octave: scripts/geometry/tsearchn.m annotate

annotate scripts/geometry/tsearchn.m @ 21546:f7f97d7e9294

doc: Wrap m-file docstrings to 79 characters + newline (80 total). * isrecording.m, soundsc.m, delaunay3.m, cell2mat.m, cumtrapz.m, del2.m, inputParser.m, interp1.m, interp3.m, narginchk.m, profile.m, validateattributes.m, delaunayn.m, tsearchn.m, voronoin.m, brighten.m, cmunique.m, colorcube.m, imfinfo.m, imshow.m, edit.m, orderfields.m, run.m, warning_ids.m, ode23.m, ode45.m, odeget.m, integrate_adaptive.m, kahan.m, ode_struct_value_check.m, runge_kutta_23.m, fminunc.m, fsolve.m, fzero.m, pkg.m, build.m, specular.m, view.m, bar.m, barh.m, contour3.m, isosurface.m, line.m, pie.m, pie3.m, quiver3.m, scatter.m, scatter3.m, stem3.m, stemleaf.m, surfl.m, tetramesh.m, isfigure.m, mkpp.m, pchip.m, residue.m, splinefit.m, rmpref.m, unique.m, eigs.m, ilu.m, factor.m, factorial.m, gallery.m, hankel.m, histc.m, ols.m, finv.m, fpdf.m, kruskal_wallis_test.m, weekday.m: Wrap m-file docstrings to 79 characters + newline (80 total).

author	Rik <rik@octave.org>
date	Sun, 27 Mar 2016 15:50:01 -0700
parents	516bb87ea72e
children	b571fc85953f

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	1 ## Copyright (C) 2007-2015 David Bateman
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	2 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	3 ## This file is part of Octave.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	4 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	8 ## your option) any later version.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	9 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	13 ## General Public License for more details.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	14 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	17 ## <http://www.gnu.org/licenses/>.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	18
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	19 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	20 ## @deftypefn {} {@var{idx} =} tsearchn (@var{x}, @var{t}, @var{xi})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	21 ## @deftypefnx {} {[@var{idx}, @var{p}] =} tsearchn (@var{x}, @var{t}, @var{xi})
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	22 ## Search for the enclosing Delaunay convex hull.
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	23 ##
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	24 ## For @code{@var{t} = delaunayn (@var{x})}, finds the index in @var{t}
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	25 ## containing the points @var{xi}. For points outside the convex hull,
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	26 ## @var{idx} is NaN.
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	27 ##
21546 f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	28 ## If requested @code{tsearchn} also returns the Barycentric coordinates
f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	29 ## @var{p} of the enclosing triangles.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	30 ## @seealso{delaunay, delaunayn}
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	31 ## @end deftypefn
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	32
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	33 function [idx, p] = tsearchn (x, t, xi)
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	34 if (nargin != 3)
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	35 print_usage ();
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	36 endif
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	37
14872 c2dbdeaa25df maint: use rows() and columns() to clarify m-files. Rik <octave@nomad.inbox5.com> parents: 14868 diff changeset	38 nt = rows (t);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	39 [m, n] = size (x);
14872 c2dbdeaa25df maint: use rows() and columns() to clarify m-files. Rik <octave@nomad.inbox5.com> parents: 14868 diff changeset	40 mi = rows (xi);
10548 479536c5bb10 Replace lowercase nan with NaN for visual cue in scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	41 idx = NaN (mi, 1);
479536c5bb10 Replace lowercase nan with NaN for visual cue in scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	42 p = NaN (mi, n + 1);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	43
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	44 ni = [1:mi].';
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	45 for i = 1 : nt
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	46 ## Only calculate the Barycentric coordinates for points that have not
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	47 ## already been found in a triangle.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	48 b = cart2bary (x (t (i, :), :), xi(ni,:));
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	49
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	50 ## Our points xi are in the current triangle if
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	51 ## (all (b >= 0) && all (b <= 1)). However as we impose that
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	52 ## sum (b,2) == 1 we only need to test all(b>=0). Note need to add
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	53 ## a small margin for rounding errors
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	54 intri = all (b >= -1e-12, 2);
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	55 idx(ni(intri)) = i;
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	56 p(ni(intri),:) = b(intri, :);
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	57 ni(intri) = [];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	58 endfor
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	59 endfunction
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	60
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	61 function Beta = cart2bary (T, P)
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	62 ## Conversion of Cartesian to Barycentric coordinates.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	63 ## Given a reference simplex in N dimensions represented by a
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	64 ## (N+1)-by-(N) matrix, and arbitrary point P in cartesion coordinates,
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	65 ## represented by a N-by-1 row vector can be written as
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	66 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	67 ## P = Beta * T
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	68 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	69 ## Where Beta is a N+1 vector of the barycentric coordinates. A criteria
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	70 ## on Beta is that
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	71 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	72 ## sum (Beta) == 1
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	73 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	74 ## and therefore we can write the above as
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	75 ##
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	76 ## P - T(end, :) = Beta(1:end-1) * (T(1:end-1,:) - ones (N,1) * T(end,:))
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	77 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	78 ## and then we can solve for Beta as
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	79 ##
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	80 ## Beta(1:end-1) = (P - T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:))
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	81 ## Beta(end) = sum (Beta)
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	82 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	83 ## Note below is generalize for multiple values of P, one per row.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	84 [M, N] = size (P);
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	85 Beta = (P - ones (M,1) * T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:));
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	86 Beta (:,end+1) = 1 - sum (Beta, 2);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	87 endfunction
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	88
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	89
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	90 %!shared x, tri
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	91 %! x = [-1,-1;-1,1;1,-1];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	92 %! tri = [1, 2, 3];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	93 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	94 %! [idx, p] = tsearchn (x,tri,[-1,-1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	95 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	96 %! assert (p, [1,0,0], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	97 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	98 %! [idx, p] = tsearchn (x,tri,[-1,1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	99 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	100 %! assert (p, [0,1,0], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	101 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	102 %! [idx, p] = tsearchn (x,tri,[1,-1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	103 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	104 %! assert (p, [0,0,1], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	105 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	106 %! [idx, p] = tsearchn (x,tri,[-1/3,-1/3]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	107 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	108 %! assert (p, [1/3,1/3,1/3], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	109 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	110 %! [idx, p] = tsearchn (x,tri,[1,1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	111 %! assert (idx, NaN);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	112 %! assert (p, [NaN, NaN, NaN]);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	113

Mercurial > octave

annotate scripts/geometry/tsearchn.m @ 21546:f7f97d7e9294