{1};
- filename = varargin{2};
- if (numel (nurbs) > 1)
- warning ('Automatically creating the interface information with nrbmultipatch')
- [interfaces, boundaries] = nrbmultipatch (nurbs);
- subdomains = [];
- else
- interfaces = []; boundaries = []; subdomains = [];
- end
-elseif (nargin == 4 || (nargin == 5 && ischar(varargin{4})))
- nurbs = varargin{1};
- interfaces = varargin{2};
- boundaries = varargin{3};
- filename = varargin{4};
- subdomains = [];
-elseif (nargin == 6 || (nargin == 5 && ~ischar(varargin{4})))
- nurbs = varargin{1};
- interfaces = varargin{2};
- boundaries = varargin{3};
- subdomains = varargin{4};
- filename = varargin{5};
-else
- error ('nrbexport: wrong number of input arguments')
-end
-
-fid = fopen (filename, 'w');
-if (fid < 0)
- error ('nrbexport: cannot open file %s', filename);
-end
-
-ndim = numel (nurbs(1).order);
-npatch = numel (nurbs);
-rdim = 1;
-
-if (strcmp (version, '0.7'))
- rdim = ndim;
-else
- for iptc = 1:npatch
- if (any (abs(nurbs(iptc).coefs(3,:)) > 1e-12))
- rdim = 3;
- break
- elseif (any (abs(nurbs(iptc).coefs(2,:)) > 1e-12))
- rdim = 2;
- end
- end
-end
-
-if (strcmp (version, '0.7'))
- fprintf (fid, '%s\n', '# nurbs mesh v.0.7');
-else
- fprintf (fid, '%s\n', '# nurbs mesh v.2.1');
-end
-fprintf (fid, '%s\n', '#');
-fprintf (fid, '%s\n', ['# ' date]);
-fprintf (fid, '%s\n', '#');
-
-if (strcmp (version, '0.7'))
- fprintf (fid, '%i ', ndim, npatch, numel(interfaces), numel(subdomains));
-else
- fprintf (fid, '%i ', ndim, rdim, npatch, numel(interfaces), numel(subdomains));
-end
-fprintf (fid, '\n');
-for iptc = 1:npatch
- fprintf (fid, '%s %i \n', 'PATCH', iptc);
- fprintf (fid, '%i ', nurbs(iptc).order-1);
- fprintf (fid, '\n');
- fprintf (fid, '%i ', nurbs(iptc).number);
- fprintf (fid, '\n');
- if (iscell (nurbs(iptc).knots))
- for ii = 1:ndim
- fprintf (fid, '%1.7f ', nurbs(iptc).knots{ii});
- fprintf (fid, '\n');
- end
- else
- fprintf (fid, '%1.7f ', nurbs(iptc).knots);
- fprintf (fid, '\n');
- end
-
- for ii = 1:rdim
- fprintf (fid, '%1.15f ', nurbs(iptc).coefs(ii,:,:));
- fprintf (fid, '\n');
- end
- fprintf (fid, '%1.15f ', nurbs(iptc).coefs(4,:,:));
- fprintf (fid, '\n');
-end
-
-for intrfc = 1:numel(interfaces)
- if (isfield (interfaces, 'ref'))
- fprintf (fid, '%s \n', interfaces(intrfc).ref);
- else
- fprintf (fid, '%s %i \n', 'INTERFACE', intrfc);
- end
- fprintf (fid, '%i %i \n', interfaces(intrfc).patch1, interfaces(intrfc).side1);
- fprintf (fid, '%i %i \n', interfaces(intrfc).patch2, interfaces(intrfc).side2);
- if (ndim == 2)
- fprintf (fid, '%i \n', interfaces(intrfc).ornt);
- elseif (ndim == 3)
- fprintf (fid, '%i %i %i \n', interfaces(intrfc).flag, interfaces(intrfc).ornt1, interfaces(intrfc).ornt2);
- end
-end
-
-for isubd = 1:numel(subdomains)
-% The subdomain part should be fixed
- fprintf (fid, '%s \n', subdomains(isubd).name);
- fprintf (fid, '%i ', subdomains(isubd).patches);
- fprintf (fid, '\n');
-end
-
-
-for ibnd = 1:numel (boundaries)
- if (isfield (boundaries, 'name'))
- fprintf (fid, '%s \n', boundaries(ibnd).name);
- else
- fprintf (fid, '%s %i \n', 'BOUNDARY', ibnd);
- end
- fprintf (fid, '%i \n', boundaries(ibnd).nsides);
- for ii = 1:boundaries(ibnd).nsides
- fprintf (fid, '%i %i \n', boundaries(ibnd).patches(ii), boundaries(ibnd).faces(ii));
- end
-end
-
-fclose (fid);
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbextract.m
--- a/extra/nurbs/inst/nrbextract.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,96 +0,0 @@
-function crvs = nrbextract(srf)
-
-%
-% NRBEXTRACT: construct NURBS curves by extracting the boundaries of a NURBS surface, or NURBS surfaces by extracting the boundary of a NURBS volume.
-% It only works for geometries constructed with open knot vectors.
-%
-% Calling Sequence:
-%
-% crvs = nrbextract(surf);
-%
-% INPUT:
-%
-% surf : NURBS surface or volume, see nrbmak.
-%
-% OUTPUT:
-%
-% crvs : array of NURBS curves or NURBS surfaces extracted.
-%
-% Description:
-%
-% Constructs either an array of four NURBS curves, by extracting the boundaries
-% of a NURBS surface, or an array of six surfaces, by extracting the boundaries
-% of a NURBS volume. The new entities are ordered in the following way
-%
-% 1: U = 0
-% 2: U = 1
-% 3: V = 0
-% 4: V = 1
-% 5: W = 0 (only for volumes)
-% 6: W = 1 (only for volumes)
-%
-% Copyright (C) 2010,2014 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (~iscell (srf.knots))
- error('The boundary information is only extracted for NURBS surfaces or volumes');
-end
-
-for idim = 1:numel(srf.knots)
- ord = srf.order(idim);
- if (srf.knots{idim}(1) ~= srf.knots{idim}(ord) || ...
- srf.knots{idim}(end) ~= srf.knots{idim}(end-ord+1))
- error ('nrbextract: only working for open knot vectors')
- end
-end
-
-if (numel (srf.knots) == 2)
- for ind = 1:2
- ind2 = mod (ind, 2) + 1; %ind2 = [2 1];
- bnd1 = (ind - 1) * 2 + 1;
- bnd2 = (ind - 1) * 2 + 2;
- if (ind == 1)
- coefs1 = squeeze (srf.coefs(:,1,:));
- coefs2 = squeeze (srf.coefs(:,end,:));
- elseif (ind == 2)
- coefs1 = squeeze (srf.coefs(:,:,1));
- coefs2 = squeeze (srf.coefs(:,:,end));
- end
- crvs(bnd1) = nrbmak (coefs1, srf.knots{ind2});
- crvs(bnd2) = nrbmak (coefs2, srf.knots{ind2});
- end
-elseif (numel (srf.knots) == 3)
- for ind = 1:3
- inds = setdiff (1:3, ind);
- bnd1 = (ind - 1) * 2 + 1;
- bnd2 = (ind - 1) * 2 + 2;
- if (ind == 1)
- coefs1 = squeeze (srf.coefs(:,1,:,:));
- coefs2 = squeeze (srf.coefs(:,end,:,:));
- elseif (ind == 2)
- coefs1 = squeeze (srf.coefs(:,:,1,:));
- coefs2 = squeeze (srf.coefs(:,:,end,:));
- elseif (ind == 3)
- coefs1 = squeeze (srf.coefs(:,:,:,1));
- coefs2 = squeeze (srf.coefs(:,:,:,end));
- end
- crvs(bnd1) = nrbmak (coefs1, {srf.knots{inds(1)} srf.knots{inds(2)}});
- crvs(bnd2) = nrbmak (coefs2, {srf.knots{inds(1)} srf.knots{inds(2)}});
- end
-else
- error ('The entity is not a surface nor a volume')
-end
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbextrude.m
--- a/extra/nurbs/inst/nrbextrude.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,92 +0,0 @@
-function srf = nrbextrude(curve,vector)
-
-%
-% NRBEXTRUDE: Construct a NURBS surface by extruding a NURBS curve, or
-% construct a NURBS volume by extruding a NURBS surface.
-%
-% Calling Sequence:
-%
-% srf = nrbextrude(crv,vec);
-%
-% INPUT:
-%
-% crv : NURBS curve or surface to extrude, see nrbmak.
-%
-% vec : Vector along which the entity is extruded.
-%
-% OUTPUT:
-%
-% srf : NURBS surface or volume constructed.
-%
-% Description:
-%
-% Constructs either a NURBS surface by extruding a NURBS curve along a
-% defined vector, or a NURBS volume by extruding a NURBS surface. In the
-% first case, the NURBS curve forms the U direction of the surface edge, and
-% is extruded along the vector in the V direction. In the second case, the
-% original surface forms the U and V direction of the volume, and is extruded
-% along the W direction.
-%
-% Examples:
-%
-% Form a hollow cylinder by extruding a circle along the z-axis.
-%
-% srf = nrbextrude(nrbcirc, [0,0,1]);
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin < 2)
- error('Error too few input arguments!');
-end
-
-if (iscell (curve.knots))
- if (numel (curve.knots) == 3)
- error('Nurbs volumes cannot be extruded!');
- end
- for ii = 1:size(curve.coefs,3)
- coefs(:,:,ii) = vectrans(vector) * squeeze (curve.coefs(:,:,ii));
- end
- coefs = cat(4,curve.coefs,coefs);
- srf = nrbmak(coefs,{curve.knots{:}, [0 0 1 1]});
-else
- coefs = cat(3,curve.coefs,vectrans(vector)*curve.coefs);
- srf = nrbmak(coefs,{curve.knots, [0 0 1 1]});
-end
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! srf = nrbextrude(crv,[0 0 5]);
-%! nrbplot(srf,[40 10]);
-%! title('Extrusion of a test curve along the z-axis');
-%! hold off
-%
-%!demo
-%! crv1 = nrbcirc (1, [0 0], 0, pi/2);
-%! crv2 = nrbcirc (2, [0 0], 0, pi/2);
-%! srf = nrbruled (crv1, crv2);
-%! vol = nrbextrude (srf, [0 0 1]);
-%! nrbplot (vol, [30 10 10])
-%! title ('Extrusion of the quarter of a ring')
-%
-%!demo
-%! srf = nrbtestsrf;
-%! vol = nrbextrude(srf, [0 0 10]);
-%! nrbplot(vol,[20 20 20]);
-%! title('Extrusion of a test surface along the z-axis');
-%! hold off
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbkntins.m
--- a/extra/nurbs/inst/nrbkntins.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,198 +0,0 @@
-function inurbs = nrbkntins(nurbs,iknots)
-%
-% NRBKNTINS: Insert a single or multiple knots into a NURBS curve,
-% surface or volume.
-%
-% Calling Sequence:
-%
-% icrv = nrbkntins(crv,iuknots);
-% isrf = nrbkntins(srf,{iuknots ivknots});
-% ivol = nrbkntins(vol,{iuknots ivknots iwknots});
-%
-% INPUT:
-%
-% crv : NURBS curve, see nrbmak.
-%
-% srf : NURBS surface, see nrbmak.
-%
-% srf : NURBS volume, see nrbmak.
-%
-% iuknots : Knots to be inserted along U direction.
-%
-% ivknots : Knots to be inserted along V direction.
-%
-% iwknots : Knots to be inserted along W direction.
-%
-% OUTPUT:
-%
-% icrv : new NURBS structure for a curve with knots inserted.
-%
-% isrf : new NURBS structure for a surface with knots inserted.
-%
-% ivol : new NURBS structure for a volume with knots inserted.
-%
-% Description:
-%
-% Inserts knots into the NURBS data structure, these can be knots at
-% new positions or at the location of existing knots to increase the
-% multiplicity. Note that the knot multiplicity cannot be increased
-% beyond the order of the spline. Knots along the V direction can only
-% inserted into NURBS surfaces, not curve that are always defined along
-% the U direction. This function use the B-Spline function bspkntins,
-% which interfaces to an internal 'C' routine.
-%
-% Examples:
-%
-% Insert two knots into a curve, one at 0.3 and another
-% twice at 0.4
-%
-% icrv = nrbkntins(crv, [0.3 0.4 0.4])
-%
-% Insert into a surface two knots as (1) into the U knot
-% sequence and one knot into the V knot sequence at 0.5.
-%
-% isrf = nrbkntins(srf, {[0.3 0.4 0.4] [0.5]})
-%
-% See also:
-%
-% bspkntins
-%
-% Note:
-%
-% No knot multiplicity will be increased beyond the order of the spline.
-%
-% Copyright (C) 2000 Mark Spink, 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 2
- error('Input argument must include the NURBS and knots to be inserted');
-end
-
-if ~isstruct(nurbs)
- error('NURBS representation is not structure!');
-end
-
-if ~strcmp(nurbs.form,'B-NURBS')
- error('Not a recognised NURBS representation');
-end
-
-degree = nurbs.order-1;
-
-if iscell(nurbs.knots)
- fmax = @(x,y) any (y > max(x)); fmin = @(x,y) any (y < min(x));
- if (any(cellfun(fmax, nurbs.knots, iknots)) || any(cellfun(fmin, nurbs.knots, iknots)))
- error ('Trying to insert a knot outside the interval of definition')
- end
-
- if size(nurbs.knots,2)==3
- % NURBS represents a volume
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
- num3 = nurbs.number(3);
-
- % Insert knots along the w direction
- if isempty(iknots{3})
- coefs = nurbs.coefs;
- knots{3} = nurbs.knots{3};
- else
- coefs = reshape(nurbs.coefs,4*num1*num2,num3);
- [coefs,knots{3}] = bspkntins(degree(3),coefs,nurbs.knots{3},iknots{3});
- num3 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num2 num3]);
- end
-
- % Insert knots along the v direction
- if isempty(iknots{2})
- knots{2} = nurbs.knots{2};
- else
- coefs = permute(coefs,[1 2 4 3]);
- coefs = reshape(coefs,4*num1*num3,num2);
- [coefs,knots{2}] = bspkntins(degree(2),coefs,nurbs.knots{2},iknots{2});
- num2 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num3 num2]);
- coefs = permute(coefs,[1 2 4 3]);
- end
-
- % Insert knots along the u direction
- if isempty(iknots{1})
- knots{1} = nurbs.knots{1};
- else
- coefs = permute(coefs,[1 3 4 2]);
- coefs = reshape(coefs,4*num2*num3,num1);
- [coefs,knots{1}] = bspkntins(degree(1),coefs,nurbs.knots{1},iknots{1});
- coefs = reshape(coefs,[4 num2 num3 size(coefs,2)]);
- coefs = permute(coefs,[1 4 2 3]);
- end
-
- elseif size(nurbs.knots,2)==2
- % NURBS represents a surface
- num1 = nurbs.number(1);
- num2 = nurbs.number(2);
-
- % Insert knots along the v direction
- if isempty(iknots{2})
- coefs = nurbs.coefs;
- knots{2} = nurbs.knots{2};
- else
- coefs = reshape(nurbs.coefs,4*num1,num2);
- [coefs,knots{2}] = bspkntins(degree(2),coefs,nurbs.knots{2},iknots{2});
- num2 = size(coefs,2);
- coefs = reshape(coefs,[4 num1 num2]);
- end
-
- % Insert knots along the u direction
- if isempty(iknots{1})
- knots{1} = nurbs.knots{1};
- else
- coefs = permute(coefs,[1 3 2]);
- coefs = reshape(coefs,4*num2,num1);
- [coefs,knots{1}] = bspkntins(degree(1),coefs,nurbs.knots{1},iknots{1});
- coefs = reshape(coefs,[4 num2 size(coefs,2)]);
- coefs = permute(coefs,[1 3 2]);
- end
- end
-else
-
- if (any(iknots > max(nurbs.knots)) || any(iknots < min(nurbs.knots)))
- error ('Trying to insert a knot outside the interval of definition')
- end
- % NURBS represents a curve
- if isempty(iknots)
- coefs = nurbs.coefs;
- knots = nurbs.knots;
- else
- [coefs,knots] = bspkntins(degree,nurbs.coefs,nurbs.knots,iknots);
- end
-
-end
-
-% construct new NURBS
-inurbs = nrbmak(coefs,knots);
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! plot(crv.coefs(1,:),crv.coefs(2,:),'bo')
-%! title('Knot insertion along test curve: curve and control polygons.');
-%! hold on;
-%! plot(crv.coefs(1,:),crv.coefs(2,:),'b--');
-%!
-%! nrbplot(crv,48);
-%!
-%! icrv = nrbkntins(crv,[0.125 0.375 0.625 0.875] );
-%! plot(icrv.coefs(1,:),icrv.coefs(2,:),'ro')
-%! plot(icrv.coefs(1,:),icrv.coefs(2,:),'r--');
-%! hold off
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbkntplot.m
--- a/extra/nurbs/inst/nrbkntplot.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,206 +0,0 @@
-function nrbkntplot (nurbs)
-
-% NRBKNTPLOT: Plot a NURBS entity with the knots subdivision.
-%
-% Calling Sequence:
-%
-% nrbkntplot(nurbs)
-%
-% INPUT:
-%
-% nurbs: NURBS curve, surface or volume, see nrbmak.
-%
-% Example:
-%
-% Plot the test surface with its knot vector
-%
-% nrbkntplot(nrbtestsrf)
-%
-% See also:
-%
-% nrbctrlplot
-%
-% Copyright (C) 2011, 2012 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin < 1)
- error ('nrbkntplot: Need a NURBS to plot!');
-end
-
-% Default values
-light='on';
-cmap='summer';
-
-colormap (cmap);
-
-hold_flag = ishold;
-
-if (iscell (nurbs.knots))
- if (size (nurbs.knots,2) == 2) % plot a NURBS surface
- nsub = 100;
- nrbplot (nurbs, [nsub nsub], 'light', light, 'colormap', cmap);
- hold on
-
- % And plot the knots
- knt1 = unique (nurbs.knots{1}(nurbs.order(1):end-nurbs.order(1)+1));
- knt2 = unique (nurbs.knots{2}(nurbs.order(2):end-nurbs.order(2)+1));
- p1 = nrbeval (nurbs, {knt1, linspace(knt2(1),knt2(end),nsub)});
- p2 = nrbeval (nurbs, {linspace(knt1(1),knt1(end),nsub), knt2});
-
- if (any (nurbs.coefs(3,:)))
- % surface in a 3D space
- for ii = 1:numel(knt1)
- plot3 (squeeze(p1(1,ii,:)), squeeze(p1(2,ii,:)), squeeze(p1(3,ii,:)),'k');
- end
- for ii = 1:numel(knt2)
- plot3 (squeeze(p2(1,:,ii)), squeeze(p2(2,:,ii)), squeeze(p2(3,:,ii)),'k');
- end
- else
- % plain surface
- for ii = 1:numel(knt1)
- plot (squeeze(p1(1,ii,:)), squeeze (p1(2,ii,:)),'k');
- end
- for ii = 1:numel(knt2)
- plot (p2(1,:,ii),p2(2,:,ii),'k');
- end
- end
-
-
-
- elseif (size (nurbs.knots,2) == 3) % plot a NURBS volume
- % Plot the boundaries
- bnd = nrbextract (nurbs);
- nrbkntplot (bnd(1));
- hold on
- for iface = 2:6
- nrbkntplot (bnd(iface));
- end
- end
-else % plot a NURBS curve
- nsub = 1000;
- nrbplot (nurbs, nsub);
- hold on
-
- % And plot the knots
- order = nurbs.order;
- p = nrbeval (nurbs, unique (nurbs.knots(order:end-order+1)));
-
- if (any (nurbs.coefs(3,:))) % plot a 3D curve
- plot3 (p(1,:), p(2,:), p(3,:), 'rx');
- else % plot a 2D curve
- plot (p(1,:), p(2,:), 'rx');
- end
-
-end
-
-if (~hold_flag)
- hold off
-end
-
-end
-%!demo
-%! crv = nrbtestcrv;
-%! nrbkntplot(crv)
-%! title('Test curve')
-%! hold off
-
-%!demo
-%! sphere = nrbrevolve(nrbcirc(1,[],0.0,pi),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbkntplot(sphere);
-%! title('Ball and torus - surface construction by revolution');
-%! hold on;
-%! torus = nrbrevolve(nrbcirc(0.2,[0.9 1.0]),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbkntplot(torus);
-%! hold off
-
-%!demo
-%! knots = {[0 0 0 1/2 1 1 1] [0 0 0 1 1 1]...
-%! [0 0 0 1/6 2/6 1/2 1/2 4/6 5/6 1 1 1]};
-%!
-%! coefs = [-1.0000 -0.9734 -0.7071 1.4290 1.0000 3.4172
-%! 0 2.4172 0 0.0148 -2.0000 -1.9734
-%! 0 2.0000 4.9623 9.4508 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -0.8536 0 -0.6036 1.9571 1.2071 3.5000
-%! 0.3536 2.5000 0.2500 0.5429 -1.7071 -1.0000
-%! 0 2.0000 4.4900 8.5444 3.4142 2.0000
-%! 0.8536 1.0000 0.6036 1.0000 0.8536 1.0000
-%! -0.3536 -4.0000 -0.2500 -1.2929 1.7071 1.0000
-%! 0.8536 0 0.6036 -2.7071 -1.2071 -5.0000
-%! 0 2.0000 4.4900 10.0711 3.4142 2.0000
-%! 0.8536 1.0000 0.6036 1.0000 0.8536 1.0000
-%! 0 -4.0000 0 0.7071 2.0000 5.0000
-%! 1.0000 4.0000 0.7071 -0.7071 -1.0000 -5.0000
-%! 0 2.0000 4.9623 14.4142 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -2.5000 -4.0000 -1.7678 0.7071 1.0000 5.0000
-%! 0 4.0000 0 -0.7071 -3.5000 -5.0000
-%! 0 2.0000 6.0418 14.4142 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -2.4379 0 -1.7238 2.7071 1.9527 5.0000
-%! 0.9527 4.0000 0.6737 1.2929 -3.4379 -1.0000
-%! 0 2.0000 6.6827 10.0711 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -0.9734 -1.0000 -0.6883 0.7071 3.4172 1.0000
-%! 2.4172 0 1.7092 -1.4142 -1.9734 -2.0000
-%! 0 4.0000 6.6827 4.9623 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! 0 -0.8536 0 0.8536 3.5000 1.2071
-%! 2.5000 0.3536 1.7678 -1.2071 -1.0000 -1.7071
-%! 0 3.4142 6.0418 4.4900 4.0000 0
-%! 1.0000 0.8536 0.7071 0.6036 1.0000 0.8536
-%! -4.0000 -0.3536 -2.8284 1.2071 1.0000 1.7071
-%! 0 0.8536 0 -0.8536 -5.0000 -1.2071
-%! 0 3.4142 7.1213 4.4900 4.0000 0
-%! 1.0000 0.8536 0.7071 0.6036 1.0000 0.8536
-%! -4.0000 0 -2.8284 1.4142 5.0000 2.0000
-%! 4.0000 1.0000 2.8284 -0.7071 -5.0000 -1.0000
-%! 0 4.0000 10.1924 4.9623 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! -4.0000 -2.5000 -2.8284 0.7071 5.0000 1.0000
-%! 4.0000 0 2.8284 -2.4749 -5.0000 -3.5000
-%! 0 4.0000 10.1924 6.0418 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! 0 -2.4379 0 1.3808 5.0000 1.9527
-%! 4.0000 0.9527 2.8284 -2.4309 -1.0000 -3.4379
-%! 0 4.0000 7.1213 6.6827 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! -1.0000 -0.9734 0.2071 2.4163 1.0000 3.4172
-%! 0 2.4172 -1.2071 -1.3954 -2.0000 -1.9734
-%! 2.0000 4.0000 7.0178 6.6827 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -0.8536 0 0.3536 2.4749 1.2071 3.5000
-%! 0.3536 2.5000 -0.8536 -0.7071 -1.7071 -1.0000
-%! 1.7071 4.0000 6.3498 6.0418 1.7071 0
-%! 0.8536 1.0000 0.8536 0.7071 0.8536 1.0000
-%! -0.3536 -4.0000 0.8536 0.7071 1.7071 1.0000
-%! 0.8536 0 -0.3536 -3.5355 -1.2071 -5.0000
-%! 1.7071 4.0000 6.3498 7.1213 1.7071 0
-%! 0.8536 1.0000 0.8536 0.7071 0.8536 1.0000
-%! 0 -4.0000 1.2071 3.5355 2.0000 5.0000
-%! 1.0000 4.0000 -0.2071 -3.5355 -1.0000 -5.0000
-%! 2.0000 4.0000 7.0178 10.1924 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -2.5000 -4.0000 -0.5429 3.5355 1.0000 5.0000
-%! 0 4.0000 -1.9571 -3.5355 -3.5000 -5.0000
-%! 2.0000 4.0000 8.5444 10.1924 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -2.4379 0 -0.0355 3.5355 1.9527 5.0000
-%! 0.9527 4.0000 -1.4497 -0.7071 -3.4379 -1.0000
-%! 2.0000 4.0000 9.4508 7.1213 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000];
-%! coefs = reshape (coefs, 4, 4, 3, 9);
-%! horseshoe = nrbmak (coefs, knots);
-%! nrbkntplot (horseshoe);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbline.m
--- a/extra/nurbs/inst/nrbline.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,59 +0,0 @@
-function curve = nrbline(p1,p2)
-%
-% NRBLINE: Construct a straight line.
-%
-% Calling Sequence:
-%
-% crv = nrbline()
-% crv = nrbline(p1,p2)
-%
-% INPUT:
-%
-% p1 : 2D or 3D cartesian coordinate of the start point.
-%
-% p2 : 2D or 3D cartesian coordinate of the end point.
-%
-% OUTPUT:
-%
-% crv : NURBS curve for a straight line.
-%
-% Description:
-%
-% Constructs NURBS data structure for a straight line. If no rhs
-% coordinates are included the function returns a unit straight
-% line along the x-axis.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-coefs = [zeros(3,2); ones(1,2)];
-
-if nargin < 2
- coefs(1,2) = 1.0;
-else
- coefs(1:length(p1),1) = p1(:);
- coefs(1:length(p2),2) = p2(:);
-end
-
-curve = nrbmak(coefs, [0 0 1 1]);
-
-end
-
-%!demo
-%! crv = nrbline([0.0 0.0 0.0]',[5.0 4.0 2.0]');
-%! nrbplot(crv,1);
-%! grid on;
-%! title('3D straight line.');
-%! hold off
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbmak.m
--- a/extra/nurbs/inst/nrbmak.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,250 +0,0 @@
-function nurbs = nrbmak(coefs,knots)
-%
-% NRBMAK: Construct the NURBS structure given the control points
-% and the knots.
-%
-% Calling Sequence:
-%
-% nurbs = nrbmak(cntrl,knots);
-%
-% INPUT:
-%
-% cntrl : Control points, these can be either Cartesian or
-% homogeneous coordinates.
-%
-% For a curve the control points are represented by a
-% matrix of size (dim,nu), for a surface a multidimensional
-% array of size (dim,nu,nv), for a volume a multidimensional array
-% of size (dim,nu,nv,nw). Where nu is number of points along
-% the parametric U direction, nv the number of points along
-% the V direction and nw the number of points along the W direction.
-% dim is the dimension. Valid options
-% are
-% 2 .... (x,y) 2D Cartesian coordinates
-% 3 .... (x,y,z) 3D Cartesian coordinates
-% 4 .... (wx,wy,wz,w) 4D homogeneous coordinates
-%
-% knots : Non-decreasing knot sequence spanning the interval
-% [0.0,1.0]. It's assumed that the geometric entities
-% are clamped to the start and end control points by knot
-% multiplicities equal to the spline order (open knot vector).
-% For curve knots form a vector and for surfaces (volumes)
-% the knots are stored by two (three) vectors for U and V (and W)
-% in a cell structure {uknots vknots} ({uknots vknots wknots}).
-%
-% OUTPUT:
-%
-% nurbs : Data structure for representing a NURBS entity
-%
-% NURBS Structure:
-%
-% Both curves and surfaces are represented by a structure that is
-% compatible with the Spline Toolbox from Mathworks
-%
-% nurbs.form .... Type name 'B-NURBS'
-% nurbs.dim .... Dimension of the control points
-% nurbs.number .... Number of Control points
-% nurbs.coefs .... Control Points
-% nurbs.order .... Order of the spline
-% nurbs.knots .... Knot sequence
-%
-% Note: the control points are always converted and stored within the
-% NURBS structure as 4D homogeneous coordinates. A curve is always stored
-% along the U direction, and the vknots element is an empty matrix. For
-% a surface the spline order is a vector [du,dv] containing the order
-% along the U and V directions respectively. For a volume the order is
-% a vector [du dv dw]. Recall that order = degree + 1.
-%
-% Description:
-%
-% This function is used as a convenient means of constructing the NURBS
-% data structure. Many of the other functions in the toolbox rely on the
-% NURBS structure been correctly defined as shown above. The nrbmak not
-% only constructs the proper structure, but also checks for consistency.
-% The user is still free to build his own structure, in fact a few
-% functions in the toolbox do this for convenience.
-%
-% Examples:
-%
-% Construct a 2D line from (0.0,0.0) to (1.5,3.0).
-% For a straight line a spline of order 2 is required.
-% Note that the knot sequence has a multiplicity of 2 at the
-% start (0.0,0.0) and end (1.0 1.0) in order to clamp the ends.
-%
-% line = nrbmak([0.0 1.5; 0.0 3.0],[0.0 0.0 1.0 1.0]);
-% nrbplot(line, 2);
-%
-% Construct a surface in the x-y plane i.e
-%
-% ^ (0.0,1.0) ------------ (1.0,1.0)
-% | | |
-% | V | |
-% | | Surface |
-% | | |
-% | | |
-% | (0.0,0.0) ------------ (1.0,0.0)
-% |
-% |------------------------------------>
-% U
-%
-% coefs = cat(3,[0 0; 0 1],[1 1; 0 1]);
-% knots = {[0 0 1 1] [0 0 1 1]}
-% plane = nrbmak(coefs,knots);
-% nrbplot(plane, [2 2]);
-%
-% Copyright (C) 2000 Mark Spink, 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-nurbs = struct ('form', 'B-NURBS', 'dim', 4, 'number', [], 'coefs', [], ...
- 'knots', [], 'order', []);
-
-nurbs.form = 'B-NURBS';
-nurbs.dim = 4;
-np = size(coefs);
-dim = np(1);
-if iscell(knots)
- if size(knots,2) == 3
- if (numel(np) == 3)
- np(4) = 1;
- elseif (numel(np)==2)
- np(3:4) = 1;
- end
- % constructing a volume
- nurbs.number = np(2:4);
- if (dim < 4)
- nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2:4)]);
- nurbs.coefs(1:dim,:,:,:) = coefs;
- else
- nurbs.coefs = coefs;
- end
- uorder = size(knots{1},2)-np(2);
- vorder = size(knots{2},2)-np(3);
- worder = size(knots{3},2)-np(4);
- uknots = sort(knots{1});
- vknots = sort(knots{2});
- wknots = sort(knots{3});
-% uknots = (uknots-uknots(uorder))/(uknots(end-uorder+1)-uknots(uorder));
-% vknots = (vknots-vknots(vorder))/(vknots(end-vorder+1)-vknots(vorder));
-% wknots = (wknots-wknots(worder))/(wknots(end-worder+1)-wknots(worder));
- nurbs.knots = {uknots vknots wknots};
- nurbs.order = [uorder vorder worder];
-
- elseif size(knots,2) == 2
- if (numel(np)==2); np(3) = 1; end
- % constructing a surface
- nurbs.number = np(2:3);
- if (dim < 4)
- nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2:3)]);
- nurbs.coefs(1:dim,:,:) = coefs;
- else
- nurbs.coefs = coefs;
- end
- uorder = size(knots{1},2)-np(2);
- vorder = size(knots{2},2)-np(3);
- uknots = sort(knots{1});
- vknots = sort(knots{2});
-% uknots = (uknots-uknots(uorder))/(uknots(end-uorder+1)-uknots(uorder));
-% vknots = (vknots-vknots(vorder))/(vknots(end-vorder+1)-vknots(vorder));
- nurbs.knots = {uknots vknots};
- nurbs.order = [uorder vorder];
-
- end
-
-else
-
- % constructing a curve
- nurbs.number = np(2);
- if (dim < 4)
- nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2)]);
- nurbs.coefs(1:dim,:) = coefs;
- else
- nurbs.coefs = coefs;
- end
- order = size (knots,2) - np(2);
- nurbs.order = order;
- knots = sort(knots);
-% nurbs.knots = (knots-knots(order))/(knots(end-order+1)-knots(order));
- nurbs.knots = knots;
-
-end
-
-end
-
-%!demo
-%! pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
-%! 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
-%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
-%! crv = nrbmak(pnts,[0 0 0 1/4 1/2 3/4 3/4 1 1 1]);
-%! nrbplot(crv,100)
-%! title('Test curve')
-%! hold off
-
-%!demo
-%! pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
-%! 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
-%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
-%! crv = nrbmak(pnts,[0 0 0 0.1 1/2 3/4 3/4 1 1 1]);
-%! nrbplot(crv,100)
-%! title('Test curve with a slight variation of the knot vector')
-%! hold off
-
-%!demo
-%! pnts = zeros(3,5,5);
-%! pnts(:,:,1) = [ 0.0 3.0 5.0 8.0 10.0;
-%! 0.0 0.0 0.0 0.0 0.0;
-%! 2.0 2.0 7.0 7.0 8.0];
-%! pnts(:,:,2) = [ 0.0 3.0 5.0 8.0 10.0;
-%! 3.0 3.0 3.0 3.0 3.0;
-%! 0.0 0.0 5.0 5.0 7.0];
-%! pnts(:,:,3) = [ 0.0 3.0 5.0 8.0 10.0;
-%! 5.0 5.0 5.0 5.0 5.0;
-%! 0.0 0.0 5.0 5.0 7.0];
-%! pnts(:,:,4) = [ 0.0 3.0 5.0 8.0 10.0;
-%! 8.0 8.0 8.0 8.0 8.0;
-%! 5.0 5.0 8.0 8.0 10.0];
-%! pnts(:,:,5) = [ 0.0 3.0 5.0 8.0 10.0;
-%! 10.0 10.0 10.0 10.0 10.0;
-%! 5.0 5.0 8.0 8.0 10.0];
-%!
-%! knots{1} = [0 0 0 1/3 2/3 1 1 1];
-%! knots{2} = [0 0 0 1/3 2/3 1 1 1];
-%!
-%! srf = nrbmak(pnts,knots);
-%! nrbplot(srf,[20 20])
-%! title('Test surface')
-%! hold off
-
-%!demo
-%! coefs =[ 6.0 0.0 6.0 1;
-%! -5.5 0.5 5.5 1;
-%! -5.0 1.0 -5.0 1;
-%! 4.5 1.5 -4.5 1;
-%! 4.0 2.0 4.0 1;
-%! -3.5 2.5 3.5 1;
-%! -3.0 3.0 -3.0 1;
-%! 2.5 3.5 -2.5 1;
-%! 2.0 4.0 2.0 1;
-%! -1.5 4.5 1.5 1;
-%! -1.0 5.0 -1.0 1;
-%! 0.5 5.5 -0.5 1;
-%! 0.0 6.0 0.0 1]';
-%! knots = [0 0 0 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1 1 1];
-%!
-%! crv = nrbmak(coefs,knots);
-%! nrbplot(crv,100);
-%! grid on;
-%! title('3D helical curve.');
-%! hold off
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbmeasure.m
--- a/extra/nurbs/inst/nrbmeasure.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,115 +0,0 @@
-% NRBMEASURE: Compute the distance between two given points along a NURBS curve.
-%
-% Calling Sequence:
-%
-% [dist, ddistds, ddistde] = nrbmeasure (nrb)
-% [dist, ddistds, ddistde] = nrbmeasure (nrb, s, e)
-% [dist, ddistds, ddistde] = nrbmeasure (nrb, s, e, tol)
-%
-% INPUT:
-%
-% nrb : a NURBS curve, see nrbmak.
-% s : starting point in the parametric domain.
-% e : ending point in the parametric domain.
-% tol : tolerance for numerical quadrature, to be used in quad.
-%
-% OUTPUT:
-%
-% dist : distance between the two points along the NURBS curve.
-% ddistds: derivative of the distance function with respect to the point s.
-% ddistde: derivative of the distance function with respect to the point e.
-%
-% Description:
-%
-% Compute the distance between two given points along a NURBS curve, using
-% quad for numerical integration. The points are given by their coordinates
-% in the parametric domain.
-%
-% Examples:
-%
-% Compute the length of a circular arc constructed as a NURBS.
-%
-% c = nrbcirc (1, [0 0], 0, pi/2);
-% s = 0; e = 1;
-% l = nrbmeasure (c, s, e, 1e-7);
-%
-% Copyright (C) 2013 Carlo de Falco
-%
-% This program is free software; you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation; either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with Octave; see the file COPYING. If not, see
-% .
-
-function [dist, ddistds, ddistde] = nrbmeasure (nrb, s, e, tol)
-
- if (nargin < 4)
- tol = 1e-6;
- if (nargin < 3)
- e = 1;
- if (nargin < 2)
- s = 0;
- end
- end
- end
-
- nrb.knots = (nrb.knots - nrb.knots(1)) / (nrb.knots(end) - nrb.knots(1));
-
- if (numel (s) > 1 && isscalar (e))
- e = e * ones (size(s));
- elseif (numel (e) > 1 && isscalar (s))
- s = s * ones (size(e));
- end
-
- ders = nrbderiv (nrb);
- dist = arrayfun (@(x, y) quad (@(u) len (u, nrb, ders), x, ...
- y, tol), s, e);
-
- if (nargout > 1)
- ddistds = -len (s, nrb, ders);
- if (nargout > 2)
- ddistde = +len (e, nrb, ders);
- end
- end
-
-end
-
-function l = len (u, nrb, ders)
- [~, d] = nrbdeval (nrb, ders, u);
- f = d(1, :);
- g = d(2, :);
- h = d(3, :);
- l = sqrt (f.^2 + g.^2 + h.^2);
-end
-
-%!test
-%! c = nrbcirc (1, [0 0], 0, pi/3);
-%! l = nrbmeasure(c, 0, 1, 1e-7);
-%! assert (l, pi/3, 1e-7)
-
-%!test
-%! c = nrbcirc (1, [0 0], 0, pi/2);
-%! s = zeros (1, 100); e = linspace (0, 1, 100);
-%! for ii = 1:100
-%! l(ii) = nrbmeasure (c, s(ii), e(ii), 1e-7);
-%! endfor
-%! xx = nrbeval (c, e);
-%! theta = atan2 (xx(2,:), xx(1,:));
-%! assert (l, theta, 1e-7)
-
-%!test
-%! c = nrbcirc (1, [0 0], 0, pi/2);
-%! s = 0; e = linspace (0, 1, 100);
-%! for ii = 1:100
-%! l(ii) = nrbmeasure (c, s, e(ii), 1e-7);
-%! endfor
-%! l2 = nrbmeasure (c, s, e, 1e-7);
-%! assert (l, l2, eps)
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbmultipatch.m
--- a/extra/nurbs/inst/nrbmultipatch.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,177 +0,0 @@
-function [interfaces, boundary] = nrbmultipatch (nurbs)
-
-%
-% NRBMULTIPATCH: construct the information for gluing conforming NURBS patches, using the same format as in GeoPDEs.
-%
-% Calling Sequence:
-%
-% [interfaces, boundary] = nrbmultipatch (nurbs);
-%
-% INPUT:
-%
-% nurbs : an array of NURBS surfaces or volumes (not both), see nrbmak.
-%
-% OUTPUT:
-%
-% interfaces: array with the information for each interface, that is:
-% - number of the first patch (patch1), and the local side number (side1)
-% - number of the second patch (patch2), and the local side number (side2)
-% - flag (faces and volumes), ornt1, ornt2 (only volumes): information
-% on how the two patches match, see below.
-% boundary: array with the boundary faces that do not belong to any interface
-% - nsides: total number of sides on the boundary array (numel(boundary))
-% - patches: number of the patch to which the boundary belongs to
-% - sides: number of the local side on the patch
-%
-% Copyright (C) 2014 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-
-npatch = numel (nurbs);
-if (~iscell (nurbs(1).knots))
- error ('Multipatch only works for 2D and 3D geometries')
-elseif (size(nurbs(1).knots,2) == 2)
- ndim = 2;
- face_corners = @(x) x.coefs(:, [1 end]);
- compare_corners = @(nrb1, nrb2) compare_corners_univariate (nrb1, nrb2);
-elseif (size(nurbs(1).knots,2) == 3)
- ndim = 3;
- face_corners = @(x) x.coefs(:, [1 end], [1 end]);
- compare_corners = @(nrb1, nrb2) compare_corners_bivariate (nrb1, nrb2);
-end
-
-non_set_faces = cell (npatch, 1);
-for ii = 1:npatch
- if (~iscell (nurbs(ii).knots))
- error ('Multipatch only works for 2D and 3D geometries')
- elseif (ndim ~= size(nurbs(ii).knots,2))
- error ('All the patches must have the same dimension (at least for now)')
- end
- non_set_faces{ii} = 1:2*ndim;
-end
-
-num_interfaces = 0;
-
-boundary.nsides = 0;
-boundary.patches = [];
-boundary.faces = [];
-
-for i1 = 1:npatch
- nrb_faces1 = nrbextract (nurbs(i1));
- for j1 = non_set_faces{i1}
-
-% This is to fix a bug when two faces of the same patch form an interface
-% (for instance, in a ring or a torus)
- if (isempty (intersect (non_set_faces{i1}, j1))); continue; end
-
- nrb1 = nrb_faces1(j1);
- corners1 = face_corners (nrb1);
-
- non_set_faces{i1} = setdiff (non_set_faces{i1}, j1);
- flag = 0;
-
- i2 = i1 - 1;
- while (~flag && i2 < npatch)
- i2 = i2 + 1;
- nrb_faces2 = nrbextract (nurbs(i2));
- j2 = 0;
- while (~flag && j2 < numel (non_set_faces{i2}))
- j2 = j2 + 1;
- nrb2 = nrb_faces2(non_set_faces{i2}(j2));
- if (numel(nrb1.coefs) ~= numel(nrb2.coefs))
- continue
- else
- corners2 = face_corners (nrb2);
- if (ndim == 2)
- flag = compare_corners (corners1, corners2);
- elseif (ndim == 3)
- [flag, ornt1, ornt2] = compare_corners (corners1, corners2);
- end
- end
- end
- end
-
- if (flag)
- intrfc.patch1 = i1;
- intrfc.side1 = j1;
- intrfc.patch2 = i2;
- intrfc.side2 = non_set_faces{i2}(j2);
- if (ndim ==3)
- intrfc.flag = flag;
- intrfc.ornt1 = ornt1;
- intrfc.ornt2 = ornt2;
- else
- intrfc.ornt = flag;
- end
-
- non_set_faces{i2} = setdiff (non_set_faces{i2}, non_set_faces{i2}(j2));
- num_interfaces = num_interfaces + 1;
- interfaces(num_interfaces) = intrfc;
- else
- boundary.nsides = boundary.nsides + 1;
- boundary.patches = [boundary.patches; i1];
- boundary.faces = [boundary.faces; j1];
- end
- end
-end
-
-if (num_interfaces == 0)
- interfaces = [];
-end
-if (boundary.nsides == 0)
- boundary = [];
-end
-
-end
-
-
-
-function [flag, ornt1, ornt2] = compare_corners_bivariate (coefs1, coefs2)
- coefs1 = reshape (coefs1, 4, []);
- coefs2 = reshape (coefs2, 4, []);
-% Should use some sort of relative error
- if (max (max (abs (coefs1 - coefs2))) < 1e-13)
- flag = 1; ornt1 = 1; ornt2 = 1;
- elseif (max (max (abs (coefs1 - coefs2(:,[1 3 2 4])))) < 1e-13)
- flag = -1; ornt1 = 1; ornt2 = 1;
- elseif (max (max (abs (coefs1 - coefs2(:,[3 1 4 2])))) < 1e-13)
- flag = -1; ornt1 = -1; ornt2 = 1;
- elseif (max (max (abs (coefs1 - coefs2(:,[2 1 4 3])))) < 1e-13)
- flag = 1; ornt1 = -1; ornt2 = 1;
- elseif (max (max (abs (coefs1 - coefs2(:,[4 3 2 1])))) < 1e-13)
- flag = 1; ornt1 = -1; ornt2 = -1;
- elseif (max (max (abs (coefs1 - coefs2(:,[4 2 3 1])))) < 1e-13)
- flag = -1; ornt1 = -1; ornt2 = -1;
- elseif (max (max (abs (coefs1 - coefs2(:,[2 4 1 3])))) < 1e-13)
- flag = -1; ornt1 = 1; ornt2 = -1;
- elseif (max (max (abs (coefs1 - coefs2(:,[3 4 1 2])))) < 1e-13)
- flag = 1; ornt1 = 1; ornt2 = -1;
- else
- flag = 0; ornt1 = 0; ornt2 = 0;
- end
-end
-
-function flag = compare_corners_univariate (coefs1, coefs2)
- coefs1 = reshape (coefs1, 4, []);
- coefs2 = reshape (coefs2, 4, []);
-% Should use some sort of relative error
- if (max (max (abs (coefs1 - coefs2))) < 1e-13)
- flag = 1;
- elseif (max (max (abs (coefs1 - coefs2(:,[end 1])))) < 1e-13)
- flag = -1;
- else
- flag = 0;
- end
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbnumbasisfun.m
--- a/extra/nurbs/inst/nrbnumbasisfun.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,87 +0,0 @@
-function idx = nrbnumbasisfun (points, nrb)
-%
-% NRBNUMBASISFUN: Numbering of basis functions for NURBS
-%
-% Calling Sequence:
-%
-% N = nrbnumbasisfun (u, crv)
-% N = nrbnumbasisfun ({u, v}, srf)
-% N = nrbnumbasisfun (p, srf)
-%
-% INPUT:
-%
-% u or p(1,:,:) - parametric points along u direction
-% v or p(2,:,:) - parametric points along v direction
-% crv - NURBS curve
-% srf - NURBS surface
-%
-% OUTPUT:
-%
-% N - Indices of the basis functions that are nonvanishing at each
-% point. size(N) == size(B)
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- if ( (nargin<2) ...
- || (nargout>1) ...
- || (~isstruct(nrb)) ...
- || (iscell(points) && ~iscell(nrb.knots)) ...
- || (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=2)) ...
- )
- error('Incorrect input arguments in nrbnumbasisfun');
- end
-
-
- if (~iscell(nrb.knots)) %% NURBS curve
-
- iv = findspan (nrb.number-1, nrb.order-1, points, nrb.knots);
- idx = numbasisfun (iv, points, nrb.order-1, nrb.knots);
-
- elseif size(nrb.knots,2) == 2 %% NURBS surface
-
- if (iscell(points))
- [v, u] = meshgrid(points{2}, points{1});
- p(1,:,:) = u;
- p(2,:,:) = v;
- p = reshape(p, 2, []);
- else
- p = points;
- end
-
- idx = nrb_srf_numbasisfun__ (p, nrb);
- else
- error('The function nrbnumbasisfun is not yet ready for volumes')
- end
-
-end
-
-
-%!test
-%! p = 2; q = 3; m = 4; n = 5;
-%! Lx = 1; Ly = 1;
-%! nrb = nrb4surf ([0 0], [1 0], [0 1], [1 1]);
-%! nrb = nrbdegelev (nrb, [p-1, q-1]);
-%! ikx = linspace(0,1,m); iky = linspace(0,1,n);
-%! nrb = nrbkntins (nrb, {ikx(2:end-1), iky(2:end-1)});
-%! nrb.coefs (4,:,:) = nrb.coefs (4,:,:) + rand (size (nrb.coefs (4,:,:)));
-%! u = rand (1, 30); v = rand (1, 10);
-%! u = (u-min (u))/max (u-min (u));
-%! v = (v-min (v))/max (v-min (v));
-%! N = nrbnumbasisfun ({u, v}, nrb);
-%! assert (all (all (N>0)), true)
-%! assert (all (all (N <= prod (nrb.number))), true)
-%! assert (max (max (N)), prod (nrb.number))
-%! assert (min (min (N)), 1)
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbpermute.m
--- a/extra/nurbs/inst/nrbpermute.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,72 +0,0 @@
-function tvol = nrbpermute (vol, ord)
-%
-% NRBPERMUTE: Rearrange the directions of a NURBS volume or surface.
-%
-% Calling Sequence:
-%
-% tvol = nrbpermute(vol,order)
-%
-% INPUT:
-%
-% vol : NURBS volume or surface, see nrbmak.
-% order : the order to rearrange the directions of the NURBS entity.
-%
-% OUTPUT:
-%
-% tvol : NURBS volume or surface with rearranged directions.
-%
-% Description:
-%
-% Utility function that rearranges the directions of a NURBS volume or
-% surface. For surfaces, nrbpermute(srf,[1 2]) is the same as
-% nrbtransp(srf). NURBS curves cannot be rearranged.
-%
-% Example:
-%
-% nrbpermute (vol, [1 3 2])
-%
-% Copyright (C) 2013 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (~iscell(vol.knots))
- error('A NURBS curve cannot be rearranged.');
-end
-
-tvol = nrbmak (permute (vol.coefs, [1, ord+1]), {vol.knots{ord}});
-
-%!demo
-%! vol = nrbrevolve (nrb4surf ([1 0], [2 0], [1 1], [2 1]), [0 0 0], [0 1 0], pi/8);
-%! nrbplot(vol,[5 10 20]);
-%! title('NURBS volume and the same after reordering the directions')
-%! hold on
-%! vol.coefs(1,:,:) = vol.coefs(1,:,:) + 2;
-%! vol = nrbpermute(vol,[2 3 1]);
-%! nrbplot(vol,[5 10 20]);
-%! hold off
-
-%!test
-%! vol = nrbrevolve (nrb4surf ([1 0], [2 0], [1 1], [2 1]), [0 0 0], [0 1 0], pi/8);
-%! perm1 = [1 3 2];
-%! perm2 = [2 1 3];
-%! vol2 = nrbpermute (vol, perm1);
-%! vol3 = nrbpermute (vol, perm2);
-%! assert (vol.number(perm1), vol2.number)
-%! assert (vol.order(perm1), vol2.order)
-%! assert ({vol.knots{perm1}}, vol2.knots)
-%! assert (permute(vol.coefs, [1, perm1+1]), vol2.coefs)
-%! assert (vol.number(perm2), vol3.number)
-%! assert (vol.order(perm2), vol3.order)
-%! assert ({vol.knots{perm2}}, vol3.knots)
-%! assert (permute(vol.coefs, [1, perm2+1]), vol3.coefs)
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbplot.m
--- a/extra/nurbs/inst/nrbplot.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,269 +0,0 @@
-function nrbplot (nurbs, subd, varargin)
-%
-% NRBPLOT: Plot a NURBS curve or surface, or the boundary of a NURBS volume.
-%
-% Calling Sequence:
-%
-% nrbplot (nrb, subd)
-% nrbplot (nrb, subd, p, v)
-%
-% INPUT:
-%
-% nrb : NURBS curve, surface or volume, see nrbmak.
-%
-% npnts : Number of evaluation points, for a surface or volume, a row
-% vector with the number of points along each direction.
-%
-% [p,v] : property/value options
-%
-% Valid property/value pairs include:
-%
-% Property Value/{Default}
-% -----------------------------------
-% light {off} | on
-% colormap {'copper'}
-%
-% Example:
-%
-% Plot the test surface with 20 points along the U direction
-% and 30 along the V direction
-%
-% nrbplot(nrbtestsrf, [20 30])
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
-% Copyright (C) 2012 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-nargs = nargin;
-if nargs < 2
- error ('Need a NURBS to plot and the number of subdivisions!');
-elseif rem(nargs+2,2)
- error ('Param value pairs expected')
-end
-
-% Default values
-light='off';
-cmap='summer';
-
-% Recover Param/Value pairs from argument list
-for i=1:2:nargs-2
- Param = varargin{i};
- Value = varargin{i+1};
- if (~ischar (Param))
- error ('Parameter must be a string')
- elseif size(Param,1)~=1
- error ('Parameter must be a non-empty single row string.')
- end
- switch lower (Param)
- case 'light'
- light = lower (Value);
- if (~ischar (light))
- error ('light must be a string.')
- elseif ~(strcmp(light,'off') | strcmp(light,'on'))
- error ('light must be off | on')
- end
- case 'colormap'
- if ischar (Value)
- cmap = lower(Value);
- elseif size (Value, 2) ~= 3
- error ('colormap must be a string or have exactly three columns.')
- else
- cmap=Value;
- end
- otherwise
- error ('Unknown parameter: %s', Param)
- end
-end
-
-colormap (cmap);
-
-% convert the number of subdivisions in number of points
-subd = subd+1;
-
-% plot the curve or surface
-if (iscell (nurbs.knots))
- if (size (nurbs.knots,2) == 2) % plot a NURBS surface
- knt = nurbs.knots;
- order = nurbs.order;
- p = nrbeval (nurbs, {linspace(knt{1}(order(1)),knt{1}(end-order(1)+1),subd(1)) ...
- linspace(knt{2}(order(2)),knt{2}(end-order(2)+1),subd(2))});
- if (strcmp (light,'on'))
- % light surface
- surfl (squeeze(p(1,:,:)), squeeze(p(2,:,:)), squeeze(p(3,:,:)));
- shading interp;
- else
- surf (squeeze (p(1,:,:)), squeeze (p(2,:,:)), squeeze (p(3,:,:)));
- shading faceted;
- end
- elseif (size (nurbs.knots,2) == 3) % plot the boundaries of a NURBS volume
- bnd = nrbextract (nurbs);
- hold_flag = ishold;
- nrbplot (bnd(1), subd(2:3), varargin{:});
- hold on
- nrbplot (bnd(2), subd(2:3), varargin{:});
- nrbplot (bnd(3), subd([1 3]), varargin{:});
- nrbplot (bnd(4), subd([1 3]), varargin{:});
- nrbplot (bnd(5), subd(1:2), varargin{:});
- nrbplot (bnd(6), subd(1:2), varargin{:});
-
- if (~hold_flag)
- hold off
- end
-
- else
- error ('nrbplot: some argument is not correct')
- end
-else
- % plot a NURBS curve
- order = nurbs.order;
- p = nrbeval (nurbs, linspace (nurbs.knots(order), nurbs.knots(end-order+1), subd));
-
- if (any (nurbs.coefs(3,:)))
- % 3D curve
- plot3 (p(1,:), p(2,:), p(3,:));
- grid on;
- else
- % 2D curve
- plot (p(1,:), p(2,:));
- end
-end
-axis equal;
-
-end
-
-% plot the control surface
-% hold on;
-% mesh(squeeze(pnts(1,:,:)),squeeze(pnts(2,:,:)),squeeze(pnts(3,:,:)));
-% hold off;
-
-%!demo
-%! crv = nrbtestcrv;
-%! nrbplot(crv,100)
-%! title('Test curve')
-%! hold off
-
-%!demo
-%! coefs = [0.0 7.5 15.0 25.0 35.0 30.0 27.5 30.0;
-%! 0.0 2.5 0.0 -5.0 5.0 15.0 22.5 30.0];
-%! knots = [0.0 0.0 0.0 1/6 1/3 1/2 2/3 5/6 1.0 1.0 1.0];
-%!
-%! geom = [
-%! nrbmak(coefs,knots)
-%! nrbline([30.0 30.0],[20.0 30.0])
-%! nrbline([20.0 30.0],[20.0 20.0])
-%! nrbcirc(10.0,[10.0 20.0],1.5*pi,0.0)
-%! nrbline([10.0 10.0],[0.0 10.0])
-%! nrbline([0.0 10.0],[0.0 0.0])
-%! nrbcirc(5.0,[22.5 7.5])
-%! ];
-%!
-%! ng = length(geom);
-%! for i = 1:ng
-%! nrbplot(geom(i),500);
-%! hold on;
-%! end
-%! hold off;
-%! axis equal;
-%! title('2D Geometry formed by a series of NURBS curves');
-
-%!demo
-%! sphere = nrbrevolve(nrbcirc(1,[],0.0,pi),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbplot(sphere,[40 40],'light','on');
-%! title('Ball and torus - surface construction by revolution');
-%! hold on;
-%! torus = nrbrevolve(nrbcirc(0.2,[0.9 1.0]),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbplot(torus,[40 40],'light','on');
-%! hold off
-
-%!demo
-%! knots = {[0 0 0 1/2 1 1 1] [0 0 0 1 1 1]...
-%! [0 0 0 1/6 2/6 1/2 1/2 4/6 5/6 1 1 1]};
-%!
-%! coefs = [-1.0000 -0.9734 -0.7071 1.4290 1.0000 3.4172
-%! 0 2.4172 0 0.0148 -2.0000 -1.9734
-%! 0 2.0000 4.9623 9.4508 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -0.8536 0 -0.6036 1.9571 1.2071 3.5000
-%! 0.3536 2.5000 0.2500 0.5429 -1.7071 -1.0000
-%! 0 2.0000 4.4900 8.5444 3.4142 2.0000
-%! 0.8536 1.0000 0.6036 1.0000 0.8536 1.0000
-%! -0.3536 -4.0000 -0.2500 -1.2929 1.7071 1.0000
-%! 0.8536 0 0.6036 -2.7071 -1.2071 -5.0000
-%! 0 2.0000 4.4900 10.0711 3.4142 2.0000
-%! 0.8536 1.0000 0.6036 1.0000 0.8536 1.0000
-%! 0 -4.0000 0 0.7071 2.0000 5.0000
-%! 1.0000 4.0000 0.7071 -0.7071 -1.0000 -5.0000
-%! 0 2.0000 4.9623 14.4142 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -2.5000 -4.0000 -1.7678 0.7071 1.0000 5.0000
-%! 0 4.0000 0 -0.7071 -3.5000 -5.0000
-%! 0 2.0000 6.0418 14.4142 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -2.4379 0 -1.7238 2.7071 1.9527 5.0000
-%! 0.9527 4.0000 0.6737 1.2929 -3.4379 -1.0000
-%! 0 2.0000 6.6827 10.0711 4.0000 2.0000
-%! 1.0000 1.0000 0.7071 1.0000 1.0000 1.0000
-%! -0.9734 -1.0000 -0.6883 0.7071 3.4172 1.0000
-%! 2.4172 0 1.7092 -1.4142 -1.9734 -2.0000
-%! 0 4.0000 6.6827 4.9623 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! 0 -0.8536 0 0.8536 3.5000 1.2071
-%! 2.5000 0.3536 1.7678 -1.2071 -1.0000 -1.7071
-%! 0 3.4142 6.0418 4.4900 4.0000 0
-%! 1.0000 0.8536 0.7071 0.6036 1.0000 0.8536
-%! -4.0000 -0.3536 -2.8284 1.2071 1.0000 1.7071
-%! 0 0.8536 0 -0.8536 -5.0000 -1.2071
-%! 0 3.4142 7.1213 4.4900 4.0000 0
-%! 1.0000 0.8536 0.7071 0.6036 1.0000 0.8536
-%! -4.0000 0 -2.8284 1.4142 5.0000 2.0000
-%! 4.0000 1.0000 2.8284 -0.7071 -5.0000 -1.0000
-%! 0 4.0000 10.1924 4.9623 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! -4.0000 -2.5000 -2.8284 0.7071 5.0000 1.0000
-%! 4.0000 0 2.8284 -2.4749 -5.0000 -3.5000
-%! 0 4.0000 10.1924 6.0418 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! 0 -2.4379 0 1.3808 5.0000 1.9527
-%! 4.0000 0.9527 2.8284 -2.4309 -1.0000 -3.4379
-%! 0 4.0000 7.1213 6.6827 4.0000 0
-%! 1.0000 1.0000 0.7071 0.7071 1.0000 1.0000
-%! -1.0000 -0.9734 0.2071 2.4163 1.0000 3.4172
-%! 0 2.4172 -1.2071 -1.3954 -2.0000 -1.9734
-%! 2.0000 4.0000 7.0178 6.6827 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -0.8536 0 0.3536 2.4749 1.2071 3.5000
-%! 0.3536 2.5000 -0.8536 -0.7071 -1.7071 -1.0000
-%! 1.7071 4.0000 6.3498 6.0418 1.7071 0
-%! 0.8536 1.0000 0.8536 0.7071 0.8536 1.0000
-%! -0.3536 -4.0000 0.8536 0.7071 1.7071 1.0000
-%! 0.8536 0 -0.3536 -3.5355 -1.2071 -5.0000
-%! 1.7071 4.0000 6.3498 7.1213 1.7071 0
-%! 0.8536 1.0000 0.8536 0.7071 0.8536 1.0000
-%! 0 -4.0000 1.2071 3.5355 2.0000 5.0000
-%! 1.0000 4.0000 -0.2071 -3.5355 -1.0000 -5.0000
-%! 2.0000 4.0000 7.0178 10.1924 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -2.5000 -4.0000 -0.5429 3.5355 1.0000 5.0000
-%! 0 4.0000 -1.9571 -3.5355 -3.5000 -5.0000
-%! 2.0000 4.0000 8.5444 10.1924 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000
-%! -2.4379 0 -0.0355 3.5355 1.9527 5.0000
-%! 0.9527 4.0000 -1.4497 -0.7071 -3.4379 -1.0000
-%! 2.0000 4.0000 9.4508 7.1213 2.0000 0
-%! 1.0000 1.0000 1.0000 0.7071 1.0000 1.0000];
-%! coefs = reshape (coefs, 4, 4, 3, 9);
-%! horseshoe = nrbmak (coefs, knots);
-%! nrbplot (horseshoe, [6, 6, 50], 'light', 'on');
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbrect.m
--- a/extra/nurbs/inst/nrbrect.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,70 +0,0 @@
-function curve = nrbrect(w,h)
-%
-% NRBRECT: Construct NURBS representation of a rectangular curve.
-%
-% Calling Sequence:
-%
-% crv = nrbrect()
-% crv = nrbrect(size)
-% crv = nrbrect(width, height)
-%
-% INPUT:
-%
-% size : Size of the square (width = height).
-%
-% width : Width of the rectangle (along x-axis).
-%
-% height : Height of the rectangle (along y-axis).
-%
-% OUTPUT:
-%
-% crv : NURBS curve, see nrbmak.
-%
-%
-% Description:
-%
-% Construct a rectangle or square in the x-y plane with the bottom
-% lhs corner at (0,0,0). If no rhs arguments provided the function
-% constructs a unit square.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 1
- w = 1;
- h = 1;
-end
-
-if nargin < 2
- h = w;
-end
-
-coefs = [0 w w w w 0 0 0;
- 0 0 0 h h h h 0;
- 0 0 0 0 0 0 0 0;
- 1 1 1 1 1 1 1 1];
-
-knots = [0 0 0.25 0.25 0.5 0.5 0.75 0.75 1 1];
-
-curve = nrbmak(coefs, knots);
-
-end
-
-%!demo
-%! crv = nrbtform(nrbrect(2,1), vecrotz(deg2rad(35)));
-%! nrbplot(crv,4);
-%! axis equal
-%! title('Construction and rotation of a rectangular curve.');
-%! hold off
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbreverse.m
--- a/extra/nurbs/inst/nrbreverse.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,100 +0,0 @@
-function nrb = nrbreverse(nrb, idir)
-%
-% NRBREVERSE: Reverse the evaluation directions of a NURBS geometry.
-%
-% Calling Sequence:
-%
-% rnrb = nrbreverse(nrb);
-% rnrb = nrbreverse(nrb, idir);
-%
-% INPUT:
-%
-% nrb : NURBS data structure, see nrbmak.
-% idir : vector of directions to reverse.
-%
-% OUTPUT:
-%
-% rnrb : Reversed NURBS.
-%
-% Description:
-%
-% Utility function to reverse the evaluation direction of a NURBS
-% curve or surface.
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2013 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin > 2)
- error('Incorrect number of input arguments');
-end
-
-if (iscell(nrb.knots))
- % reverse a NURBS surface or volume
- ndim = numel (nrb.knots);
- if (nargin == 1 || isempty (idir))
- idir = 1:ndim;
- end
- for ii = idir
- nrb.knots{ii} = sort (nrb.knots{ii}(end) - nrb.knots{ii});
- nrb.coefs = flipdim (nrb.coefs, ii+1);
- end
-
-else
- % reverse a NURBS curve
- nrb.knots = sort (nrb.knots(end) - nrb.knots);
- nrb.coefs = fliplr (nrb.coefs);
-end
-
-end
-
-%!demo
-%! pnts = [0.5 1.5 3.0 7.5 8.5;
-%! 3.0 5.5 1.5 4.0 4.5;
-%! 0.0 0.0 0.0 0.0 0.0];
-%! crv1 = nrbmak(pnts,[0 0 0 1/2 3/4 1 1 1]);
-%! crv2 = nrbreverse(crv1);
-%! fprintf('Knots of the original curve\n')
-%! disp(crv1.knots)
-%! fprintf('Knots of the reversed curve\n')
-%! disp(crv2.knots)
-%! fprintf('Control points of the original curve\n')
-%! disp(crv1.coefs(1:2,:))
-%! fprintf('Control points of the reversed curve\n')
-%! disp(crv2.coefs(1:2,:))
-%! nrbplot(crv1,100)
-%! hold on
-%! nrbplot(crv2,100)
-%! title('The curve and its reverse are the same')
-%! hold off
-
-%!test
-%! srf = nrbrevolve(nrbline([1 0],[2 0]), [0 0 0], [0 0 1], pi/2);
-%! srf = nrbkntins (srf, {0.3, 0.6});
-%! srf2 = nrbreverse (srf);
-%! assert (srf.knots, cellfun(@(x) sort(1-x), srf2.knots, 'UniformOutput', false), 1e-15)
-%! assert (srf.coefs, srf2.coefs(:,end:-1:1,end:-1:1))
-
-%!test
-%! srf = nrbrevolve(nrbline([1 0],[2 0]), [0 0 0], [0 0 1], pi/2);
-%! srf = nrbkntins (srf, {0.3, 0.6});
-%! srf2 = nrbreverse (srf, 1);
-%! knt{1} = sort(1-srf2.knots{1}); knt{2} = srf2.knots{2};
-%! assert (srf.knots, knt, 1e-15)
-%! assert (srf.coefs, srf2.coefs(:,end:-1:1,:))
-%! srf2 = nrbreverse (srf, 2);
-%! knt{1} = srf2.knots{1}; knt{2} = sort(1-srf2.knots{2});
-%! assert (srf.knots, knt, 1e-15)
-%! assert (srf.coefs, srf2.coefs(:,:,end:-1:1))
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbrevolve.m
--- a/extra/nurbs/inst/nrbrevolve.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,180 +0,0 @@
-function surf = nrbrevolve(curve,pnt,vec,theta)
-
-%
-% NRBREVOLVE: Construct a NURBS surface by revolving a NURBS curve, or
-% construct a NURBS volume by revolving a NURBS surface.
-%
-% Calling Sequence:
-%
-% srf = nrbrevolve(crv,pnt,vec[,ang])
-%
-% INPUT:
-%
-% crv : NURBS curve or surface to revolve, see nrbmak.
-%
-% pnt : Coordinates of the point used to define the axis
-% of rotation.
-%
-% vec : Vector defining the direction of the rotation axis.
-%
-% ang : Angle to revolve the curve, default 2*pi
-%
-% OUTPUT:
-%
-% srf : constructed surface or volume
-%
-% Description:
-%
-% Construct a NURBS surface by revolving the profile NURBS curve around
-% an axis defined by a point and vector.
-%
-% Examples:
-%
-% Construct a sphere by rotating a semicircle around a x-axis.
-%
-% crv = nrbcirc(1.0,[0 0 0],0,pi);
-% srf = nrbrevolve(crv,[0 0 0],[1 0 0]);
-% nrbplot(srf,[20 20]);
-%
-% NOTE:
-%
-% The algorithm:
-%
-% 1) vectrans the point to the origin (0,0,0)
-% 2) rotate the vector into alignment with the z-axis
-%
-% for each control point along the curve
-%
-% 3) determine the radius and angle of control
-% point to the z-axis
-% 4) construct a circular arc in the x-y plane with
-% this radius and start angle and sweep angle theta
-% 5) combine the arc and profile, coefs and weights.
-%
-% next control point
-%
-% 6) rotate and vectrans the surface back into position
-% by reversing 1 and 2.
-%
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (nargin < 3)
- error('Not enough arguments to construct revolved surface');
-end
-
-if (nargin < 4)
- theta = 2.0*pi;
-end
-
-if (iscell (curve.knots) && numel(curve.knots) == 3)
- error('The function nrbrevolve is not yet ready to create volumes')
-end
-
-% Translate curve the center point to the origin
-if isempty(pnt)
- pnt = zeros(3,1);
-end
-
-if length(pnt) ~= 3
- error('All point and vector coordinates must be 3D');
-end
-
-% Translate and rotate the original curve or surface into alignment with the z-axis
-T = vectrans(-pnt);
-angx = vecangle(vec(1),vec(3));
-RY = vecroty(-angx);
-vectmp = RY*[vecnorm(vec(:));1.0];
-angy = vecangle(vectmp(2),vectmp(3));
-RX = vecrotx(angy);
-curve = nrbtform(curve,RX*RY*T);
-
-% Construct an arc
-arc = nrbcirc(1.0,[],0.0,theta);
-
-if (iscell (curve.knots))
-% Construct the revolved volume
- coefs = zeros([4 arc.number curve.number]);
- angle = squeeze (vecangle(curve.coefs(2,:,:),curve.coefs(1,:,:)));
- radius = squeeze (vecmag(curve.coefs(1:2,:,:)));
- for i = 1:curve.number(1)
- for j = 1:curve.number(2)
- coefs(:,:,i,j) = vecrotz(angle(i,j))*vectrans([0.0 0.0 curve.coefs(3,i,j)])*...
- vecscale([radius(i,j) radius(i,j)])*arc.coefs;
- coefs(4,:,i,j) = coefs(4,:,i,j)*curve.coefs(4,i,j);
- end
- end
- surf = nrbmak(coefs,{arc.knots, curve.knots{:}});
-else
-% Construct the revolved surface
- coefs = zeros(4, arc.number, curve.number);
- angle = vecangle(curve.coefs(2,:),curve.coefs(1,:));
- radius = vecmag(curve.coefs(1:2,:));
- for i = 1:curve.number
- coefs(:,:,i) = vecrotz(angle(i))*vectrans([0.0 0.0 curve.coefs(3,i)])*...
- vecscale([radius(i) radius(i)])*arc.coefs;
- coefs(4,:,i) = coefs(4,:,i)*curve.coefs(4,i);
- end
- surf = nrbmak(coefs,{arc.knots, curve.knots});
-end
-
-% Rotate and vectrans the surface back into position
-T = vectrans(pnt);
-RX = vecrotx(-angy);
-RY = vecroty(angx);
-surf = nrbtform(surf,T*RY*RX);
-
-end
-
-%!demo
-%! sphere = nrbrevolve(nrbcirc(1,[],0.0,pi),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbplot(sphere,[40 40],'light','on');
-%! title('Ball and tori - surface construction by revolution');
-%! hold on;
-%! torus = nrbrevolve(nrbcirc(0.2,[0.9 1.0]),[0.0 0.0 0.0],[1.0 0.0 0.0]);
-%! nrbplot(torus,[40 40],'light','on');
-%! nrbplot(nrbtform(torus,vectrans([-1.8])),[20 10],'light','on');
-%! hold off;
-
-%!demo
-%! pnts = [3.0 5.5 5.5 1.5 1.5 4.0 4.5;
-%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0;
-%! 0.5 1.5 4.5 3.0 7.5 6.0 8.5];
-%! crv = nrbmak(pnts,[0 0 0 1/4 1/2 3/4 3/4 1 1 1]);
-%!
-%! xx = vecrotz(deg2rad(25))*vecroty(deg2rad(15))*vecrotx(deg2rad(20));
-%! nrb = nrbtform(crv,vectrans([5 5])*xx);
-%!
-%! pnt = [5 5 0]';
-%! vec = xx*[0 0 1 1]';
-%! srf = nrbrevolve(nrb,pnt,vec(1:3));
-%!
-%! p = nrbeval(srf,{linspace(0.0,1.0,100) linspace(0.0,1.0,100)});
-%! surfl(squeeze(p(1,:,:)),squeeze(p(2,:,:)),squeeze(p(3,:,:)));
-%! title('Construct of a 3D surface by revolution of a curve.');
-%! shading interp;
-%! colormap(copper);
-%! axis equal;
-%! hold off
-
-%!demo
-%! crv1 = nrbcirc(1,[0 0],0, pi/2);
-%! crv2 = nrbcirc(2,[0 0],0, pi/2);
-%! srf = nrbruled (crv1, crv2);
-%! srf = nrbtform (srf, [1 0 0 0; 0 1 0 1; 0 0 1 0; 0 0 0 1]);
-%! vol = nrbrevolve (srf, [0 0 0], [1 0 0], pi/2);
-%! nrbplot(vol, [30 30 30], 'light', 'on')
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbruled.m
--- a/extra/nurbs/inst/nrbruled.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,89 +0,0 @@
-function srf = nrbruled (crv1, crv2)
-
-% NRBRULED: Construct a ruled surface between two NURBS curves.
-%
-% Calling Sequence:
-%
-% srf = nrbruled(crv1, crv2)
-%
-% INPUT:
-%
-% crv1 : First NURBS curve, see nrbmak.
-%
-% crv2 : Second NURBS curve, see nrbmak.
-%
-% OUTPUT:
-%
-% srf : Ruled NURBS surface.
-%
-% Description:
-%
-% Constructs a ruled surface between two NURBS curves. The ruled surface is
-% ruled along the V direction.
-%
-% Examples:
-%
-% Construct a ruled surface between a semicircle and a straight line.
-%
-% cir = nrbcirc(1,[0 0 0],0,pi);
-% line = nrbline([-1 0.5 1],[1 0.5 1]);
-% srf = nrbruled(cir,line);
-% nrbplot(srf,[20 20]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (iscell(crv1.knots) || iscell(crv2.knots))
- error ('Both NURBS must be curves');
-end
-
-% ensure both curves have a common degree
-d = max ([crv1.order, crv2.order]);
-crv1 = nrbdegelev (crv1, d - crv1.order);
-crv2 = nrbdegelev (crv2, d - crv2.order);
-
-% merge the knot vectors, to obtain a common knot vector
-k1 = crv1.knots;
-k2 = crv2.knots;
-ku = unique ([k1 k2]);
-n = length (ku);
-ka = [];
-kb = [];
-for i = 1:n
- i1 = length (find (k1 == ku(i)));
- i2 = length (find (k2 == ku(i)));
- m = max (i1, i2);
- ka = [ka ku(i)*ones(1,m-i1)];
- kb = [kb ku(i)*ones(1,m-i2)];
-end
-crv1 = nrbkntins (crv1, ka);
-crv2 = nrbkntins (crv2, kb);
-
-coefs(:,:,1) = crv1.coefs;
-coefs(:,:,2) = crv2.coefs;
-srf = nrbmak (coefs, {crv1.knots, [0 0 1 1]});
-
-end
-
-%!demo
-%! pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
-%! 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
-%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
-%! crv1 = nrbmak (pnts,[0 0 0 1/4 1/2 3/4 3/4 1 1 1]);
-%! crv2 = nrbtform (nrbcirc (4,[4.5;0],pi,0.0),vectrans([0.0 4.0 -4.0]));
-%! srf = nrbruled (crv1,crv2);
-%! nrbplot (srf,[40 20]);
-%! title ('Ruled surface construction from two NURBS curves.');
-%! hold off
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbsurfderiveval.m
--- a/extra/nurbs/inst/nrbsurfderiveval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,294 +0,0 @@
-function skl = nrbsurfderiveval (srf, uv, d)
-
-%
-% NRBSURFDERIVEVAL: Evaluate n-th order derivatives of a NURBS surface
-%
-% usage: skl = nrbsurfderiveval (srf, [u; v], d)
-%
-% INPUT:
-%
-% srf : NURBS surface structure, see nrbmak
-%
-% u, v : parametric coordinates of the point where we compute the
-% derivatives
-%
-% d : number of partial derivatives to compute
-%
-%
-% OUTPUT:
-%
-% skl (i, j, k, l) = i-th component derived j-1,k-1 times at the
-% l-th point.
-%
-% Adaptation of algorithm A4.4 from the NURBS book, pg137
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- skl = zeros (3, d+1, d+1, size (uv, 2));
-
- for iu = 1:size(uv, 2);
- wders = squeeze (surfderiveval (srf.number(1)-1, srf.order(1)-1, ...
- srf.knots{1}, srf.number(2)-1, ...
- srf.order(2)-1, srf.knots{2}, ...
- squeeze (srf.coefs(4, :, :)), uv(1,iu), ...
- uv(2,iu), d));
-
- for idim = 1:3
- Aders = squeeze (surfderiveval (srf.number(1)-1, srf.order(1)-1, ...
- srf.knots{1}, srf.number(2)-1, ...
- srf.order(2)-1, srf.knots{2}, ...
- squeeze (srf.coefs(idim, :, :)), uv(1,iu),...
- uv(2,iu), d));
-
- for k=0:d
- for l=0:d-k
- v = Aders(k+1, l+1);
- for j=1:l
- v = v - nchoosek(l,j)*wders(1,j+1)*skl(idim, k+1, l-j+1,iu);
- end
- for i=1:k
- v = v - nchoosek(k,i)*wders(i+1,1)*skl(idim, k-i+1, l+1, iu);
- v2 =0;
- for j=1:l
- v2 = v2 + nchoosek(l,j)*wders(i+1,j+1)*skl(idim, k-i+1, l-j+1, iu);
- end
- v = v - nchoosek(k,i)*v2;
- end
- skl(idim, k+1, l+1, iu) = v/wders(1,1);
- end
- end
- end
-
- end
-
-end
-
-%!test
-%! k = [0 0 1 1];
-%! c = [0 1];
-%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
-%! coef(3,:,:) = coef(1,:,:);
-%! srf = nrbmak (coef, {k, k});
-%! [u, v] = meshgrid (linspace(0,1,11));
-%! uv = [u(:)';v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 0);
-%! aux = nrbeval(srf,uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-
-
-%!test
-%! k = [0 0 1 1];
-%! c = [0 1];
-%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
-%! coef(3,:,:) = coef(1,:,:);
-%! srf = nrbmak (coef, {k, k});
-%! srf = nrbkntins (srf, {[], rand(2,1)});
-%! [u, v] = meshgrid (linspace(0,1,11));
-%! uv = [u(:)';v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 0);
-%! aux = nrbeval(srf,uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-
-%!shared srf, uv
-%!test
-%! k = [0 0 0 1 1 1];
-%! c = [0 1/2 1];
-%! [coef(1,:,:), coef(2,:,:)] = meshgrid (c, c);
-%! coef(3,:,:) = coef(1,:,:);
-%! srf = nrbmak (coef, {k, k});
-%! ders= nrbderiv (srf);
-%! [u, v] = meshgrid (linspace(0,1,11));
-%! uv = [u(:)';v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 1);
-%! [fun, der] = nrbdeval (srf, ders, uv);
-%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
-%!
-%!test
-%! srf = nrbdegelev (srf, [3, 1]);
-%! ders= nrbderiv (srf);
-%! [fun, der] = nrbdeval (srf, ders, uv);
-%! skl = nrbsurfderiveval (srf, uv, 1);
-%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
-
-%!shared uv
-%!test
-%! k = [0 0 0 1 1 1];
-%! c = [0 1/2 1];
-%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
-%! coef(3,:,:) = coef(1,:,:);
-%! srf = nrbmak (coef, {k, k});
-%! ders= nrbderiv (srf);
-%! [u, v] = meshgrid (linspace(0,1,11));
-%! uv = [u(:)';v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 1);
-%! [fun, der] = nrbdeval (srf, ders, uv);
-%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
-%!
-%!test
-%! p = 3; q = 3;
-%! mcp = 5; ncp = 5;
-%! Lx = 10*rand(1); Ly = Lx;
-%! srf = nrbdegelev (nrb4surf ([0 0], [Lx, 0], [0 Ly], [Lx Ly]), [p-1, q-1]);
-%! %%srf = nrbkntins (srf, {linspace(0,1,mcp-p+2)(2:end-1), linspace(0,1,ncp-q+2)(2:end-1)});
-%! %%srf.coefs = permute (srf.coefs, [1 3 2]);
-%! ders= nrbderiv (srf);
-%! [fun, der] = nrbdeval (srf, ders, uv);
-%! skl = nrbsurfderiveval (srf, uv, 1);
-%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
-%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
-
-%!shared srf, uv, P, dPdx, d2Pdx2, c1, c2
-%!test
-%! [u, v] = meshgrid (linspace(0,1,10));
-%! uv = [u(:)';v(:)'];
-%! c1 = nrbmak([0 1/2 1; 0 1 0],[0 0 0 1 1 1]);
-%! c1 = nrbtform (c1, vecrotx (pi/2));
-%! c2 = nrbtform(c1, vectrans([0 1 0]));
-%! srf = nrbdegelev (nrbruled (c1, c2), [3, 1]);
-%! skl = nrbsurfderiveval (srf, uv, 2);
-%! P = squeeze(skl(:,1,1,:));
-%! dPdx = squeeze(skl(:,2,1,:));
-%! d2Pdx2 = squeeze(skl(:,3,1,:));
-%!assert(P(3,:), 2*(P(1,:)-P(1,:).^2),100*eps)
-%!assert(dPdx(3,:), 2-4*P(1,:), 100*eps)
-%!assert(d2Pdx2(3,:), -4+0*P(1,:), 100*eps)
-%! srf = nrbdegelev (nrbruled (c1, c2), [5, 6]);
-%! skl = nrbsurfderiveval (srf, uv, 2);
-%! P = squeeze(skl(:,1,1,:));
-%! dPdx = squeeze(skl(:,2,1,:));
-%! d2Pdx2 = squeeze(skl(:,3,1,:));
-%! aux = nrbeval(srf,uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-%!assert(P(3,:), 2*(P(1,:)-P(1,:).^2),100*eps)
-%!assert(dPdx(3,:), 2-4*P(1,:), 100*eps)
-%!assert(d2Pdx2(3,:), -4+0*P(1,:), 100*eps)
-%!
-%!test
-%! skl = nrbsurfderiveval (srf, uv, 0);
-%! aux = nrbeval (srf, uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-
-%!shared dPdu, d2Pdu2, P, srf, uv
-%!test
-%! [u, v] = meshgrid (linspace(0,1,10));
-%! uv = [u(:)';v(:)'];
-%! c1 = nrbmak([0 1/2 1; 0.1 1.6 1.1; 0 0 0],[0 0 0 1 1 1]);
-%! c2 = nrbmak([0 1/2 1; 0.1 1.6 1.1; 1 1 1],[0 0 0 1 1 1]);
-%! srf = nrbdegelev (nrbruled (c1, c2), [0, 1]);
-%! skl = nrbsurfderiveval (srf, uv, 2);
-%! P = squeeze(skl(:,1,1,:));
-%! dPdu = squeeze(skl(:,2,1,:));
-%! dPdv = squeeze(skl(:,1,2,:));
-%! d2Pdu2 = squeeze(skl(:,3,1,:));
-%! aux = nrbeval(srf,uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-%!assert(dPdu(2,:), 3-4*P(1,:),100*eps)
-%!assert(d2Pdu2(2,:), -4+0*P(1,:),100*eps)
-%!
-%!test
-%! skl = nrbsurfderiveval (srf, uv, 0);
-%! aux = nrbeval(srf,uv);
-%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
-
-%!test
-%! srf = nrb4surf([0 0], [1 0], [0 1], [1 1]);
-%! geo = nrbdegelev (srf, [3 3]);
-%1 geo.coefs (4, 2:end-1, 2:end-1) = geo.coefs (4, 2:end-1, 2:end-1) + .1 * rand (1, geo.number(1)-2, geo.number(2)-2);
-%! geo = nrbkntins (geo, {[.1:.1:.9], [.2:.2:.8]});
-%! [u, v] = meshgrid (linspace(0,1,10));
-%! uv = [u(:)';v(:)'];
-%! skl = nrbsurfderiveval (geo, uv, 2);
-%! dgeo = nrbderiv (geo);
-%! [pnts, ders] = nrbdeval (geo, dgeo, uv);
-%! assert (ders{1}, squeeze(skl(:,2,1,:)), 1e-9)
-%! assert (ders{2}, squeeze(skl(:,1,2,:)), 1e-9)
-
-%!test
-%! crv = nrbline ([1 0], [2 0]);
-%! srf = nrbrevolve (crv, [0 0 0], [0 0 1], pi/2);
-%! srf = nrbtransp (srf);
-%! [v, u] = meshgrid (linspace (0, 1, 11));
-%! uv = [u(:)'; v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 2);
-%! c = sqrt(2);
-%! w = @(x, y) (2 - c)*y.^2 + (c-2)*y + 1;
-%! dwdy = @(x, y) 2*(2-c)*y + c - 2;
-%! d2wdy2 = @(x, y) 2*(2-c);
-%! F1 = @(x, y) (x+1) .* ((1-y).^2 + c*y.*(1-y)) ./ w(x,y);
-%! F2 = @(x, y) (x+1) .* (y.^2 + c*y.*(1-y)) ./ w(x,y);
-%! dF1dx = @(x, y) ((1-y).^2 + c*y.*(1-y)) ./ w(x,y);
-%! dF2dx = @(x, y) (y.^2 + c*y.*(1-y)) ./ w(x,y);
-%! dF1dy = @(x, y) (x+1) .* ((2 - 2*c)*y + c - 2) ./ w(x,y) - (x+1) .* ((1-y).^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
-%! dF2dy = @(x, y) (x+1) .* ((2 - 2*c)*y + c) ./ w(x,y) - (x+1) .* (y.^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
-%! d2F1dx2 = @(x, y) zeros (size (x));
-%! d2F2dx2 = @(x, y) zeros (size (x));
-%! d2F1dxdy = @(x, y) ((2 - 2*c)*y + c - 2) ./ w(x,y) - ((1-y).^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
-%! d2F2dxdy = @(x, y) ((2 - 2*c)*y + c) ./ w(x,y) - (y.^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
-%! d2F1dy2 = @(x, y) (x+1)*(2 - 2*c) ./ w(x,y) - 2*(x+1) .* ((2 - 2*c)*y + c - 2) .* dwdy(x,y) ./ w(x,y).^2 - ...
-%! (x+1) .* ((1-y).^2 + c*y.*(1-y)) * d2wdy2(x,y) ./ w(x,y).^2 + ...
-%! 2 * (x+1) .* ((1-y).^2 + c*y.*(1-y)) .* w(x,y) .*dwdy(x,y).^2 ./ w(x,y).^4;
-%! d2F2dy2 = @(x, y) (x+1)*(2 - 2*c) ./ w(x,y) - 2*(x+1) .* ((2 - 2*c)*y + c) .* dwdy(x,y) ./ w(x,y).^2 - ...
-%! (x+1) .* (y.^2 + c*y.*(1-y)) * d2wdy2(x,y) ./ w(x,y).^2 + ...
-%! 2 * (x+1) .* (y.^2 + c*y.*(1-y)) .* w(x,y) .*dwdy(x,y).^2 ./ w(x,y).^4;
-%! assert ([F1(u(:),v(:)), F2(u(:),v(:))], squeeze(skl(1:2,1,1,:))', 1e2*eps);
-%! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:))], squeeze(skl(1:2,2,1,:))', 1e2*eps);
-%! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:))], squeeze(skl(1:2,1,2,:))', 1e2*eps);
-%! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:))], squeeze(skl(1:2,3,1,:))', 1e2*eps);
-%! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:))], squeeze(skl(1:2,2,2,:))', 1e2*eps);
-%! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:))], squeeze(skl(1:2,1,3,:))', 1e2*eps);
-
-%!test
-%! knots = {[0 0 1 1] [0 0 1 1]};
-%! coefs(:,1,1) = [0;0;0;1];
-%! coefs(:,2,1) = [1;0;0;1];
-%! coefs(:,1,2) = [0;1;0;1];
-%! coefs(:,2,2) = [1;1;1;2];
-%! srf = nrbmak (coefs, knots);
-%! [v, u] = meshgrid (linspace (0, 1, 3));
-%! uv = [u(:)'; v(:)'];
-%! skl = nrbsurfderiveval (srf, uv, 2);
-%! w = @(x, y) x.*y + 1;
-%! F1 = @(x, y) x ./ w(x,y);
-%! F2 = @(x, y) y ./ w(x,y);
-%! F3 = @(x, y) x .* y ./ w(x,y);
-%! dF1dx = @(x, y) 1./w(x,y) - x.*y./w(x,y).^2;
-%! dF1dy = @(x, y) - x.^2./w(x,y).^2;
-%! dF2dx = @(x, y) - y.^2./w(x,y).^2;
-%! dF2dy = @(x, y) 1./w(x,y) - x.*y./w(x,y).^2;
-%! dF3dx = @(x, y) y./w(x,y) - x.*(y./w(x,y)).^2;
-%! dF3dy = @(x, y) x./w(x,y) - y.*(x./w(x,y)).^2;
-%! d2F1dx2 = @(x, y) -2*y./w(x,y).^2 + 2*x.*y.^2./w(x,y).^3;
-%! d2F1dy2 = @(x, y) 2*x.^3./w(x,y).^3;
-%! d2F1dxdy = @(x, y) -x./w(x,y).^2 - x./w(x,y).^2 + 2*x.^2.*y./w(x,y).^3;
-%! d2F2dx2 = @(x, y) 2*y.^3./w(x,y).^3;
-%! d2F2dy2 = @(x, y) -2*x./w(x,y).^2 + 2*y.*x.^2./w(x,y).^3;
-%! d2F2dxdy = @(x, y) -y./w(x,y).^2 - y./w(x,y).^2 + 2*y.^2.*x./w(x,y).^3;
-%! d2F3dx2 = @(x, y) -2*y.^2./w(x,y).^2 + 2*x.*y.^3./w(x,y).^3;
-%! d2F3dy2 = @(x, y) -2*x.^2./w(x,y).^2 + 2*y.*x.^3./w(x,y).^3;
-%! d2F3dxdy = @(x, y) 1./w(x,y) - 3*x.*y./w(x,y).^2 + 2*(x.*y).^2./w(x,y).^3;
-%! assert ([F1(u(:),v(:)), F2(u(:),v(:)), F3(u(:),v(:))], squeeze(skl(1:3,1,1,:))', 1e2*eps);
-%! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:)), dF3dx(u(:),v(:))], squeeze(skl(1:3,2,1,:))', 1e2*eps);
-%! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:)), dF3dy(u(:),v(:))], squeeze(skl(1:3,1,2,:))', 1e2*eps);
-%! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:)), d2F3dx2(u(:),v(:))], squeeze(skl(1:3,3,1,:))', 1e2*eps);
-%! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:)), d2F3dy2(u(:),v(:))], squeeze(skl(1:3,1,3,:))', 1e2*eps);
-%! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:)), d2F3dxdy(u(:),v(:))], squeeze(skl(1:3,2,2,:))', 1e2*eps);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbtestcrv.m
--- a/extra/nurbs/inst/nrbtestcrv.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,31 +0,0 @@
-function crv = nrbtestcrv
-% NRBTESTCRV: Constructs a simple test curve.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
- 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
- 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
-crv = nrbmak(pnts,[0 0 0 1/4 1/2 3/4 3/4 1 1 1]);
-
-end
-
-%!demo
-%! crv = nrbtestcrv;
-%! nrbplot(crv,100)
-%! title('Test curve')
-%! hold off
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbtestsrf.m
--- a/extra/nurbs/inst/nrbtestsrf.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,61 +0,0 @@
-function srf = nrbtestsrf
-% NRBTESTSRF: Constructs a simple test surface.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-% allocate multi-dimensional array of control points
-pnts = zeros(3,5,5);
-
-% define a grid of control points
-% in this case a regular grid of u,v points
-% pnts(3,u,v)
-%
-
-pnts(:,:,1) = [ 0.0 3.0 5.0 8.0 10.0; % w*x
- 0.0 0.0 0.0 0.0 0.0; % w*y
- 2.0 2.0 7.0 7.0 8.0]; % w*z
-
-pnts(:,:,2) = [ 0.0 3.0 5.0 8.0 10.0;
- 3.0 3.0 3.0 3.0 3.0;
- 0.0 0.0 5.0 5.0 7.0];
-
-pnts(:,:,3) = [ 0.0 3.0 5.0 8.0 10.0;
- 5.0 5.0 5.0 5.0 5.0;
- 0.0 0.0 5.0 5.0 7.0];
-
-pnts(:,:,4) = [ 0.0 3.0 5.0 8.0 10.0;
- 8.0 8.0 8.0 8.0 8.0;
- 5.0 5.0 8.0 8.0 10.0];
-
-pnts(:,:,5) = [ 0.0 3.0 5.0 8.0 10.0;
- 10.0 10.0 10.0 10.0 10.0;
- 5.0 5.0 8.0 8.0 10.0];
-
-% knots
-knots{1} = [0 0 0 1/3 2/3 1 1 1]; % knots along u
-knots{2} = [0 0 0 1/3 2/3 1 1 1]; % knots along v
-
-% make and draw nurbs surface
-srf = nrbmak(pnts,knots);
-
-end
-
-%!demo
-%! srf = nrbtestsrf;
-%! nrbplot(srf,[20 30])
-%! title('Test surface')
-%! hold off
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbtform.m
--- a/extra/nurbs/inst/nrbtform.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,82 +0,0 @@
-function nurbs = nrbtform(nurbs,tmat)
-%
-% NRBTFORM: Apply transformation matrix to the NURBS.
-%
-% Calling Sequence:
-%
-% tnurbs = nrbtform(nurbs,tmatrix);
-%
-% INPUT:
-%
-% nurbs : NURBS data structure (see nrbmak for details).
-%
-% tmatrix : Transformation matrix, a matrix of size (4,4) defining
-% a single or multiple transformations.
-%
-% OUTPUT:
-%
-% tnurbs : The return transformed NURBS data structure.
-%
-% Description:
-%
-% The NURBS is transform as defined a transformation matrix of size (4,4),
-% such as a rotation, translation or change in scale. The transformation
-% matrix can define a single transformation or multiple series of
-% transformations. The matrix can be simply constructed by the functions
-% vecscale, vectrans and vecrot, and also vecrotx, vecroty, and vecrotz.
-%
-% Examples:
-%
-% Rotate a square by 45 degrees about the z axis.
-%
-% rsqr = nrbtform(nrbrect(), vecrotz(deg2rad(45)));
-% nrbplot(rsqr, 1000);
-%
-% See also:
-%
-% vecscale, vectrans, vecrot, vecrotx, vecroty, vecrotz
-%
-% Copyright (C) 2000 Mark Spink
-% Copyright (C) 2010 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 2
- error('Not enough input arguments!');
-end;
-
-if iscell(nurbs.knots)
- if size(nurbs.knots,2) == 2
- % NURBS is a surface
- [dim,nu,nv] = size(nurbs.coefs);
- nurbs.coefs = reshape(tmat*reshape(nurbs.coefs,dim,nu*nv),[dim nu nv]);
- elseif size(nurbs.knots,2) == 3
- % NURBS is a volume
- [dim,nu,nv,nw] = size(nurbs.coefs);
- nurbs.coefs = reshape(tmat*reshape(nurbs.coefs,dim,nu*nv*nw),[dim nu nv nw]);
- end
-else
- % NURBS is a curve
- nurbs.coefs = tmat*nurbs.coefs;
-end
-
-end
-
-%!demo
-%! xx = vectrans([2.0 1.0])*vecroty(pi/8)*vecrotx(pi/4)*vecscale([1.0 2.0]);
-%! c0 = nrbtform(nrbcirc, xx);
-%! nrbplot(c0,50);
-%! grid on
-%! title('Construction of an ellipse by transforming a unit circle.');
-%! hold off
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbtransp.m
--- a/extra/nurbs/inst/nrbtransp.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,63 +0,0 @@
-function tsrf = nrbtransp(srf)
-%
-% NRBTRANSP: Transpose a NURBS surface, by swapping U and V directions.
-%
-% Calling Sequence:
-%
-% tsrf = nrbtransp(srf)
-%
-% INPUT:
-%
-% srf : NURBS surface, see nrbmak.
-%
-% OUTPUT:
-%
-% tsrf : NURBS surface with U and V diretions transposed.
-%
-% Description:
-%
-% Utility function that transposes a NURBS surface, by swapping U and
-% V directions. NURBS curves cannot be transposed.
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if ~iscell(srf.knots)
- error(' A NURBS curve cannot be transposed.');
-elseif size(srf.knots,2) == 3
- error('The transposition of NURBS volumes has not been implemented.');
-end
-
-tsrf = nrbmak(permute(srf.coefs,[1 3 2]), fliplr(srf.knots));
-
-end
-
-%!demo
-%! srf = nrb4surf([0 0 0], [1 0 1], [0 1 1], [1 1 2]);
-%! nrbplot(srf,[20 5]);
-%! title('Plane surface and its transposed (translated)')
-%! hold on
-%! srf.coefs(3,:,:) = srf.coefs(3,:,:) + 10;
-%! srf = nrbtransp(srf);
-%! nrbplot(srf,[20 5]);
-%! hold off
-
-%!test
-%! srf = nrbrevolve(nrbline([1 0],[2 0]), [0 0 0], [0 0 1], pi/2);
-%! srft = nrbtransp(srf);
-%! assert (srf.number, fliplr(srft.number));
-%! assert (srf.order, fliplr(srft.order));
-%! assert (srf.knots, fliplr(srft.knots));
-%! assert (srf.coefs, permute(srft.coefs, [1 3 2]));
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/nrbunclamp.m
--- a/extra/nurbs/inst/nrbunclamp.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,130 +0,0 @@
-function ucrv = nrbunclamp (crv, k, xdim)
-
-% NRBUNCLAMP: Compute the knot vector and control points of the unclamped curve
-%
-% Calling Sequence:
-%
-% ucrv = nrbrunclamp (crv, k)
-% ucrv = nrbrunclamp (crv, k, dim)
-%
-% INPUT:
-%
-% crv : NURBS curve, see nrbmak.
-% k : continuity for the unclamping (from 0 up to p-1)
-% dim : dimension in which to unclamp (all by default).
-%
-% OUTPUT:
-%
-% ucrv: NURBS curve with unclamped knot vector, see nrbmak
-%
-% Description:
-%
-% Unclamps a curve, removing the open knot vector. Computes the new
-% knot vector and control points of the unclamped curve.
-%
-% Adapted from Algorithm A12.1 from 'The NURBS BOOK' pg577.
-%
-% Copyright (C) 2013, 2014 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if (iscell (crv.knots))
- knt = crv.knots;
- curve = false;
-else
- knt = {crv.knots};
- curve = true;
-end
-
-ndim = numel (knt);
-if (nargin < 3)
- xdim = 1:ndim;
-end
-
-%if (iscell (crv.knots))
- if (numel(k) ~= ndim)
- k = k * ones(1, ndim);
- end
-
- Pw = crv.coefs;
- for idim = xdim
- p = crv.order(idim) - 1;
- U = knt{idim};
- n = crv.number(idim);
- m = n + p + 1;
- kk = k(idim);
-
- if (kk >= p)
- warning ('Taking the maximum k allowed, degree - 1')
- kk = p - 1;
- end
-
- % Unclamp at left end
- for ii=0:kk
- U(kk-ii+1) = U(kk-ii+2) - (U(n+1-ii) - U(n-ii));
- end
-
- Pw = permute (Pw, [1, circshift([2 3 4], [0, 1-idim])]);
- for ii = p-kk-1:p-2
- for jj = ii:-1:0
- alpha = (U(p+1) - U(p+jj-ii)) / (U(p+jj+2) - U(p+jj-ii));
- Pw(:,jj+1,:,:) = (Pw(:,jj+1,:,:) - alpha*Pw(:,jj+2,:,:))/(1-alpha);
- end
- end
-
-
- % Unclamp at right end
- for ii=0:kk
- U(m-kk+ii) = U(m-kk+ii-1) + U(p+ii+1+1) - U(p+ii+1);
- end
-
- for ii = p-kk-1:p-2
- for jj = ii:-1:0
- alpha = (U(n+1)-U(n-jj))/(U(n+2-jj+ii)-U(n-jj));
- Pw(:,n-jj,:,:) = (Pw(:,n-jj,:,:) - (1-alpha)*Pw(:,n-jj-1,:,:))/alpha;
- end
- end
-
- Pw = permute (Pw, [1, circshift([2 3 4], [0, idim-1])]);
- knt{idim} = U;
-
- end
- if (~curve)
- ucrv = nrbmak (Pw, knt);
- else
- ucrv = nrbmak (Pw, knt{:});
- end
-
-%!demo
-%! crv = nrbcirc (1,[],0,2*pi/3);
-%! crv = nrbdegelev (crv, 2);
-%! figure
-%! nrbctrlplot (crv); hold on
-%! nrbctrlplot (nrbtform (nrbunclamp (crv, 1), vectrans([-0.4, -0.4])));
-%! nrbctrlplot (nrbtform (nrbunclamp (crv, 2), vectrans([-0.8, -0.8])));
-%! nrbctrlplot (nrbtform (nrbunclamp (crv, 3), vectrans([-1.6, -1.6])));
-%! title ('Original curve and unclamped versions')
-
-%!test
-%! crv = nrbdegelev (nrbtestcrv,2);
-%! x = linspace (0, 1, 100);
-%! F = nrbeval (crv, x);
-%! ucrv = nrbunclamp (crv, 0);
-%! assert (F, nrbeval(ucrv, x));
-%! ucrv = nrbunclamp (crv, 1);
-%! assert (F, nrbeval(ucrv, x), 1e-14);
-%! ucrv = nrbunclamp (crv, 2);
-%! assert (F, nrbeval(ucrv, x), 1e-14);
-%! ucrv = nrbunclamp (crv, 3);
-%! assert (F, nrbeval(ucrv, x), 1e-14);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/numbasisfun.m
--- a/extra/nurbs/inst/numbasisfun.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,53 +0,0 @@
-function B = numbasisfun (iv, uv, p, U)
-
-% NUMBASISFUN: List non-zero Basis functions for B-Spline in a given knot-span
-%
-% Calling Sequence:
-%
-% N = numbasisfun(i,u,p,U)
-%
-% INPUT:
-%
-% i - knot span ( from FindSpan() )
-% u - parametric point
-% p - spline degree
-% U - knot sequence
-%
-% OUTPUT:
-%
-% N - Basis functions (numel(u)x(p+1))
-%
-% See also:
-%
-% basisfun, basisfunder
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-B = bsxfun (@(a, b) a+b,iv-p, (0:p).').';
-
-end
-
-%!test
-%! n = 3;
-%! U = [0 0 0 1/2 1 1 1];
-%! p = 2;
-%! u = linspace (0, 1, 10);
-%! s = findspan (n, p, u, U);
-%! Bref = [0 0 0 0 0 1 1 1 1 1; ...
-%! 1 1 1 1 1 2 2 2 2 2; ...
-%! 2 2 2 2 2 3 3 3 3 3].';
-%! B = numbasisfun (s, u, p, U);
-%! assert (B, Bref)
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/nrb_crv_basisfun__.m
--- a/extra/nurbs/inst/private/nrb_crv_basisfun__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,20 +0,0 @@
- function [B, nbfu] = nrb_crv_basisfun__ (points, nrb);
-% __NRB_CRV_BASISFUN__: Undocumented internal function
-%
-% Copyright (C) 2009 Carlo de Falco
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
- n = size (nrb.coefs, 2) -1;
- p = nrb.order -1;
- u = points;
- U = nrb.knots;
- w = nrb.coefs(4,:);
-
- spu = findspan (n, p, u, U);
- nbfu = numbasisfun (spu, u, p, U);
-
- N = w(nbfu+1) .* basisfun (spu, u, p, U);
- B = bsxfun (@(x,y) x./y, N, sum (N,2));
-
- end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/nrb_crv_basisfun_der__.m
--- a/extra/nurbs/inst/private/nrb_crv_basisfun_der__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,34 +0,0 @@
- function [Bu, nbfu] = nrb_crv_basisfun_der__ (points, nrb)
-% __NRB_CRV_BASISFUN_DER__: Undocumented internal function
-%
-% Copyright (C) 2009 Carlo de Falco
-% Copyright (C) 2013 Rafael Vazquez
-%
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- n = size (nrb.coefs, 2) -1;
- p = nrb.order -1;
- u = points;
- U = nrb.knots;
- w = nrb.coefs(4,:);
-
- spu = findspan (n, p, u, U);
- nbfu = numbasisfun (spu, u, p, U);
-
- Nprime = basisfunder (spu, p, u, U, 1);
- N = reshape (Nprime(:,1,:), numel(u), p+1);
- Nprime = reshape (Nprime(:,2,:), numel(u), p+1);
-
-
- [Dpc, Dpk] = bspderiv (p, w, U);
- D = bspeval (p, w, U, u);
- Dprime = bspeval (p-1, Dpc, Dpk, u);
-
-
- Bu1 = bsxfun (@(np, d) np/d , Nprime.', D);
- Bu2 = bsxfun (@(n, dp) n*dp, N.', Dprime./D.^2);
- Bu = w(nbfu+1) .* (Bu1 - Bu2).';
-
- end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/nrb_srf_basisfun__.m
--- a/extra/nurbs/inst/private/nrb_srf_basisfun__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,41 +0,0 @@
-function [B, N] = nrb_srf_basisfun__ (points, nrb);
-
-% __NRB_SRF_BASISFUN__: Undocumented internal function
-%
-% Copyright (C) 2009 Carlo de Falco
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- m = size (nrb.coefs, 2) -1;
- n = size (nrb.coefs, 3) -1;
-
- p = nrb.order(1) -1;
- q = nrb.order(2) -1;
-
- u = points(1,:);
- v = points(2,:);
- npt = length(u);
-
- U = nrb.knots{1};
- V = nrb.knots{2};
-
- w = squeeze(nrb.coefs(4,:,:));
-
- spu = findspan (m, p, u, U);
- spv = findspan (n, q, v, V);
- NuIkuk = basisfun (spu, u, p, U);
- NvJkvk = basisfun (spv, v, q, V);
-
- indIkJk = nrbnumbasisfun (points, nrb);
-
- for k=1:npt
- wIkaJkb(1:p+1, 1:q+1) = reshape (w(indIkJk(k, :)), p+1, q+1);
- NuIkukaNvJkvk(1:p+1, 1:q+1) = (NuIkuk(k, :).' * NvJkvk(k, :));
- RIkJk(k, :) = reshape((NuIkukaNvJkvk .* wIkaJkb ./ sum(sum(NuIkukaNvJkvk .* wIkaJkb))),1,[]);
- end
-
- B = RIkJk;
- N = indIkJk;
-
- end
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/nrb_srf_basisfun_der__.m
--- a/extra/nurbs/inst/private/nrb_srf_basisfun_der__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,52 +0,0 @@
-function [Bu, Bv, N] = nrb_srf_basisfun_der__ (points, nrb);
-
-% __NRB_SRF_BASISFUN_DER__: Undocumented internal function
-%
-% Copyright (C) 2009 Carlo de Falco
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- m = size (nrb.coefs, 2) -1;
- n = size (nrb.coefs, 3) -1;
-
- p = nrb.order(1) -1;
- q = nrb.order(2) -1;
-
- u = points(1,:);
- v = points(2,:);
- npt = length(u);
-
- U = nrb.knots{1};
- V = nrb.knots{2};
-
- w = squeeze(nrb.coefs(4,:,:));
-
- spu = findspan (m, p, u, U);
- spv = findspan (n, q, v, V);
- N = nrbnumbasisfun (points, nrb);
-
- NuIkuk = basisfun (spu, u, p, U);
- NvJkvk = basisfun (spv, v, q, V);
-
- NuIkukprime = basisfunder (spu, p, u, U, 1);
- NuIkukprime = reshape (NuIkukprime(:,2,:), npt, []);
-
- NvJkvkprime = basisfunder (spv, q, v, V, 1);
- NvJkvkprime = reshape (NvJkvkprime(:,2,:), npt, []);
-
- for k=1:npt
- wIkaJkb(1:p+1, 1:q+1) = reshape (w(N(k, :)), p+1, q+1);
-
- Num = (NuIkuk(k, :).' * NvJkvk(k, :)) .* wIkaJkb;
- Num_du = (NuIkukprime(k, :).' * NvJkvk(k, :)) .* wIkaJkb;
- Num_dv = (NuIkuk(k, :).' * NvJkvkprime(k, :)) .* wIkaJkb;
- Denom = sum(sum(Num));
- Denom_du = sum(sum(Num_du));
- Denom_dv = sum(sum(Num_dv));
-
- Bu(k, :) = reshape((Num_du/Denom - Denom_du.*Num/Denom.^2),1,[]);
- Bv(k, :) = reshape((Num_dv/Denom - Denom_dv.*Num/Denom.^2),1,[]);
- end
-
-end
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/nrb_srf_numbasisfun__.m
--- a/extra/nurbs/inst/private/nrb_srf_numbasisfun__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,34 +0,0 @@
-function idx = nrb_srf_numbasisfun__ (points, nrb)
-
-% __NRB_SRF_NUMBASISFUN__: Undocumented internal function
-%
-% Copyright (C) 2009 Carlo de Falco
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- m = nrb.number(1)-1;
- n = nrb.number(2)-1;
-
- npt = size(points,2);
- u = points(1,:);
- v = points(2,:);
-
- U = nrb.knots{1};
- V = nrb.knots{2};
-
- p = nrb.order(1)-1;
- q = nrb.order(2)-1;
-
- spu = findspan (m, p, u, U);
- Ik = numbasisfun (spu, u, p, U);
-
- spv = findspan (n, q, v, V);
- Jk = numbasisfun (spv, v, q, V);
-
- for k=1:npt
- [Jkb, Ika] = meshgrid(Jk(k, :), Ik(k, :));
- idx(k, :) = sub2ind([m+1, n+1], Ika(:)+1, Jkb(:)+1);
- end
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/onebasisfun__.m
--- a/extra/nurbs/inst/private/onebasisfun__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,56 +0,0 @@
-function Nip = onebasisfun__ (u, p, U)
-
-% __ONEBASISFUN__: Undocumented internal function
-%
-% Adapted from Algorithm A2.4 from 'The NURBS BOOK' pg74.
-%
-% Copyright (C) 2009 Carlo de Falco
-% Copyright (C) 2012 Rafael Vazquez
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- Nip = zeros (size (u));
- N = zeros (p+1, 1);
-
- for ii = 1:numel(u)
- if ((u(ii) == U(1)) && (U(1) == U(end-1)) || ...
- (u(ii) == U(end)) && (U(end) == U(2)))
- Nip(ii) = 1;
- continue
- end
- if (~ any (U <= u(ii))) || (~ any (U > u(ii)))
- continue;
- end
- for jj = 1:p+1 % Initialize zero-th degree functions
- if (u(ii) >= U(jj) && u(ii) < U(jj+1))
- N(jj) = 1;
- else
- N(jj) = 0;
- end
- end
- for k = 1:p
- if (N(1) == 0)
- saved = 0;
- else
- saved = (u(ii) - U(1))*N(1) / (U(k+1)-U(1));
- end
-
- for jj = 1:p-k+1
- Uleft = U(1+jj);
- Uright = U(1+jj+k);
- if (N(jj+1) == 0)
- N(jj) = saved;
- saved = 0;
- else
- temp = N(jj+1)/(Uright-Uleft);
- N(jj) = saved + (Uright - u(ii))*temp;
- saved = (u(ii) - Uleft)*temp;
- end
- end
- end
- Nip(ii) = N(1);
- end
-
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/private/onebasisfunder__.m
--- a/extra/nurbs/inst/private/onebasisfunder__.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,39 +0,0 @@
-function [N, Nder] = onebasisfunder__ (u, p, U)
-
-% __ONEBASISFUNDER__: Undocumented internal function
-%
-% Copyright (C) 2012 Rafael Vazquez
-% This software comes with ABSOLUTELY NO WARRANTY; see the file
-% COPYING for details. This is free software, and you are welcome
-% to distribute it under the conditions laid out in COPYING.
-
- N = zeros (size (u));
- Nder = zeros (size (u));
-
- for ii = 1:numel (u)
- if (~ any (U <= u(ii))) || (~ any (U > u(ii)))
- continue;
- elseif (p == 0)
- N(ii) = 1;
- Nder(ii) = 0;
- continue;
- else
- ln = u(ii) - U(1);
- ld = U(end-1) - U(1);
- if (ld ~= 0)
- aux = onebasisfun__ (u(ii), p-1, U(1:end-1))/ ld;
- N(ii) = N(ii) + ln * aux;
- Nder(ii) = Nder(ii) + p * aux;
- end
-
- dn = U(end) - u(ii);
- dd = U(end) - U(2);
- if (dd ~= 0)
- aux = onebasisfun__ (u(ii), p-1, U(2:end))/ dd;
- N(ii) = N(ii) + dn * aux;
- Nder(ii) = Nder(ii) - p * aux;
- end
- end
- end
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/rad2deg.m
--- a/extra/nurbs/inst/rad2deg.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,45 +0,0 @@
-function deg = rad2deg(rad)
-%
-% RAD2DEG: Convert radians to degrees.
-%
-% Calling Sequence:
-%
-% rad = rad2deg(deg);
-%
-% INPUT:
-%
-% rad : Angle in radians.
-%
-% OUTPUT:
-%
-% deg : Angle in degrees.
-%
-% Description:
-%
-% Convenient utility function for converting radians to degrees, which are
-% often the required angular units for functions in the NURBS toolbox.
-%
-% Examples:
-%
-% Convert 0.3 radians to degrees
-%
-% deg = rad2deg(0.3);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-deg = 180.0*rad/pi;
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/surfderivcpts.m
--- a/extra/nurbs/inst/surfderivcpts.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,79 +0,0 @@
-function pkl = surfderivcpts (n, p, U, m, q, V, P, d, r1, r2, s1, s2)
-%
-% SURFDERIVCPTS: Compute control points of n-th derivatives of a NURBS surface.
-%
-% usage: pkl = surfderivcpts (n, p, U, m, q, V, P, d)
-%
-% INPUT:
-%
-% n+1, m+1 = number of control points
-% p, q = spline order
-% U, V = knots
-% P = control points
-% d = derivative order
-%
-% OUTPUT:
-%
-% pkl (k+1, l+1, i+1, j+1) = i,jth control point
-% of the surface differentiated k
-% times in the u direction and l
-% times in the v direction
-%
-% Adaptation of algorithm A3.7 from the NURBS book, pg114
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- if (nargin <= 8)
- r1 = 0; r2 = n;
- s1 = 0; s2 = m;
- end
- r = r2-r1;
- s = s2-s1;
-
- du = min (d, p); dv = min (d, q);
-
- for j=s1:s2
- temp = curvederivcpts (n, p, U, P(:,j+1:end), du, r1, r2);
- for k=0:du
- for i=0:r-k
- pkl (k+1, 1, i+1, j-s1+1) = temp (k+1, i+1);
- end
- end
- end
-
- for k=0:du
- for i=0:r-k
- dd = min (d-k, dv);
- temp = curvederivcpts (m, q, V(s1+1:end), pkl(k+1, 1, i+1, :), ...
- dd, 0, s);
- for l=1:dd
- for j=0:s-l
- pkl (k+1, l+1, i+1, j+1) = temp (l+1, j+1);
- end
- end
- end
- end
-
-end
-
-%!test
-%! coefs = cat(3,[0 0; 0 1],[1 1; 0 1]);
-%! knots = {[0 0 1 1] [0 0 1 1]};
-%! plane = nrbmak(coefs,knots);
-%! pkl = surfderivcpts (plane.number(1)-1, plane.order(1)-1,...
-%! plane.knots{1}, plane.number(2)-1,...
-%! plane.order(2)-1, plane.knots{2}, ...
-%! squeeze (plane.coefs(1,:,:)), 1);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/surfderiveval.m
--- a/extra/nurbs/inst/surfderiveval.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,95 +0,0 @@
-function skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
-%
-% SURFDERIVEVAL: Compute the derivatives of a B-spline surface
-%
-% usage: skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
-%
-% INPUT:
-%
-% n+1, m+1 = number of control points
-% p, q = spline order
-% U, V = knots
-% P = control points
-% u,v = evaluation points
-% d = derivative order
-%
-% OUTPUT:
-%
-% skl (k+1, l+1) = surface differentiated k
-% times in the u direction and l
-% times in the v direction
-%
-% Adaptation of algorithm A3.8 from the NURBS book, pg115
-%
-% Copyright (C) 2009 Carlo de Falco
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- skl = zeros (d+1, d+1);
- du = min (d, p);
- dv = min (d, q);
-
- uspan = findspan (n, p, u, U);
- for ip=0:p
- Nu(1:ip+1,ip+1) = basisfun (uspan, u, ip, U)';
- end
-
- vspan = findspan (m, q, v, V);
- for ip=0:q
- Nv(1:ip+1,ip+1) = basisfun (vspan, v, ip, V)';
- end
-
- pkl = surfderivcpts (n, p, U, m, q, V, P, d, uspan-p, uspan, ...
- vspan-q, vspan);
-
- for k = 0:du
- dd = min (d-k, dv);
- for l = 0:dd
- skl(k+1,l+1) =0;
- for i=0:q-l
- tmp = 0;
- for j = 0:p-k
- tmp = tmp + Nu(j+1,p-k+1) * pkl(k+1,l+1,j+1,i+1);
- end
- skl(k+1,l+1) = skl(k+1,l+1) + Nv(i+1,q-l+1)*tmp;
- end
- end
- end
-
-end
-
-%!shared srf
-%!test
-%! k = [0 0 0 1 1 1];
-%! c = [0 1/2 1];
-%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
-%! srf = nrbmak (coef, {k, k});
-%! skl = surfderiveval (srf.number(1)-1, ...
-%! srf.order(1)-1, ...
-%! srf.knots{1}, ...
-%! srf.number(2)-1, ...
-%! srf.order(2)-1, ...
-%! srf.knots{2},...
-%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
-%! assert (skl, [.5 0; 1 0])
-%!test
-%! srf = nrbkntins (srf, {[], rand(1,2)});
-%! skl = surfderiveval (srf.number(1)-1,...
-%! srf.order(1)-1, ...
-%! srf.knots{1},...
-%! srf.number(2)-1,...
-%! srf.order(2)-1, ...
-%! srf.knots{2},...
-%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
-%! assert (skl, [.5 0; 1 0], 100*eps)
\ No newline at end of file
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/tbasisfun.m
--- a/extra/nurbs/inst/tbasisfun.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,131 +0,0 @@
-function [N, Nder] = tbasisfun (u, p, U)
-%
-% TBASISFUN: Compute a B- or T-Spline basis function, and its derivatives, from its local knot vector.
-%
-% usage:
-%
-% [N, Nder] = tbasisfun (u, p, U)
-% [N, Nder] = tbasisfun ([u; v], [p q], {U, V})
-% [N, Nder] = tbasisfun ([u; v; w], [p q r], {U, V, W})
-%
-% INPUT:
-%
-% u or [u; v] : points in parameter space where the basis function is to be
-% evaluated
-%
-% U or {U, V} : local knot vector
-%
-% p or [p q] : polynomial order of the basis function
-%
-% OUTPUT:
-%
-% N : basis function evaluated at the given parametric points
-% Nder : basis function gradient evaluated at the given parametric points
-%
-% Copyright (C) 2009 Carlo de Falco
-% Copyright (C) 2012 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
- if (~ iscell (U))
- U = sort (U);
- if (numel (U) ~= p+2)
- error ('tbasisfun: knot vector and degree do not correspond')
- end
-
- if (nargout == 1)
- N = onebasisfun__ (u, p, U);
- else
- [N, Nder] = onebasisfunder__ (u, p, U);
- end
-
- elseif (size(U,2) == 2)
- U{1} = sort(U{1}); U{2} = sort(U{2});
- if (numel(U{1}) ~= p(1)+2 || numel(U{2}) ~= p(2)+2)
- error ('tbasisfun: knot vector and degree do not correspond')
- end
-
- if (nargout == 1)
- Nu = onebasisfun__ (u(1,:), p(1), U{1});
- Nv = onebasisfun__ (u(2,:), p(2), U{2});
-
- N = Nu.*Nv;
- elseif (nargout == 2)
- [Nu, Ndu] = onebasisfunder__ (u(1,:), p(1), U{1});
- [Nv, Ndv] = onebasisfunder__ (u(2,:), p(2), U{2});
-
- N = Nu.*Nv;
- Nder(1,:) = Ndu.*Nv;
- Nder(2,:) = Nu.*Ndv;
- end
-
- elseif (size(U,2) == 3)
- U{1} = sort(U{1}); U{2} = sort(U{2}); U{3} = sort(U{3});
- if (numel(U{1}) ~= p(1)+2 || numel(U{2}) ~= p(2)+2 || numel(U{3}) ~= p(3)+2)
- error ('tbasisfun: knot vector and degree do not correspond')
- end
-
- if (nargout == 1)
- Nu = onebasisfun__ (u(1,:), p(1), U{1});
- Nv = onebasisfun__ (u(2,:), p(2), U{2});
- Nw = onebasisfun__ (u(3,:), p(3), U{3});
-
- N = Nu.*Nv.*Nw;
- else
- [Nu, Ndu] = onebasisfunder__ (u(1,:), p(1), U{1});
- [Nv, Ndv] = onebasisfunder__ (u(2,:), p(2), U{2});
- [Nw, Ndw] = onebasisfunder__ (u(3,:), p(3), U{3});
-
- N = Nu.*Nv.*Nw;
- Nder(1,:) = Ndu.*Nv.*Nw;
- Nder(2,:) = Nu.*Ndv.*Nw;
- Nder(3,:) = Nu.*Nv.*Ndw;
- end
- end
-
-end
-
-%!demo
-%! U = {[0 0 1/2 1 1], [0 0 0 1 1]};
-%! p = [3, 3];
-%! [X, Y] = meshgrid (linspace(0, 1, 30));
-%! u = [X(:), Y(:)]';
-%! N = tbasisfun (u, p, U);
-%! surf (X, Y, reshape (N, size(X)))
-%! title('Basis function associated to a local knot vector')
-%! hold off
-
-%!test
-%! U = [0 1/2 1];
-%! p = 1;
-%! u = [0.3 0.4 0.6 0.7];
-%! [N, Nder] = tbasisfun (u, p, U);
-%! assert (N, [0.6 0.8 0.8 0.6], 1e-12);
-%! assert (Nder, [2 2 -2 -2], 1e-12);
-
-%!test
-%! U = {[0 1/2 1] [0 1/2 1]};
-%! p = [1 1];
-%! u = [0.3 0.4 0.6 0.7; 0.3 0.4 0.6 0.7];
-%! [N, Nder] = tbasisfun (u, p, U);
-%! assert (N, [0.36 0.64 0.64 0.36], 1e-12);
-%! assert (Nder, [1.2 1.6 -1.6 -1.2; 1.2 1.6 -1.6 -1.2], 1e-12);
-
-%!test
-%! U = {[0 1/2 1] [0 1/2 1] [0 1/2 1]};
-%! p = [1 1 1];
-%! u = [0.4 0.4 0.6 0.6; 0.4 0.4 0.6 0.6; 0.4 0.6 0.4 0.6];
-%! [N, Nder] = tbasisfun (u, p, U);
-%! assert (N, [0.512 0.512 0.512 0.512], 1e-12);
-%! assert (Nder, [1.28 1.28 -1.28 -1.28; 1.28 1.28 -1.28 -1.28; 1.28 -1.28 1.28 -1.28], 1e-12);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecangle.m
--- a/extra/nurbs/inst/vecangle.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,50 +0,0 @@
-function ang = vecangle(num,den)
-
-%
-% VECANGLE: An alternative to atan, returning an arctangent in the
-% range 0 to 2*pi.
-%
-% Calling Sequence:
-%
-% ang = vecmag2(num,dum)
-%
-% INPUT:
-%
-% num : Numerator, vector of size (1,nv).
-% dem : Denominator, vector of size (1,nv).
-%
-% OUTPUT:
-% ang : Arctangents, row vector of angles.
-%
-% Description:
-%
-% The components of the vector ang are the arctangent of the corresponding
-% enties of num./dem. This function is an alternative for
-% atan, returning an angle in the range 0 to 2*pi.
-%
-% Examples:
-%
-% Find the atan(1.2,2.0) and atan(1.5,3.4) using vecangle
-%
-% ang = vecangle([1.2 1.5], [2.0 3.4]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-ang = atan2(num,den);
-index = find(ang < 0.0);
-ang(index) = 2*pi+ang(index);
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/veccross.m
--- a/extra/nurbs/inst/veccross.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,59 +0,0 @@
-function cross = veccross(vec1,vec2)
-%
-% VECCROSS: The cross product of two vectors.
-%
-% Calling Sequence:
-%
-% cross = veccross(vec1,vec2);
-%
-% INPUT:
-%
-% vec1 : An array of column vectors represented by a matrix of
-% vec2 size (dim,nv), where is the dimension of the vector and
-% nv the number of vectors.
-%
-% OUTPUT:
-%
-% cross : Array of column vectors, each element is corresponding
-% to the cross product of the respective components in vec1
-% and vec2.
-%
-% Description:
-%
-% Cross product of two vectors.
-%
-% Examples:
-%
-% Determine the cross products of:
-% (2.3,3.4,5.6) and (1.2,4.5,1.2)
-% (5.1,0.0,2.3) and (2.5,3.2,4.0)
-%
-% cross = veccross([2.3 5.1; 3.4 0.0; 5.6 2.3],[1.2 2.5; 4.5 3.2; 1.2 4.0]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if size(vec1,1) == 2
- % 2D vector
- cross = zeros(size(vec1));
- cross(3,:) = vec1(1,:).*vec2(2,:)-vec1(2,:).*vec2(1,:);
-else
- % 3D vector
- cross = [vec1(2,:).*vec2(3,:)-vec1(3,:).*vec2(2,:);
- vec1(3,:).*vec2(1,:)-vec1(1,:).*vec2(3,:);
- vec1(1,:).*vec2(2,:)-vec1(2,:).*vec2(1,:)];
-end
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecdot.m
--- a/extra/nurbs/inst/vecdot.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,50 +0,0 @@
-function dot = vecdot(vec1,vec2)
-%
-% VECDOT: The dot product of two vectors.
-%
-% Calling Sequence:
-%
-% dot = vecdot(vec1,vec2);
-%
-% INPUT:
-%
-% vec1 : An array of column vectors represented by a matrix of
-% vec2 size (dim,nv), where is the dimension of the vector and
-% nv the number of vectors.
-%
-% OUTPUT:
-%
-% dot : Row vector of scalars, each element corresponding to
-% the dot product of the respective components in vec1 and
-% vec2.
-%
-% Description:
-%
-% Scalar dot product of two vectors.
-%
-% Examples:
-%
-% Determine the dot product of
-% (2.3,3.4,5.6) and (1.2,4.5,1.2)
-% (5.1,0.0,2.3) and (2.5,3.2,4.0)
-%
-% dot = vecdot([2.3 5.1; 3.4 0.0; 5.6 2.3],[1.2 2.5; 4.5 3.2; 1.2 4.0]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-dot = sum(vec1.*vec2);
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecmag.m
--- a/extra/nurbs/inst/vecmag.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,46 +0,0 @@
-function mag = vecmag(vec)
-%
-% VECMAG: Magnitude of the vectors.
-%
-% Calling Sequence:
-%
-% mvec = vecmag(vec)
-%
-% INPUT:
-%
-% vec : An array of column vectors represented by a matrix of
-% size (dim,nv), where is the dimension of the vector and
-% nv the number of vectors.
-%
-% OUTPUT:
-%
-% mvec : Magnitude of the vectors, vector of size (1,nv).
-%
-% Description:
-%
-% Determines the magnitude of the vectors.
-%
-% Examples:
-%
-% Find the magnitude of the two vectors (0.0,2.0,1.3) and (1.5,3.4,2.3)
-%
-% mvec = vecmag([0.0 1.5; 2.0 3.4; 1.3 2.3]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-mag = sqrt(sum(vec.^2));
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecmag2.m
--- a/extra/nurbs/inst/vecmag2.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,47 +0,0 @@
-function mag = vecmag2(vec)
-%
-% VECMAG2: Squared magnitude of a set of vectors.
-%
-% Calling Sequence:
-%
-% mvec = vecmag2(vec)
-%
-% INPUT:
-%
-% vec : An array of column vectors represented by a matrix of
-% size (dim,nv), where dim is the dimension of the vector and
-% nv the number of vectors.
-%
-% OUTPUT:
-%
-% mvec : Squared magnitude of the vectors, vector of size (1,nv).
-%
-% Description:
-%
-% Determines the squared magnitude of the vectors.
-%
-% Examples:
-%
-% Find the squared magnitude of the two vectors (0.0,2.0,1.3)
-% and (1.5,3.4,2.3)
-%
-% mvec = vecmag2([0.0 1.5; 2.0 3.4; 1.3 2.3]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-mag = sum(vec.^2);
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecnorm.m
--- a/extra/nurbs/inst/vecnorm.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,46 +0,0 @@
-function nvec = vecnorm(vec)
-%
-% VECNORM: Normalise the vectors.
-%
-% Calling Sequence:
-%
-% nvec = vecnorn(vec);
-%
-% INPUT:
-%
-% vec : An array of column vectors represented by a matrix of
-% size (dim,nv), where is the dimension of the vector and
-% nv the number of vectors.
-%
-% OUTPUT:
-%
-% nvec : Normalised vectors, matrix the smae size as vec.
-%
-% Description:
-%
-% Normalises the array of vectors, returning the unit vectors.
-%
-% Examples:
-%
-% Normalise the two vectors (0.0,2.0,1.3) and (1.5,3.4,2.3)
-%
-% nvec = vecnorm([0.0 1.5; 2.0 3.4; 1.3 2.3]);
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-nvec = vec./repmat(sqrt(sum(vec.^2)),[size(vec,1) ones(1,ndims(vec)-1)]);
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecrot.m
--- a/extra/nurbs/inst/vecrot.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,53 +0,0 @@
-function rx = vecrot(angle, vector)
-%
-% VECROT: Transformation matrix for a rotation around the axis given by a vector.
-%
-% Calling Sequence:
-%
-% rx = vecrot (angle, vector);
-%
-% INPUT:
-%
-% angle : rotation angle defined in radians
-% vector: vector defining the rotation axis
-%
-% OUTPUT:
-%
-% rx: (4x4) Transformation matrix.
-%
-%
-% Description:
-%
-% Return the (4x4) Transformation matrix for a rotation about the axis
-% defined by vector, and by the given angle.
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2011 Rafael Vazquez
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-% Normalize the vector
-vec = vector / norm (vector);
-
-sn = sin (angle);
-cn = cos (angle);
-rx = [cn+vec(1)^2*(1-cn), vec(1)*vec(2)*(1-cn)-vec(3)*sn, vec(1)*vec(3)*(1-cn)+vec(2)*sn, 0;
- vec(1)*vec(2)*(1-cn)+vec(3)*sn, cn+vec(2)^2*(1-cn), vec(2)*vec(3)*(1-cn)-vec(1)*sn, 0;
- vec(1)*vec(3)*(1-cn)-vec(2)*sn, vec(2)*vec(3)*(1-cn)+vec(1)*sn, cn+vec(3)^2*(1-cn), 0;
- 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecrotx.m
--- a/extra/nurbs/inst/vecrotx.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,62 +0,0 @@
-function rx = vecrotx(angle)
-%
-% VECROTX: Transformation matrix for a rotation around the x axis.
-%
-% Calling Sequence:
-%
-% rx = vecrotx(angle);
-%
-% INPUT:
-%
-% angle : rotation angle defined in radians
-%
-% OUTPUT:
-%
-% rx : (4x4) Transformation matrix.
-%
-%
-% Description:
-%
-% Return the (4x4) Transformation matrix for a rotation about the x axis
-% by the defined angle.
-%
-% The matrix is:
-%
-% [ 1 0 0 0]
-% [ 0 cos(angle) -sin(angle) 0]
-% [ 0 sin(angle) cos(angle) 0]
-% [ 0 0 0 1]
-%
-% Examples:
-%
-% Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
-% around the x-axis
-%
-% line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
-% trans = vecrotx(%pi/4);
-% rline = nrbtform(line, trans);
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-sn = sin(angle);
-cn = cos(angle);
-rx = [1 0 0 0; 0 cn -sn 0; 0 sn cn 0; 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecroty.m
--- a/extra/nurbs/inst/vecroty.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,62 +0,0 @@
-function ry = vecroty(angle)
-%
-% VECROTY: Transformation matrix for a rotation around the y axis.
-%
-% Calling Sequence:
-%
-% ry = vecroty(angle);
-%
-% INPUT:
-%
-% angle : rotation angle defined in radians
-%
-% OUTPUT:
-%
-% ry : (4x4) Transformation matrix.
-%
-%
-% Description:
-%
-% Return the (4x4) Transformation matrix for a rotation about the y axis
-% by the defined angle.
-%
-% The matrix is:
-%
-% [ cos(angle) 0 sin(angle) 0]
-% [ 0 1 0 0]
-% [ -sin(angle) 0 cos(angle) 0]
-% [ 0 0 0 1]
-%
-% Examples:
-%
-% Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
-% around the y-axis
-%
-% line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
-% trans = vecroty(%pi/4);
-% rline = nrbtform(line, trans);
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-sn = sin(angle);
-cn = cos(angle);
-ry = [cn 0 sn 0; 0 1 0 0; -sn 0 cn 0; 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecrotz.m
--- a/extra/nurbs/inst/vecrotz.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,62 +0,0 @@
-function rz = vecrotz(angle)
-%
-% VECROTZ: Transformation matrix for a rotation around the z axis.
-%
-% Calling Sequence:
-%
-% rz = vecrotz(angle);
-%
-% INPUT:
-%
-% angle : rotation angle defined in radians
-%
-% OUTPUT:
-%
-% rz : (4x4) Transformation matrix.
-%
-%
-% Description:
-%
-% Return the (4x4) Transformation matrix for a rotation about the z axis
-% by the defined angle.
-%
-% The matrix is:
-%
-% [ cos(angle) -sin(angle) 0 0]
-% [ -sin(angle) cos(angle) 0 0]
-% [ 0 0 1 0]
-% [ 0 0 0 1]
-%
-% Examples:
-%
-% Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
-% around the z-axis
-%
-% line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
-% trans = vecrotz(%pi/4);
-% rline = nrbtform(line, trans);
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-sn = sin(angle);
-cn = cos(angle);
-rz = [cn -sn 0 0; sn cn 0 0; 0 0 1 0; 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vecscale.m
--- a/extra/nurbs/inst/vecscale.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,65 +0,0 @@
-function ss = vecscale(vector)
-
-%
-% VECSCALE: Transformation matrix for a scaling.
-%
-% Calling Sequence:
-%
-% ss = vecscale(svec)
-%
-% INPUT:
-%
-% svec : A vectors defining the scaling along the x,y and z axes.
-% i.e. [sx, sy, sy]
-%
-% OUTPUT:
-%
-% ss : Scaling Transformation Matrix
-%
-% Description:
-%
-% Returns a (4x4) Transformation matrix for scaling.
-%
-% The matrix is:
-%
-% [ sx 0 0 0]
-% [ 0 sy 0 0]
-% [ 0 0 sz 0]
-% [ 0 0 0 1]
-%
-% Example:
-%
-% Scale up the NURBS line (0.0,0.0,0.0) - (1.0,1.0,1.0) by 3 along
-% the x-axis, 2 along the y-axis and 4 along the z-axis.
-%
-% line = nrbline([0.0 0.0 0.0],[1.0 1.0 1.0]);
-% trans = vecscale([3.0 2.0 4.0]);
-% sline = nrbtform(line, trans);
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-if nargin < 1
- error('Scaling vector not specified');
-end
-
-s = [vector(:);0;0];
-ss = [s(1) 0 0 0; 0 s(2) 0 0; 0 0 s(3) 0; 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/inst/vectrans.m
--- a/extra/nurbs/inst/vectrans.m Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,65 +0,0 @@
-function dd = vectrans(vector)
-%
-% VECTRANS: Transformation matrix for a translation.
-%
-% Calling Sequence:
-%
-% st = vectrans(tvec)
-%
-% INPUT:
-%
-% tvec : A vectors defining the translation along the x,y and
-% z axes. i.e. [tx, ty, ty]
-%
-% OUTPUT:
-%
-% st : Translation Transformation Matrix
-%
-% Description:
-%
-% Returns a (4x4) Transformation matrix for translation.
-%
-% The matrix is:
-%
-% [ 1 0 0 tx ]
-% [ 0 1 0 ty ]
-% [ 0 0 1 tz ]
-% [ 0 0 0 1 ]
-%
-% Examples:
-%
-% Translate the NURBS line (0.0,0.0,0.0) - (1.0,1.0,1.0) by 3 along
-% the x-axis, 2 along the y-axis and 4 along the z-axis.
-%
-% line = nrbline([0.0 0.0 0.0],[1.0 1.0 1.0]);
-% trans = vectrans([3.0 2.0 4.0]);
-% tline = nrbtform(line, trans);
-%
-% See also:
-%
-% nrbtform
-%
-% Copyright (C) 2000 Mark Spink
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see .
-
-
-if nargin < 1
- error('Translation vector required');
-end
-
-v = [vector(:);0;0];
-dd = [1 0 0 v(1); 0 1 0 v(2); 0 0 1 v(3); 0 0 0 1];
-
-end
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/Makefile
--- a/extra/nurbs/src/Makefile Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,17 +0,0 @@
-OCTFILES=basisfun.oct bspeval.oct nrb_srf_basisfun__.oct surfderivcpts.oct basisfunder.oct \
-curvederivcpts.oct nrb_srf_basisfun_der__.oct surfderiveval.oct bspderiv.oct \
-nrbsurfderiveval.oct tbasisfun.oct
-
-MKOCTFILE ?= mkoctfile
-
-all: $(OCTFILES)
-
-low_level_functions.o: low_level_functions.cc
- $(MKOCTFILE) -c $<
-
-%.oct: %.cc low_level_functions.o
- $(MKOCTFILE) $< low_level_functions.o
-
-clean:
- -rm -f *.o core octave-core *.oct *~
-
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/basisfun.cc
--- a/extra/nurbs/src/basisfun.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,86 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include "low_level_functions.h"
-
-DEFUN_DLD(basisfun, args, nargout, "\n\
- BASISFUN: Compute B-Spline Basis Functions \n\
-\n\
-Calling Sequence:\n\
-\n\
- N = basisfun(iv,uv,p,U)\n\
-\n\
- INPUT:\n\
-\n\
- iv - knot span ( from FindSpan() )\n\
- uv - parametric point\n\
- p - spline degree\n\
- U - knot sequence\n\
-\n\
- OUTPUT:\n\
-\n\
- N - Basis functions vector(numel(uv)*(p+1))\n\
-\n\
- Algorithm A2.2 from 'The NURBS BOOK' pg70.\n\
-\n\
-")
-{
-
- octave_value_list retval;
- const NDArray i = args(0).array_value();
- const NDArray u = args(1).array_value();
- int p = args(2).idx_type_value();
- const RowVector U = args(3).row_vector_value();
- RowVector N(p+1, 0.0);
- Matrix B(u.numel (), p+1, 0.0);
-
- if (!error_state)
- {
- for (octave_idx_type ii(0); ii < u.numel (); ii++)
- {
- basisfun(int(i(ii)), u(ii), p, U, N);
- B.insert(N, ii, 0);
- }
-
- retval(0) = octave_value(B);
- }
- return retval;
-}
-
-/*
-%!shared n, U, p, u, s
-%!test
-%! n = 3;
-%! U = [0 0 0 1/2 1 1 1];
-%! p = 2;
-%! u = linspace(0, 1, 10);
-%! s = findspan(n, p, u, U);
-%! assert (s, [2*ones(1, 5) 3*ones(1, 5)]);
-%!test
-%! Bref = [1.00000 0.00000 0.00000
-%! 0.60494 0.37037 0.02469
-%! 0.30864 0.59259 0.09877
-%! 0.11111 0.66667 0.22222
-%! 0.01235 0.59259 0.39506
-%! 0.39506 0.59259 0.01235
-%! 0.22222 0.66667 0.11111
-%! 0.09877 0.59259 0.30864
-%! 0.02469 0.37037 0.60494
-%! 0.00000 0.00000 1.00000];
-%! B = basisfun(s, u, p, U);
-%! assert (B, Bref, 1e-5);
-*/
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/basisfunder.cc
--- a/extra/nurbs/src/basisfunder.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,71 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include "low_level_functions.h"
-
-DEFUN_DLD(basisfunder, args, nargout,"\n\
- BASISFUNDER: B-Spline Basis function derivatives\n\
-\n\
- Calling Sequence:\n\
-\n\
- ders = basisfunder (ii, pl, uu, k, nd)\n\
-\n\
- INPUT:\n\
-\n\
- ii - knot span\n\
- pl - degree of curve\n\
- uu - parametric points\n\
- k - knot vector\n\
- nd - number of derivatives to compute\n\
-\n\
- OUTPUT:\n\
-\n\
- ders - ders(n, i, :) (i-1)-th derivative at n-th point\n\
-\n\
- Adapted from Algorithm A2.3 from 'The NURBS BOOK' pg72. \n\
-\n\
-")
-{
- octave_value_list retval;
-
- const NDArray i = args(0).array_value ();
- int pl = args(1).int_value ();
- const NDArray u = args(2).array_value ();
- const RowVector U = args(3).row_vector_value ();
- int nd = args(4).int_value ();
-
- if (!error_state)
- {
- if (i.numel () != u.numel ())
- print_usage ();
-
- NDArray dersv (dim_vector (i.numel (), nd+1, pl+1), 0.0);
- NDArray ders(dim_vector(nd+1, pl+1), 0.0);
- for ( octave_idx_type jj(0); jj < i.numel (); jj++)
- {
- basisfunder (int (i(jj)), pl, u(jj), U, nd, ders);
-
- for (octave_idx_type kk(0); kk < nd+1; kk++)
- for (octave_idx_type ll(0); ll < pl+1; ll++)
- {
- dersv(jj, kk, ll) = ders(kk, ll);
- }
- }
- retval(0) = dersv;
- }
- return retval;
-}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/bspderiv.cc
--- a/extra/nurbs/src/bspderiv.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,73 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include "low_level_functions.h"
-
-DEFUN_DLD(bspderiv, args, nargout,"\n\
- BSPDERIV: B-Spline derivative\n\
-\n\
-\n\
- Calling Sequence:\n\
-\n\
- [dc,dk] = bspderiv(d,c,k)\n\
-\n\
- INPUT:\n\
- \n\
- d - degree of the B-Spline\n\
- c - control points double matrix(mc,nc)\n\
- k - knot sequence double vector(nk)\n\
- \n\
- OUTPUT:\n\
- \n\
- dc - control points of the derivative double matrix(mc,nc)\n\
- dk - knot sequence of the derivative double vector(nk)\n\
- \n\
- Modified version of Algorithm A3.3 from 'The NURBS BOOK' pg98.\n\
-")
-{
- //if (bspderiv_bad_arguments(args, nargout))
- // return octave_value_list();
-
- int d = args(0).int_value();
- const Matrix c = args(1).matrix_value();
- const RowVector k = args(2).row_vector_value();
- octave_value_list retval;
- octave_idx_type mc = c.rows(), nc = c.cols(), nk = k.numel();
- Matrix dc (mc, nc-1, 0.0);
- RowVector dk(nk-2, 0.0);
-
- if (!error_state)
- {
- double tmp;
-
- for (octave_idx_type i(0); i<=nc-2; i++)
- {
- tmp = (double)d / (k(i+d+1) - k(i+1));
- for ( octave_idx_type j(0); j<=mc-1; j++)
- dc(j,i) = tmp*(c(j,i+1) - c(j,i));
- }
-
- for ( octave_idx_type i(1); i <= nk-2; i++)
- dk(i-1) = k(i);
-
- if (nargout>1)
- retval(1) = octave_value(dk);
- retval(0) = octave_value(dc);
- }
-
- return(retval);
-}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/bspeval.cc
--- a/extra/nurbs/src/bspeval.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,122 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include "low_level_functions.h"
-#include
-
-static bool bspeval_bad_arguments(const octave_value_list& args);
-
-DEFUN_DLD(bspeval, args, nargout,"\
- BSPEVAL: Evaluate B-Spline at parametric points\n\
-\n\
-\n\
- Calling Sequence:\n\
-\n\
- p = bspeval(d,c,k,u)\n\
-\n\
- INPUT:\n\
-\n\
- d - Degree of the B-Spline.\n\
- c - Control Points, matrix of size (dim,nc).\n\
- k - Knot sequence, row vector of size nk.\n\
- u - Parametric evaluation points, row vector of size nu.\n\
- \n\
- OUTPUT:\n\
-\n\
- p - Evaluated points, matrix of size (dim,nu)\n\
-")
-{
-
- octave_value_list retval;
- if (!bspeval_bad_arguments (args))
- {
- int d = args(0).int_value();
- Matrix c = args(1).matrix_value();
- RowVector k = args(2).row_vector_value();
- NDArray u = args(3).array_value();
-
- octave_idx_type nu = u.numel ();
- octave_idx_type mc = c.rows(),
- nc = c.cols();
-
- Matrix p(mc, nu, 0.0);
-
- if (!error_state)
- {
- if (nc + d == k.numel () - 1)
- {
- //#pragma omp parallel default (none) shared (d, c, k, u, nu, mc, nc, p)
- {
- RowVector N(d+1,0.0);
- int s, tmp1;
- double tmp2;
- //#pragma omp for
- for (octave_idx_type col=0; col.
-*/
-
-#include
-#include "low_level_functions.h"
-
-
-DEFUN_DLD(curvederivcpts, args, nargout,"\
-\nCURVEDERIVCPTS: Compute control points of n-th derivatives of a B-spline curve.\n \
-\n \
-\n usage: pk = curvederivcpts (n, p, U, P, d) \
-\n pk = curvederivcpts (n, p, U, P, d, r1 r2) \
-\n \
-\n If r1, r2 are not given, all the control points are computed. \
-\n \
-\n INPUT: \
-\n n+1 = number of control points \
-\n p = degree of the spline \
-\n d = maximum derivative order (d<=p) \
-\n U = knots \
-\n P = control points \
-\n r1 = first control point to compute \
-\n r2 = auxiliary index for the last control point to compute \
-\n\
-\n OUTPUT: \
-\n pk(k,i) = i-th control point (k-1)-th derivative, r1 <= i <= r2-k \
-\n \
-\n Adaptation of algorithm A3.3 from the NURBS book\n")
-
-{
-
- octave_value_list retval;
-
- octave_idx_type n = args(0).idx_type_value ();
- octave_idx_type p = args(1).idx_type_value ();
- RowVector U = args(2).row_vector_value (false, true);
- NDArray P = args(3).array_value ();
- octave_idx_type d = args(4).idx_type_value ();
-
- octave_idx_type r1(0), r2(n);
- if (args.length () == 7)
- {
- r1 = args (5).idx_type_value ();
- r2 = args (6).idx_type_value ();
- }
- else if (args.length () > 5)
- print_usage ();
-
- if (! error_state)
- {
- octave_idx_type r = r2 - r1;
- Matrix pk (d+1 <= r+1 ? d+1 : r+1, r+1, 0.0);
-
- curvederivcpts (n, p, U, P, d, r1, r2, pk);
-
- retval(0) = octave_value (pk);
- }
- return retval;
-}
-
-/*
-%!test
-%! line = nrbmak([0.0 1.5; 0.0 3.0],[0.0 0.0 1.0 1.0]);
-%! pk = curvederivcpts (line.number-1, line.order-1, line.knots,
-%! line.coefs(1,:), 2);
-%! assert (pk, [0 3/2; 3/2 0], 100*eps);
-*/
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/low_level_functions.cc
--- a/extra/nurbs/src/low_level_functions.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,385 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
- some functions are adapted from the m-file implementation which is
- Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-
-#include
-#include "low_level_functions.h"
-#include
-
-octave_idx_type
-findspan (int n, int p, double u, const RowVector& U)
-
-// Find the knot span of the parametric point u.
-//
-// INPUT:
-//
-// n - number of control points - 1
-// p - spline degree
-// u - parametric point
-// U - knot sequence
-//
-// RETURN:
-//
-// s - knot span
-//
-// Note: This is NOT
-// Algorithm A2.1 from 'The NURBS BOOK' pg68
-// as that algorithm only works for nonperiodic
-// knot vectors, nonetheless the results should
-// be EXACTLY the same if U is nonperiodic
-
-/*
-Below is the original implementation from the NURBS Book
-{
- int low, high, mid;
- // special case
- if (u == U(n+1)) return(n);
-
- // do binary search
- low = p;
- high = n + 1;
- mid = (low + high) / 2;
- while (u < U(mid) || u >= U(mid+1))
- {
-
- if (u < U(mid))
- high = mid;
- else
- low = mid;
- mid = (low + high) / 2;
- }
-
- return(mid);
-}
-*/
-
-{
- // FIXME : this implementation has linear, rather than log complexity
- int ret = 0;
-
- if (u > U.xelem (U.numel () - 1) || u < U.xelem (0))
- error ("Value %g is outside the knot span", u);
- else
- while ((ret++ < n) && (U(ret) <= u)) { };
-
- return (ret-1);
-}
-
-void
-basisfun (int i, double u, int p, const RowVector& U, RowVector& N)
-
-// Basis Function.
-//
-// INPUT:
-//
-// i - knot span ( from FindSpan() )
-// u - parametric point
-// p - spline degree
-// U - knot sequence
-//
-// OUTPUT:
-//
-// N - Basis functions vector[p+1]
-//
-// Algorithm A2.2 from 'The NURBS BOOK' pg70.
-{
- int j,r;
- double saved, temp;
-
- // work space
- OCTAVE_LOCAL_BUFFER(double, left, p+1);
- OCTAVE_LOCAL_BUFFER(double, right, p+1);
-
- N(0) = 1.0;
- for (j = 1; j <= p; j++)
- {
- left[j] = u - U(i+1-j);
- right[j] = U(i+j) - u;
- saved = 0.0;
-
- for (r = 0; r < j; r++)
- {
- temp = N(r) / (right[r+1] + left[j-r]);
- N(r) = saved + right[r+1] * temp;
- saved = left[j-r] * temp;
- }
-
- N(j) = saved;
- }
-
-}
-
-
-void basisfunder (int i, int pl, double u, const RowVector& u_knotl, int nders, NDArray& ders)
-{
-
-// BASISFUNDER: B-Spline Basis function derivatives
-//
-// INPUT:
-//
-// i - knot span
-// pl - degree of curve
-// u - parametric points
-// k - knot vector
-// nd - number of derivatives to compute
-//
-// OUTPUT:
-//
-// ders - ders(n, i, :) (i-1)-th derivative at n-th point
-
-
- // ders = zeros(nders+1,pl+1);
- Matrix ndu(octave_idx_type(pl+1), octave_idx_type(pl+1), 0.0); // ndu = zeros(pl+1,pl+1);
- RowVector left(octave_idx_type(pl+1), 0.0); // left = zeros(pl+1);
- RowVector right(left); // right = zeros(pl+1);
- Matrix a(2, octave_idx_type(pl+1), 0.0); // a = zeros(2,pl+1);
- double saved = 0.0, d = 0.0, temp = 1.0;
- octave_idx_type s1(0), s2(1), rk, pk, j, k, r, j1, j2;
-
-
- ndu(0,0) = 1; // ndu(1,1) = 1;
-
- for (j=1; j<=pl; j++) // for j = 1:pl
- {
- left(j) = u - u_knotl(i+1-j); // left(j+1) = u - u_knotl(i+1-j);
- right(j) = u_knotl(i+j) - u; // right(j+1) = u_knotl(i+j) - u;
- saved = 0.0; // saved = 0;
- for (r=0; r<=j-1; r++) // for r = 0:j-1
- {
- ndu(j, r) = right(r+1) + left(j-r); // ndu(j+1,r+1) = right(r+2) + left(j-r+1);
- temp = ndu(r,j-1)/ndu(j,r); // temp = ndu(r+1,j)/ndu(j+1,r+1);
- ndu(r,j) = saved + right(r+1)*temp; // ndu(r+1,j+1) = saved + right(r+2)*temp;
- saved = left(j-r)*temp; // saved = left(j-r+1)*temp;
- } // end
- ndu(j,j) = saved; // ndu(j+1,j+1) = saved;
- } // end
-
- for (j=0; j<=pl; j++) // for j = 0:pl
- ders(0,j) = ndu(j,pl); // ders(1,j+1) = ndu(j+1,pl+1);
- // end
-
- for (r=0; r<=pl; r++) // for r = 0:pl
- {
- s1 = 0; // s1 = 0;
- s2 = 1; // s2 = 1;
- a(0,0) = 1; // a(1,1) = 1;
- for (k=1; k<=nders; k++) // for k = 1:nders %compute kth derivative
- {
-
- d = 0.0; // d = 0;
- rk = r-k; // rk = r-k;
- pk = pl - k; // pk = pl-k;
-
- if (r >= k) // if (r >= k)
- {
- a(s2, 0) = a(s1, 0)/ndu(pk+1,rk); // a(s2+1,1) = a(s1+1,1)/ndu(pk+2,rk+1);
- d = a(s2, 0)*ndu(rk,pk); // d = a(s2+1,1)*ndu(rk+1,pk+1);
- } // end
-
- if (rk >= -1) // if (rk >= -1)
- j1 = 1; // j1 = 1;
- else // else
- j1 = -rk; // j1 = -rk;
- // end
-
- if ((r-1) <= pk) // if ((r-1) <= pk)
- j2 = k-1; // j2 = k-1;
- else // else
- j2 = pl-r; // j2 = pl-r;
- // end
-
- for (j=j1; j <= j2; j++) // for j = j1:j2
- {
- a(s2,j) = (a(s1,j) - a(s1,j-1))/ndu(pk+1,rk+j); // a(s2+1,j+1) = (a(s1+1,j+1) - a(s1+1,j))/ndu(pk+2,rk+j+1);
- d += a(s2,j)*ndu(rk+j,pk); // d = d + a(s2+1,j+1)*ndu(rk+j+1,pk+1);
- } // end
-
- if (r <= pk) // if (r <= pk)
- {
- a(s2,k) = -a(s1,k-1)/ndu(pk+1,r); // a(s2+1,k+1) = -a(s1+1,k)/ndu(pk+2,r+1);
- d += a(s2,k)*ndu(r,pk); // d = d + a(s2+1,k+1)*ndu(r+1,pk+1);
- } // end
-
- ders(k,r) = d; // ders(k+1,r+1) = d;
- j = s1; // j = s1;
- s1 = s2; // s1 = s2;
- s2 = j; // s2 = j;
- } // end
- } // end
-
- r = pl; // r = pl;
- for (k=1; k <= nders; k++) // for k = 1:nders
- {
- for (j=0; j<=pl; j++) // for j = 0:pl
- ders(k,j) = ders(k,j)*r; // ders(k+1,j+1) = ders(k+1,j+1)*r;
- // end
- r = r*(pl-k); // r = r*(pl-k);
- } // end
-
-}
-
-
-int curvederivcpts (octave_idx_type n, octave_idx_type p,
- const RowVector &U, const NDArray &P,
- octave_idx_type d, octave_idx_type r1,
- octave_idx_type r2, Matrix &pk)
-{
- octave_idx_type r = r2 - r1;
- for (octave_idx_type i(0); i<=r; i++)
- pk(0, i) = P(r1+i);
-
- for (octave_idx_type k (1); k<=d; k++)
- {
- octave_idx_type tmp = p - k + 1;
- for (octave_idx_type i (0); i<=r-k; i++)
- {
- pk (k, i) = tmp * (pk(k-1,i+1)-pk(k-1,i)) /
- (U(r1+i+p+1)-U(r1+i+k));
- }
- }
- return 0;
-}
-
-
-
-int surfderivcpts (octave_idx_type n, octave_idx_type p, const RowVector& U,
- octave_idx_type m, octave_idx_type q, const RowVector& V,
- const Matrix& P, octave_idx_type d, octave_idx_type r1,
- octave_idx_type r2, octave_idx_type s1,
- octave_idx_type s2, NDArray &pkl)
-{
- octave_idx_type r = r2-r1, s = s2-s1;
-
- octave_idx_type du = d <= p ? d : p;
- octave_idx_type dv = d <= q ? d : q;
-
- dim_vector idxa (4, 1);
-
- Array idxta (idxa, 0);
- Array idxva (idxa, idx_vector (':'));
-
- idxa.resize (4);
- idxa(0) = (du+1); idxa(1) = (dv+1);
- idxa(2) = (r+1); idxa(3) = (s+1);
-
- pkl.resize (idxa, 0.0);
-
- for (octave_idx_type j(s1); j<=s2; j++)
- {
-
- Matrix temp (du <= n ? (du+1) : (n+1), n+1, 0.0);
- curvederivcpts (n, p, U, P.extract (0, j, P.rows()-1, P.cols ()-1), du, r1, r2, temp);
- for (octave_idx_type k(0); k<=du; k++)
- {
-
- for ( octave_idx_type i(0); i<=r-k; i++)
- {
- assert (k idx(dim_vector (4, 1), 0);
- octave_idx_type du = d <= p ? d: p;
- octave_idx_type dv = d <= q ? d: q;
-
- skl.resize (d+1, d+1, 0.0);
-
- octave_idx_type uspan = findspan (n, p, u, U);
- Matrix Nu (p+1, p+1, 0.0);
- for (octave_idx_type ip(0); ip<=p; ip++)
- {
- RowVector temp (ip+1, 0.0);
- basisfun (uspan, u, ip, U, temp);
- Nu.insert (temp.transpose (), 0,ip);
- }
-
- octave_idx_type vspan = findspan (m, q, v, V);
- Matrix Nv (q+1, q+1, 0.0);
- for (octave_idx_type iq(0); iq<=q; iq++)
- {
- RowVector temp (iq+1, 0.0);
- basisfun (vspan, v, iq, V, temp);
- Nv.insert (temp.transpose (), 0, iq);
- }
- NDArray pkl;
- surfderivcpts (n, p, U, m, q, V, P, d, uspan-p, uspan, vspan-q, vspan, pkl);
-
- for (octave_idx_type k(0); k<=du; k++)
- {
- octave_idx_type dd = d-k <= dv ? d-k : dv;
- for (octave_idx_type l(0);l <= dd; l++)
- {
- skl(k,l) = 0.0;
- for (octave_idx_type i(0); i<=q-l; i++)
- {
- double tmp = 0.0;
- for (octave_idx_type j(0); j<=p-k; j++)
- {
- idx(0) = k; idx(1)=l; idx(2)=j; idx(3) =i;
- tmp += Nu(j,p-k) * pkl(idx);
- }
- skl(k,l) += Nv(i,q-l) * tmp;
- }
- }
- }
- return (0);
-}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/low_level_functions.h
--- a/extra/nurbs/src/low_level_functions.h Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,39 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-octave_idx_type findspan(int n, int p, double u, const RowVector& U);
-
-void basisfun(int i, double u, int p, const RowVector& U, RowVector& N);
-
-void basisfunder (int i, int pl, double uu, const RowVector& u_knotl,
- int nders, NDArray& dersv);
-
-int curvederivcpts (octave_idx_type n, octave_idx_type p,
- const RowVector &U, const NDArray &P,
- octave_idx_type d, octave_idx_type r1,
- octave_idx_type r2,
- Matrix &pk);
-
-int surfderivcpts (octave_idx_type n, octave_idx_type p, const RowVector& U,
- octave_idx_type m, octave_idx_type q, const RowVector& V,
- const Matrix& P, octave_idx_type d, octave_idx_type r1,
- octave_idx_type r2, octave_idx_type s1,
- octave_idx_type s2, NDArray &pkl);
-
-int surfderiveval (octave_idx_type n, octave_idx_type p, const RowVector &U,
- octave_idx_type m, octave_idx_type q, const RowVector &V,
- const Matrix &P, double u, double v, octave_idx_type d,
- Matrix &skl);
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/nrb_srf_basisfun__.cc
--- a/extra/nurbs/src/nrb_srf_basisfun__.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,129 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include
-#include
-#include "low_level_functions.h"
-
-DEFUN_DLD(nrb_srf_basisfun__, args, nargout,"\
- NRB_SRF_BASISFUN__: Undocumented private function\
-")
-{
-
- octave_value_list retval, newargs;
-
- const NDArray points = args(0).array_value();
- const octave_scalar_map nrb = args(1).scalar_map_value();
-
- if (!error_state)
- {
-
- const Cell knots = nrb.contents("knots").cell_value();
- const NDArray coefs = nrb.contents("coefs").array_value();
- octave_idx_type m = static_cast ((nrb.contents("number").vector_value())(0)) - 1; // m = size (nrb.coefs, 2) -1;
- octave_idx_type n = static_cast ((nrb.contents("number").vector_value())(1)) - 1; // n = size (nrb.coefs, 3) -1;
- octave_idx_type p = static_cast ((nrb.contents("order").vector_value())(0)) - 1; // p = nrb.order(1) -1;
- octave_idx_type q = static_cast ((nrb.contents("order").vector_value())(1)) - 1; // q = nrb.order(2) -1;
-
- Array idx(dim_vector (2, 1), idx_vector(':'));
- idx(0) = 0;
- const NDArray u(points.index (idx).squeeze ()); // u = points(1,:);
-
- idx(0) = 1;
- const NDArray v(points.index (idx).squeeze ()); // v = points(2,:);
-
- octave_idx_type npt = u.numel (); // npt = length(u);
- RowVector M(p+1, 0.0), N (q+1, 0.0);
- Matrix RIkJk(npt, (p+1)*(q+1), 0.0);
- Matrix indIkJk(npt, (p+1)*(q+1), 0.0);
- RowVector denom(npt, 0.0);
-
- const RowVector U(knots(0).row_vector_value ()); // U = nrb.knots{1};
-
- const RowVector V(knots(1).row_vector_value ()); // V = nrb.knots{2};
-
- Array idx2(dim_vector (3, 1), idx_vector(':')); idx2(0) = 3;
- NDArray w (coefs.index (idx2).squeeze ()); // w = squeeze(nrb.coefs(4,:,:));
-
- RowVector spu(u);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- spu(ii) = findspan(m, p, u(ii), U);
- } // spu = findspan (m, p, u, U);
-
- newargs(3) = U; newargs(2) = p; newargs(1) = u; newargs(0) = spu;
- Matrix Ik = feval (std::string("numbasisfun"), newargs, 1)(0).matrix_value (); // Ik = numbasisfun (spu, u, p, U);
-
- RowVector spv(v);
- for (octave_idx_type ii(0); ii < v.numel (); ii++)
- {
- spv(ii) = findspan(n, q, v(ii), V);
- } // spv = findspan (n, q, v, V);
-
- newargs(3) = V; newargs(2) = q; newargs(1) = v; newargs(0) = spv;
- Matrix Jk = feval (std::string("numbasisfun"), newargs, 1)(0).matrix_value (); // Jk = numbasisfun (spv, v, q, V);
-
- Matrix NuIkuk(npt, p+1, 0.0);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- basisfun (int(spu(ii)), u(ii), p, U, M);
- NuIkuk.insert (M, ii, 0);
- } // NuIkuk = basisfun (spu, u, p, U);
-
- Matrix NvJkvk(v.numel (), q+1, 0.0);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- basisfun(int(spv(ii)), v(ii), q, V, N);
- NvJkvk.insert (N, ii, 0);
- } // NvJkvk = basisfun (spv, v, q, V);
-
-
- for (octave_idx_type k(0); k < npt; k++)
- for (octave_idx_type ii(0); ii < p+1; ii++)
- for (octave_idx_type jj(0); jj < q+1; jj++)
- denom(k) += NuIkuk(k, ii) * NvJkvk(k, jj) *
- w(static_cast (Ik(k, ii)),
- static_cast (Jk(k, jj)));
-
-
- for (octave_idx_type k(0); k < npt; k++)
- for (octave_idx_type ii(0); ii < p+1; ii++)
- for (octave_idx_type jj(0); jj < q+1; jj++)
- {
-
- RIkJk(k, octave_idx_type(ii+(p+1)*jj)) = NuIkuk(k, ii) * NvJkvk(k, jj) *
- w(static_cast (Ik(k, ii)), static_cast (Jk(k, jj)))
- / denom(k);
-
- indIkJk(k, octave_idx_type(ii+(p+1)*jj))= Ik(k, ii) + (m+1) * Jk(k, jj) + 1;
- }
-
- // for k=1:npt
- // [Jkb, Ika] = meshgrid(Jk(k, :), Ik(k, :));
- // indIkJk(k, :) = sub2ind([m+1, n+1], Ika(:)+1, Jkb(:)+1);
- // wIkaJkb(1:p+1, 1:q+1) = reshape (w(indIkJk(k, :)), p+1, q+1);
-
- // NuIkukaNvJkvk(1:p+1, 1:q+1) = (NuIkuk(k, :).' * NvJkvk(k, :));
- // RIkJk(k, :) = (NuIkukaNvJkvk .* wIkaJkb ./ sum(sum(NuIkukaNvJkvk .* wIkaJkb)))(:).';
- // end
-
- retval(0) = RIkJk; // B = RIkJk;
- retval(1) = indIkJk; // N = indIkJk;
-
- }
- return retval;
-}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/nrb_srf_basisfun_der__.cc
--- a/extra/nurbs/src/nrb_srf_basisfun_der__.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,164 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include
-#include
-#include "low_level_functions.h"
-
-DEFUN_DLD(nrb_srf_basisfun_der__, args, nargout,"\
- NRB_SRF_BASISFUN_DER__: Undocumented private function \
-")
-{
- //function [Bu, Bv, N] = nrb_srf_basisfun_der__ (points, nrb);
-
- octave_value_list retval, newargs;
-
- const NDArray points = args(0).array_value();
- const octave_scalar_map nrb = args(1).scalar_map_value();
-
- if (!error_state)
- {
- const Cell knots = nrb.contents("knots").cell_value();
- const NDArray coefs = nrb.contents("coefs").array_value();
- octave_idx_type m = static_cast ((nrb.contents("number").vector_value())(0)) - 1; // m = size (nrb.coefs, 2) -1;
- octave_idx_type n = static_cast ((nrb.contents("number").vector_value())(1)) - 1; // n = size (nrb.coefs, 3) -1;
- octave_idx_type p = static_cast ((nrb.contents("order").vector_value())(0)) - 1; // p = nrb.order(1) -1;
- octave_idx_type q = static_cast ((nrb.contents("order").vector_value())(1)) - 1; // q = nrb.order(2) -1;
-
- Array idx(dim_vector (2, 1), idx_vector(':'));
- idx(0) = 0;
- const NDArray u(points.index (idx).squeeze ()); // u = points(1,:);
-
- idx(0) = 1;
- const NDArray v(points.index (idx).squeeze ()); // v = points(2,:);
-
- octave_idx_type npt = u.numel (); // npt = length(u);
-
- RowVector M(p+1, 0.0), N (q+1, 0.0);
- Matrix Nout(npt, (p+1)*(q+1), 0.0);
- Matrix Bu(npt, (p+1)*(q+1), 0.0);
- Matrix Bv(npt, (p+1)*(q+1), 0.0);
- RowVector Denom(npt, 0.0);
- RowVector Denom_du(npt, 0.0);
- RowVector Denom_dv(npt, 0.0);
- Matrix Num(npt, (p+1)*(q+1), 0.0);
- Matrix Num_du(npt, (p+1)*(q+1), 0.0);
- Matrix Num_dv(npt, (p+1)*(q+1), 0.0);
-
- const RowVector U(knots(0).row_vector_value ()); // U = nrb.knots{1};
-
- const RowVector V(knots(1).row_vector_value ()); // V = nrb.knots{2};
-
- Array idx2(dim_vector (3, 1), idx_vector(':')); idx2(0) = 3;
- NDArray w (coefs.index (idx2).squeeze ()); // w = squeeze(nrb.coefs(4,:,:));
-
- RowVector spu(u);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- spu(ii) = findspan(m, p, u(ii), U);
- } // spu = findspan (m, p, u, U);
-
- newargs(3) = U; newargs(2) = p; newargs(1) = u; newargs(0) = spu;
- Matrix Ik = feval (std::string("numbasisfun"), newargs, 1)(0).matrix_value (); // Ik = numbasisfun (spu, u, p, U);
-
- RowVector spv(v);
- for (octave_idx_type ii(0); ii < v.numel (); ii++)
- {
- spv(ii) = findspan(n, q, v(ii), V);
- } // spv = findspan (n, q, v, V);
-
- newargs(3) = V; newargs(2) = q; newargs(1) = v; newargs(0) = spv;
- Matrix Jk = feval (std::string("numbasisfun"), newargs, 1)(0).matrix_value (); // Jk = numbasisfun (spv, v, q, V);
-
- Matrix NuIkuk(npt, p+1, 0.0);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- basisfun (int(spu(ii)), u(ii), p, U, M);
- NuIkuk.insert (M, ii, 0);
- } // NuIkuk = basisfun (spu, u, p, U);
-
- Matrix NvJkvk(v.numel (), q+1, 0.0);
- for (octave_idx_type ii(0); ii < npt; ii++)
- {
- basisfun(int(spv(ii)), v(ii), q, V, N);
- NvJkvk.insert (N, ii, 0);
- } // NvJkvk = basisfun (spv, v, q, V);
-
-
- newargs(4) = 1; newargs(3) = U; newargs(2) = u; newargs(1) = p; newargs(0) = spu;
- NDArray NuIkukprime = feval (std::string("basisfunder"), newargs, 1)(0).array_value (); // NuIkukprime = basisfunder (spu, p, u, U, 1);
- // NuIkukprime = squeeze(NuJkukprime(:,2,:));
-
- newargs(4) = 1; newargs(3) = V; newargs(2) = v; newargs(1) = q; newargs(0) = spv;
- NDArray NvJkvkprime = feval (std::string("basisfunder"), newargs, 1)(0).array_value (); // NvJkvkprime = basisfunder (spv, q, v, V, 1);
- // NvJkvkprime = squeeze(NvJkvkprime(:,2,:));
-
- for (octave_idx_type k(0); k < npt; k++)
- for (octave_idx_type ii(0); ii < p+1; ii++)
- for (octave_idx_type jj(0); jj < q+1; jj++)
- {
- Num(k, ii+jj*(p+1)) = NuIkuk(k, ii) * NvJkvk(k, jj) *
- w(static_cast (Ik(k, ii)),
- static_cast (Jk(k, jj)));
- Denom(k) += Num(k, ii+jj*(p+1));
-
- Num_du(k, ii+jj*(p+1)) = NuIkukprime(k, 1, ii) * NvJkvk(k, jj) *
- w(static_cast (Ik(k, ii)),
- static_cast (Jk(k, jj)));
- Denom_du(k) += Num_du(k, ii+jj*(p+1));
-
- Num_dv(k, ii+jj*(p+1)) = NuIkuk(k, ii) * NvJkvkprime(k, 1, jj) *
- w(static_cast (Ik(k, ii)),
- static_cast (Jk(k, jj)));
-
- Denom_dv(k) += Num_dv(k, ii + jj * (p+1));
- }
-
- for (octave_idx_type k(0); k < npt; k++)
- for (octave_idx_type ii(0); ii < p+1; ii++)
- for (octave_idx_type jj(0); jj < q+1; jj++)
- {
- Bu(k, octave_idx_type(ii+(p+1)*jj)) = (Num_du(k, ii+jj*(p+1))/Denom(k) - Denom_du(k)*Num(k, ii+jj*(p+1))/(Denom(k)*Denom(k)));
- Bv(k, octave_idx_type(ii+(p+1)*jj)) = (Num_dv(k, ii+jj*(p+1))/Denom(k) - Denom_dv(k)*Num(k, ii+jj*(p+1))/(Denom(k)*Denom(k)));
- Nout(k, octave_idx_type(ii+(p+1)*jj))= Ik(k, ii)+(m+1)*Jk(k, jj)+1;
- }
-
- // for k=1:npt
- // [Ika, Jkb] = meshgrid(Ik(k, :), Jk(k, :));
-
- // N(k, :) = sub2ind([m+1, n+1], Ika(:)+1, Jkb(:)+1);
- // wIkaJkb(1:p+1, 1:q+1) = reshape (w(N(k, :)), p+1, q+1);
-
- // Num = (NuIkuk(k, :).' * NvJkvk(k, :)) .* wIkaJkb;
- // Num_du = (NuIkukprime(k, :).' * NvJkvk(k, :)) .* wIkaJkb;
- // Num_dv = (NuIkuk(k, :).' * NvJkvkprime(k, :)) .* wIkaJkb;
- // Denom = sum(sum(Num));
- // Denom_du = sum(sum(Num_du));
- // Denom_dv = sum(sum(Num_dv));
-
- // Bu(k, :) = (Num_du/Denom - Denom_du.*Num/Denom.^2)(:).';
- // Bv(k, :) = (Num_dv/Denom - Denom_dv.*Num/Denom.^2)(:).';
- // end
-
-
- retval(2) = Nout;
- retval(1) = Bv;
- retval(0) = Bu;
-
- }
- return retval;
-}
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/nrbsurfderiveval.cc
--- a/extra/nurbs/src/nrbsurfderiveval.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,442 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include
-#include
-#include "low_level_functions.h"
-
-static double gammaln(double xx)
-// Compute logarithm of the gamma function
-// Algorithm from 'Numerical Recipes in C, 2nd Edition' pg214.
-{
- double x,y,tmp,ser;
- static double cof[6] = {76.18009172947146,-86.50532032291677,
- 24.01409824083091,-1.231739572450155,
- 0.12086650973866179e-2, -0.5395239384953e-5};
- int j;
- y = x = xx;
- tmp = x + 5.5;
- tmp -= (x+0.5) * log(tmp);
- ser = 1.000000000190015;
- for (j=0; j<=5; j++) ser += cof[j]/++y;
- return -tmp+log(2.5066282746310005*ser/x);
-}
-
-
-static double factln(int n)
-// computes ln(n!)
-// Numerical Recipes in C
-// Algorithm from 'Numerical Recipes in C, 2nd Edition' pg215.
-{
- static int ntop = 0;
- static double a[101];
-
- if (n <= 1) return 0.0;
- while (n > ntop)
- {
- ++ntop;
- a[ntop] = gammaln(ntop+1.0);
- }
- return a[n];
-}
-
-static double bincoeff(int n, int k)
-// Computes the binomial coefficient.
-//
-// ( n ) n!
-// ( ) = --------
-// ( k ) k!(n-k)!
-//
-// Algorithm from 'Numerical Recipes in C, 2nd Edition' pg215.
-{
- return floor(0.5+exp(factln(n)-factln(k)-factln(n-k)));
-}
-
-
-DEFUN_DLD(nrbsurfderiveval, args, nargout,"\
-\nNRBSURFDERIVEVAL: Evaluate n-th order derivatives of a NURBS surface.\n\
-\n\
-\n usage: skl = nrbsurfderiveval (srf, [u; v], d) \
-\n\
-\n INPUT :\
-\n\
-\n srf : NURBS surface structure, see nrbmak\
-\n\
-\n u, v : parametric coordinates of the point where we compute the\
-\n derivatives\
-\n\
-\n d : number of partial derivatives to compute\
-\n\
-\n OUTPUT :\
-\n\
-\n skl (i, j, k, l) = i-th component derived j-1,k-1 times at the\
-\n l-th point.\
-\n\
-\n Adaptation of algorithm A4.4 from the NURBS book\n")
-{
- //function skl = nrbsurfderiveval (srf, uv, d)
- octave_value_list retval;
-
- octave_scalar_map srf = args(0).scalar_map_value();
- Matrix uv = args(1).matrix_value ();
- octave_idx_type d = args(2).idx_type_value ();
-
- if (! error_state)
- {
- Array idxta (dim_vector (4, 1), 0);
- dim_vector idxa; idxa.resize (4);
- idxa(0) = 3; idxa(1) = d+1;
- idxa(2) = d+1; idxa(3) = uv.columns ();
- NDArray skl (idxa, 0.0);
-
- octave_idx_type n = octave_idx_type
- ((srf.contents("number").row_vector_value())(0) - 1);
- octave_idx_type m = octave_idx_type
- ((srf.contents("number").row_vector_value())(1) - 1);
- octave_idx_type p = octave_idx_type
- ((srf.contents("order").row_vector_value())(0) - 1);
- octave_idx_type q = octave_idx_type
- ((srf.contents("order").row_vector_value())(1) - 1);
-
- Cell knots = srf.contents("knots").cell_value();
- RowVector knotsu = knots.elem (0).row_vector_value ();
- RowVector knotsv = knots.elem (1).row_vector_value ();
-
- NDArray coefs = srf.contents("coefs").array_value();
-
- Array idx(dim_vector (3, 1), idx_vector(':'));
- idx (0) = idx_vector (3);
- Matrix weights (NDArray (coefs.index (idx).squeeze ()));
-
- for (octave_idx_type iu(0); iu.
-*/
-
-#include
-#include "low_level_functions.h"
-#include
-
-
-DEFUN_DLD(surfderivcpts, args, nargout,"\
-\nSURFDERIVCPTS: Compute control points of n-th derivatives of a NURBS surface.\n \
-\n \
-\nusage: pkl = surfderivcpts (n, p, U, m, q, V, P, d) \
-\n \
-\n INPUT: \
-\n\
-\n n+1, m+1 = number of control points \
-\n p, q = spline order \
-\n U, V = knots \
-\n P = control points \
-\n d = derivative order \
-\n\
-\n OUTPUT: \
-\n\
-\n pkl (k+1, l+1, i+1, j+1) = i,jth control point \
-\n of the surface differentiated k \
-\n times in the u direction and l \
-\n times in the v direction \
-\n \
-\n Adaptation of algorithm A3.7 from the NURBS book\n")
-{
- //function pkl = surfderivcpts (n, p, U, m, q, V, P, d, r1, r2, s1, s2)
-
- octave_value_list retval;
-
- octave_idx_type n = args(0).idx_type_value ();
- octave_idx_type p = args(1).idx_type_value ();
- RowVector U = args(2).row_vector_value (false, true);
- octave_idx_type m = args(3).idx_type_value ();
- octave_idx_type q = args(4).idx_type_value ();
- RowVector V = args(5).row_vector_value (false, true);
- Matrix P = args(6).matrix_value ();
- octave_idx_type d = args(7).idx_type_value ();
-
- octave_idx_type r1(0), r2 (n), s1 (0), s2 (m);
-
-
- if (args.length () == 12)
- {
- r1 = args (8).idx_type_value ();
- r2 = args (9).idx_type_value ();
- s1 = args (10).idx_type_value ();
- s2 = args (11).idx_type_value ();
- }
- else if (args.length () > 8)
- print_usage ();
-
- if (! error_state)
- {
-
- NDArray pkl;
-
- surfderivcpts (n, p, U, m, q, V, P, d, r1, r2, s1, s2, pkl);
-
- retval(0) = octave_value (pkl);
- }
- return retval;
-}
-
-
-/*
-%!test
-%! plane = nrbdegelev(nrb4surf([0 0], [0 1], [1 0], [1 1]), [1, 1]);
-%!
-%! pkl = surfderivcpts (plane.number(1)-1, plane.order(1)-1,
-%! plane.knots{1}, plane.number(2)-1,
-%! plane.order(2)-1, plane.knots{2},
-%! squeeze (plane.coefs(1,:,:)), 2);
-%!
-%!
-%! pkl2 = [ 0 0 0 1 0 0 0 0 0 0 0 0 1 0 ...
-%! 0 0 0 0 0 0 0 1 0 0 0 0 0 0.5 0 ...
-%! 0 1 0 0 0 0 0 0.5 0 0 1 0 0 0 0 ...
-%! 0 0.5 0 0 1 0 0 0 0 0 1 0 0 0 0 ...
-%! 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 ...
-%! 0 0 0 0 0 0 0]';
-%!
-%! assert (pkl(:),pkl2);
-*/
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/surfderiveval.cc
--- a/extra/nurbs/src/surfderiveval.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,94 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include "low_level_functions.h"
-#include
-
-
-DEFUN_DLD(surfderiveval, args, nargout,"\
-\nSURFDERIVEVAL: Compute the derivatives of a B-spline surface\
-\n\
-\n usage: skl = surfderiveval (n, p, U, m, q, V, P, u, v, d) \
-\n\
-\n INPUT: \
-\n\
-\n n+1, m+1 = number of control points\
-\n p, q = spline order\
-\n U, V = knots\
-\n P = control points\
-\n u,v = evaluation points\
-\n d = derivative order\
-\n\
-\n OUTPUT:\
-\n\
-\n skl (k+1, l+1) = surface differentiated k\
-\n times in the u direction and l\
-\n times in the v direction\
-\n\
-\n Adaptation of algorithm A3.8 from the NURBS book\n")
-{
-
- //function skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
-
- octave_value_list retval;
-
- octave_idx_type n = args(0).idx_type_value ();
- octave_idx_type p = args(1).idx_type_value ();
- RowVector U = args(2).row_vector_value (false, true);
- octave_idx_type m = args(3).idx_type_value ();
- octave_idx_type q = args(4).idx_type_value ();
- RowVector V = args(5).row_vector_value (false, true);
- Matrix P = args(6).matrix_value ();
- double u = args(7).double_value ();
- double v = args(8).double_value ();
- octave_idx_type d = args(9).idx_type_value ();
-
- if (! error_state)
- {
- Matrix skl;
- surfderiveval (n, p, U, m, q, V, P, u, v, d, skl);
- retval(0) = octave_value (skl);
- }
- return retval;
-}
-
-/*
-%!shared srf
-%!test
-%! k = [0 0 0 1 1 1];
-%! c = [0 1/2 1];
-%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
-%! srf = nrbmak (coef, {k, k});
-%! skl = surfderiveval (srf.number(1)-1,
-%! srf.order(1)-1,
-%! srf.knots{1},
-%! srf.number(2)-1,
-%! srf.order(2)-1,
-%! srf.knots{2},
-%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
-%! assert (skl, [.5 0; 1 0])
-%!test
-%! srf = nrbkntins (srf, {[], rand(1,2)});
-%! skl = surfderiveval (srf.number(1)-1,
-%! srf.order(1)-1,
-%! srf.knots{1},
-%! srf.number(2)-1,
-%! srf.order(2)-1,
-%! srf.knots{2},
-%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
-%! assert (skl, [.5 0; 1 0], 100*eps)
-*/
diff -r 1f7c2d121557 -r 2f6ebbb02032 extra/nurbs/src/tbasisfun.cc
--- a/extra/nurbs/src/tbasisfun.cc Sat Sep 12 19:47:29 2015 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,296 +0,0 @@
-/* Copyright (C) 2009 Carlo de Falco
- Copyright (C) 2012 Rafael Vazquez
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see .
-*/
-
-#include
-#include
-
-void onebasisfun__ (double u, octave_idx_type p, RowVector U, double *N)
-{
- *N = 0.0;
- if ((u <= U.min ()) || ( u > U.max ()))
- return;
- else if (p == 0)
- {
- *N = 1.0;
- return;
- }
- else if (p == 1)
- {
- if (u < U(1))
- {
- *N = (u - U(0)) / (U(1) - U(0));
- return;
- }
- else
- {
- *N = (U(2) - u) / (U(2) - U(1));
- return;
- }
- }
- else if (p == 2)
- {
- double ln = u - U(0);
- double dn = U(3) - u;
- double ld = U(2) - U(0);
- double dd = U(3) - U(1);
- if (u < U(1))
- {
- *N = ln*ln / (ld * (U(1) - U(0)));
- return;
- }
- else if (u > U(2))
- {
- *N = dn*dn / (dd * (U(3) - U(2)));
- return;
- }
- else
- {
- if (ld != 0)
- *N += ln * (U(2) - u) / ((U(2) - U(1)) * ld);
-
- if (dd != 0)
- *N += dn * (u - U(1)) / ((U(2) - U(1)) * dd);
- return;
- }
- }
-
- double ln = u - U(0);
- double ld = U(U.numel () - 2) - U(0);
- if (ld != 0)
- {
- double tmp;
- onebasisfun__ (u, p-1, U.extract (0, U.numel () - 2), &tmp);
- *N += ln * tmp / ld;
- }
- double dn = U(U.numel () - 1) - u;
- double dd = U(U.numel () - 1) - U(1);
- if (dd != 0)
- {
- double tmp;
- onebasisfun__ (u, p-1, U.extract (1, U.numel () - 1), &tmp);
- *N += dn * tmp / dd;
- }
- return;
-}
-
-void onebasisfun__ (double u, double p, RowVector U, double *N)
-{ onebasisfun__ (u, static_cast (p), U, N); }
-
-void onebasisfunder__ (double u, octave_idx_type p, RowVector U, double *N, double *Nder)
-{
- double aux;
- *N = 0.0; *Nder = 0.0;
- if ((u <= U.min ()) || ( u > U.max ()))
- return;
- else if (p == 0)
- {
- *N = 1.0;
- *Nder = 0.0;
- return;
- }
- else {
- double ln = u - U(0);
- double ld = U(U.numel () - 2) - U(0);
-
- if (ld != 0)
- {
- onebasisfun__ (u, p-1, U.extract (0, U.numel () - 2), &aux);
- aux = aux / ld;
- *N += ln * aux;
- *Nder += p * aux;
- }
-
- double dn = U(U.numel () - 1) - u;
- double dd = U(U.numel () - 1) - U(1);
-
- if (dd != 0)
- {
- onebasisfun__ (u, p-1, U.extract (1, U.numel () - 1), &aux);
- aux = aux / dd;
- *N += dn *aux;
- *Nder -= p * aux;
- }
- }
-}
-
-DEFUN_DLD(tbasisfun, args, nargout,"\
-TBASISFUN: Compute a B- or T-Spline basis function, and its derivatives, from its local knot vector.\n\
-\n\
- usage:\n\
-\n\
- [N, Nder] = tbasisfun (u, p, U)\n\
- [N, Nder] = tbasisfun ([u; v], [p q], {U, V})\n\
- [N, Nder] = tbasisfun ([u; v; w], [p q r], {U, V, W})\n\
- \n\
- INPUT:\n\
- u or [u; v] : points in parameter space where the basis function is to be\n\
- evaluated \n\
- \n\
- U or {U, V} : local knot vector\n\
-\n\
- p or [p q] : polynomial order of the basis function\n\
-\n\
- OUTPUT:\n\
- N : basis function evaluated at the given parametric points\n\
- Nder : gradient of the basis function evaluated at the given points\n")
-
-{
-
- octave_value_list retval;
- Matrix u = args(0).matrix_value ();
-
- RowVector N(u.cols ());
- double *Nptr = N.fortran_vec ();
-
- if (! args(2).is_cell ())
- {
-
- double p = args(1).idx_type_value ();
- RowVector U = args(2).row_vector_value (true, true);
- assert (U.numel () == p+2);
-
- if (nargout == 1)
- for (octave_idx_type ii = 0; ii < u.numel (); ii++)
- onebasisfun__ (u(ii), p, U, &(Nptr[ii]));
-
- if (nargout == 2)
- {
- RowVector Nder(u.cols ());
- double *Nderptr = Nder.fortran_vec ();
-
- for (octave_idx_type ii=0; ii