Mercurial > octave
changeset 28135:695bb31e565b stable
Rename "streamtube" to "ostreamtube" (bug #57471).
* ostreamtube.m: Rename from "streamtube.m" ahead of adding a Matlab compatible
"streamtube" function.
* stream3.m, streamline.m, module.mk, plot.txi, NEWS: Change all references.
| author | Markus Meisinger <chloros2@gmx.de> |
|---|---|
| date | Wed, 19 Feb 2020 07:53:10 +0100 |
| parents | 27c99ff83b99 |
| children | 23f667483fab |
| files | NEWS doc/interpreter/plot.txi scripts/plot/draw/module.mk scripts/plot/draw/ostreamtube.m scripts/plot/draw/stream3.m scripts/plot/draw/streamline.m scripts/plot/draw/streamtube.m |
| diffstat | 7 files changed, 371 insertions(+), 364 deletions(-) [+] |
line wrap: on
line diff
--- a/NEWS Sat Feb 22 14:50:05 2020 +0100 +++ b/NEWS Wed Feb 19 07:53:10 2020 +0100 @@ -206,6 +206,7 @@ * `mustBeReal` * `namedargs2cell` * `newline` +* `ostreamtube` * `rescale` * `rotx` * `roty` @@ -213,7 +214,6 @@ * `stream2` * `stream3` * `streamline` -* `streamtube` * `uisetfont` * `verLessThan` * `web`
--- a/doc/interpreter/plot.txi Sat Feb 22 14:50:05 2020 +0100 +++ b/doc/interpreter/plot.txi Wed Feb 19 07:53:10 2020 +0100 @@ -245,7 +245,7 @@ @DOCSTRING(quiver3) -@DOCSTRING(streamtube) +@DOCSTRING(ostreamtube) @DOCSTRING(streamline)
--- a/scripts/plot/draw/module.mk Sat Feb 22 14:50:05 2020 +0100 +++ b/scripts/plot/draw/module.mk Wed Feb 19 07:53:10 2020 +0100 @@ -61,6 +61,7 @@ %reldir%/mesh.m \ %reldir%/meshc.m \ %reldir%/meshz.m \ + %reldir%/ostreamtube.m \ %reldir%/pareto.m \ %reldir%/patch.m \ %reldir%/pcolor.m \ @@ -97,7 +98,6 @@ %reldir%/stream2.m \ %reldir%/stream3.m \ %reldir%/streamline.m \ - %reldir%/streamtube.m \ %reldir%/surf.m \ %reldir%/surface.m \ %reldir%/surfc.m \
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/plot/draw/ostreamtube.m Wed Feb 19 07:53:10 2020 +0100 @@ -0,0 +1,366 @@ +######################################################################## +## +## Copyright (C) 2019-2020 The Octave Project Developers +## +## See the file COPYRIGHT.md in the top-level directory of this +## distribution or <https://octave.org/copyright/>. +## +## This file is part of Octave. +## +## Octave 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. +## +## Octave 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 +## <https://www.gnu.org/licenses/>. +## +######################################################################## + +## -*- texinfo -*- +## @deftypefn {} {} ostreamtube (@var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) +## @deftypefnx {} {} ostreamtube (@var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) +## @deftypefnx {} {} ostreamtube (@var{xyz}, @var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}) +## @deftypefnx {} {} ostreamtube (@dots{}, @var{options}) +## @deftypefnx {} {} ostreamtube (@var{hax}, @dots{}) +## @deftypefnx {} {@var{h} =} ostreamtube (@dots{}) +## Calculate and display streamtubes. +## +## Streamtubes are approximated by connecting circular crossflow areas +## along a streamline. The expansion of the flow is determined by the local +## crossflow divergence. +## +## The vector field is given by @code{[@var{u}, @var{v}, @var{w}]} and is +## defined over a rectangular grid given by @code{[@var{x}, @var{y}, @var{z}]}. +## The streamtubes start at the seed points +## @code{[@var{sx}, @var{sy}, @var{sz}]}. +## +## The tubes are colored based on the local vector field strength. +## +## The input parameter @var{options} is a 2-D vector of the form +## @code{[@var{scale}, @var{n}]}. The first parameter scales the start radius +## of the streamtubes (default 1). The second parameter specifies the number +## of vertices that are used to construct the tube circumference (default 20). +## +## @code{ostreamtube} can be called with a cell array containing pre-computed +## streamline data. To do this, @var{xyz} must be created with the +## @code{stream3} function. This option is useful if you need to alter the +## integrator step size or the maximum number of vertices of the streamline. +## +## If the first argument @var{hax} is an axes handle, then plot into this axes, +## rather than the current axes returned by @code{gca}. +## +## The optional return value @var{h} is a graphics handle to the plot +## objects created for each streamtube. +## +## Example: +## +## @example +## @group +## [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3:0.1:0); +## u = -x / 10 - y; +## v = x - y / 10; +## w = - ones (size (x)) / 10; +## ostreamtube (x, y, z, u, v, w, 1, 0, 0); +## @end group +## @end example +## +## @seealso{stream3, streamline} +## @end deftypefn + +## References: +## +## @inproceedings{ +## title = {Visualization of 3-D vector fields - Variations on a stream}, +## author = {Dave Darmofal and Robert Haimes}, +## year = {1992} +## } +## +## @article{ +## title = {Efficient streamline, streamribbon, and streamtube constructions on unstructured grids}, +## author = {Ueng, Shyh-Kuang and Sikorski, C. and Ma, Kwan-Liu}, +## year = {1996}, +## month = {June}, +## publisher = {IEEE Transactions on Visualization and Computer Graphics}, +## } + +function h = ostreamtube (varargin) + + [hax, varargin, nargin] = __plt_get_axis_arg__ ("ostreamtube", varargin{:}); + + options = []; + xyz = []; + switch (nargin) + case 0 + print_usage (); + case 6 + [u, v, w, spx, spy, spz] = varargin{:}; + [m, n, p] = size (u); + [x, y, z] = meshgrid (1:n, 1:m, 1:p); + case 7 + if (iscell (varargin{1})) + [xyz, x, y, z, u, v, w] = varargin{:}; + else + [u, v, w, spx, spy, spz, options] = varargin{:}; + [m, n, p] = size (u); + [x, y, z] = meshgrid (1:n, 1:m, 1:p); + endif + case 8 + [xyz, x, y, z, u, v, w, options] = varargin{:}; + case 9 + [x, y, z, u, v, w, spx, spy, spz] = varargin{:}; + case 10 + [x, y, z, u, v, w, spx, spy, spz, options] = varargin{:}; + otherwise + error ("ostreamtube: invalid number of inputs"); + endswitch + + scale = 1; + num_circum = 20; + if (! isempty (options)) + switch (numel (options)) + case 1 + scale = options(1); + case 2 + scale = options(1); + num_circum = options(2); + otherwise + error ("ostreamtube: invalid number of OPTIONS elements"); + endswitch + + if (! isreal (scale) || scale <= 0) + error ("ostreamtube: SCALE must be a real scalar > 0"); + endif + if (! isreal (num_circum) || num_circum < 3) + error ("ostreamtube: number of tube vertices N must be greater than 2"); + endif + num_circum = fix (num_circum); + endif + + if (isempty (hax)) + hax = gca (); + else + hax = hax(1); + endif + + if (isempty (xyz)) + xyz = stream3 (x, y, z, u, v, w, spx, spy, spz, 0.2); + endif + + div = divergence (x, y, z, u, v, w); + + ## Use the bounding box diagonal to determine the starting radius + mxx = mnx = mxy = mny = mxz = mnz = []; + j = 1; + for i = 1 : length (xyz) + sl = xyz{i}; + if (! isempty (sl)) + slx = sl(:, 1); sly = sl(:, 2); slz = sl(:, 3); + mxx(j) = max (slx); mnx(j) = min (slx); + mxy(j) = max (sly); mny(j) = min (sly); + mxz(j) = max (slz); mnz(j) = min (slz); + j += 1; + endif + endfor + dx = max (mxx) - min (mnx); + dy = max (mxy) - min (mny); + dz = max (mxz) - min (mnz); + rstart = scale * sqrt (dx*dx + dy*dy + dz*dz) / 25; + + h = []; + for i = 1 : length (xyz) + sl = xyz{i}; + num_vertices = rows (sl); + if (! isempty (sl) && num_vertices > 2) + + usl = interp3 (x, y, z, u, sl(:, 1), sl(:, 2), sl(:, 3)); + vsl = interp3 (x, y, z, v, sl(:, 1), sl(:, 2), sl(:, 3)); + wsl = interp3 (x, y, z, w, sl(:, 1), sl(:, 2), sl(:, 3)); + vv = sqrt (usl.*usl + vsl.*vsl + wsl.*wsl); + + div_sl = interp3 (x, y, z, div, sl(:, 1), sl(:, 2), sl(:, 3)); + is_singular_div = find (isnan (div_sl), 1, "first"); + + if (! isempty (is_singular_div)) + max_vertices = is_singular_div - 1; + else + max_vertices = num_vertices; + endif + + if (max_vertices > 2) + + htmp = plottube (hax, sl, div_sl, vv, max_vertices, ... + rstart, num_circum); + h = [h; htmp]; + + endif + endif + endfor + +endfunction + +function h = plottube (hax, sl, div_sl, vv, max_vertices, rstart, num_circum) + + phi = linspace (0, 2*pi, num_circum); + cp = cos (phi); + sp = sin (phi); + + X0 = sl(1, :); + X1 = sl(2, :); + + ## 1st rotation axis + R = X1 - X0; + RE = R / norm (R); + + ## Initial radius + vold = vv(1); + vact = vv(2); + ract = rstart * exp (0.5 * div_sl(2) * norm (R) / vact) * sqrt (vold / vact); + vold = vact; + rold = ract; + + ## Guide point and its rotation to create a segment + N = get_normal1 (R); + K = ract * N; + XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); + + px = zeros (num_circum, max_vertices - 1); + py = zeros (num_circum, max_vertices - 1); + pz = zeros (num_circum, max_vertices - 1); + pc = zeros (num_circum, max_vertices - 1); + + px(:, 1) = XS(1, :).'; + py(:, 1) = XS(2, :).'; + pz(:, 1) = XS(3, :).'; + pc(:, 1) = vact * ones (num_circum, 1); + + for i = 3 : max_vertices + + KK = K; + X0 = X1; + X1 = sl(i, :); + R = X1 - X0; + RE = R / norm (R); + + ## Tube radius + vact = vv(i); + ract = rold * exp (0.5 * div_sl(i) * norm (R) / vact) * sqrt (vold / vact); + vold = vact; + rold = ract; + + ## Project KK onto RE and get the difference in order to calculate the next + ## guiding point + Kp = KK - RE * dot (KK, RE); + K = ract * Kp / norm (Kp); + + ## Rotate around RE and collect surface patches + XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); + + px(:, i - 1) = XS(1, :).'; + py(:, i - 1) = XS(2, :).'; + pz(:, i - 1) = XS(3, :).'; + pc(:, i - 1) = vact * ones (num_circum, 1); + + endfor + + h = surface (hax, px, py, pz, pc); + +endfunction + +## Arbitrary N normal to X +function N = get_normal1 (X) + + if ((X(3) == 0) && (X(1) == -X(2))) + N = [- X(2) - X(3), X(1), X(1)]; + else + N = [X(3), X(3), - X(1) - X(2)]; + endif + + N /= norm (N); + +endfunction + +## Rotate X around U where |U| = 1 +## cp = cos (angle), sp = sin (angle) +function Y = rotation (X, U, cp, sp) + + ux = U(1); + uy = U(2); + uz = U(3); + + Y(1, :) = X(1) * (cp + ux * ux * (1 - cp)) + ... + X(2) * (ux * uy * (1 - cp) - uz * sp) + ... + X(3) * (ux * uz * (1 - cp) + uy * sp); + + Y(2, :) = X(1) * (uy * ux * (1 - cp) + uz * sp) + ... + X(2) * (cp + uy * uy * (1 - cp)) + ... + X(3) * (uy * uz * (1 - cp) - ux * sp); + + Y(3, :) = X(1) * (uz * ux * (1 - cp) - uy * sp) + ... + X(2) * (uz * uy * (1 - cp) + ux * sp) + ... + X(3) * (cp + uz * uz * (1 - cp)); + +endfunction + +%!demo +%! clf; +%! [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3.5:0.1:0); +%! a = 0.1; +%! b = 0.1; +%! u = - a * x - y; +%! v = x - a * y; +%! w = - b * ones (size (x)); +%! sx = 1.0; +%! sy = 0.0; +%! sz = 0.0; +%! ostreamtube (x, y, z, u, v, w, sx, sy, sz, [1.2, 30]); +%! colormap (jet); +%! shading interp; +%! view ([-47, 24]); +%! camlight (); +%! lighting gouraud; +%! grid on; +%! view (3); +%! axis equal; +%! set (gca, "cameraviewanglemode", "manual"); +%! title ("Spiral Sink"); + +%!demo +%! clf; +%! [x, y, z] = meshgrid (-2:0.5:2); +%! t = sqrt (1.0./(x.^2 + y.^2 + z.^2)).^3; +%! u = - x.*t; +%! v = - y.*t; +%! w = - z.*t; +%! [sx, sy, sz] = meshgrid (-2:4:2); +%! xyz = stream3 (x, y, z, u, v, w, sx, sy, sz, [0.1, 60]); +%! ostreamtube (xyz, x, y, z, u, v, w, [2, 50]); +%! colormap (jet); +%! shading interp; +%! view ([-47, 24]); +%! camlight (); +%! lighting gouraud; +%! grid on; +%! view (3); +%! axis equal; +%! set (gca, "cameraviewanglemode", "manual"); +%! title ("Integration Towards Sink"); + +## Test input validation +%!error ostreamtube () +%!error <invalid number of inputs> ostreamtube (1) +%!error <invalid number of inputs> ostreamtube (1,2) +%!error <invalid number of inputs> ostreamtube (1,2,3) +%!error <invalid number of inputs> ostreamtube (1,2,3,4) +%!error <invalid number of inputs> ostreamtube (1,2,3,4,5) +%!error <invalid number of OPTIONS> ostreamtube (1,2,3,4,5,6, [1,2,3]) +%!error <SCALE must be a real scalar . 0> ostreamtube (1,2,3,4,5,6, [1i]) +%!error <SCALE must be a real scalar . 0> ostreamtube (1,2,3,4,5,6, [0]) +%!error <N must be greater than 2> ostreamtube (1,2,3,4,5,6, [1, 1i]) +%!error <N must be greater than 2> ostreamtube (1,2,3,4,5,6, [1, 2])
--- a/scripts/plot/draw/stream3.m Sat Feb 22 14:50:05 2020 +0100 +++ b/scripts/plot/draw/stream3.m Wed Feb 19 07:53:10 2020 +0100 @@ -58,7 +58,7 @@ ## @end group ## @end example ## -## @seealso{stream2, streamline, streamtube} +## @seealso{stream2, streamline, ostreamtube} ## @end deftypefn ## References:
--- a/scripts/plot/draw/streamline.m Sat Feb 22 14:50:05 2020 +0100 +++ b/scripts/plot/draw/streamline.m Wed Feb 19 07:53:10 2020 +0100 @@ -61,7 +61,7 @@ ## @end group ## @end example ## -## @seealso{stream2, stream3, streamtube} +## @seealso{stream2, stream3, ostreamtube} ## @end deftypefn function h = streamline (varargin)
--- a/scripts/plot/draw/streamtube.m Sat Feb 22 14:50:05 2020 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,359 +0,0 @@ -######################################################################## -## -## Copyright (C) 2019-2020 The Octave Project Developers -## -## See the file COPYRIGHT.md in the top-level directory of this -## distribution or <https://octave.org/copyright/>. -## -## This file is part of Octave. -## -## Octave 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. -## -## Octave 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 -## <https://www.gnu.org/licenses/>. -## -######################################################################## - -## -*- texinfo -*- -## @deftypefn {} {} streamtube (@var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) -## @deftypefnx {} {} streamtube (@var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) -## @deftypefnx {} {} streamtube (@var{vertices}, @var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}) -## @deftypefnx {} {} streamtube (@dots{}, @var{options}) -## @deftypefnx {} {} streamtube (@var{hax}, @dots{}) -## @deftypefnx {} {@var{h} =} streamtube (@dots{}) -## Calculate and display streamtubes. -## -## Streamtubes are approximated by connecting circular crossflow areas -## along a streamline. The expansion of the flow is determined by the local -## crossflow divergence. -## -## The vector field is given by @code{[@var{u}, @var{v}, @var{w}]} and is -## defined over a rectangular grid given by @code{[@var{x}, @var{y}, @var{z}]}. -## The streamtubes start at the seed points -## @code{[@var{sx}, @var{sy}, @var{sz}]}. -## -## The tubes are colored based on the local vector field strength. -## -## The input parameter @var{options} is a 2-D vector of the form -## @code{[@var{scale}, @var{n}]}. The first parameter scales the start radius -## of the streamtubes (default 1). The second parameter specifies the number -## of polygon points used for the streamtube circumference (default 20). -## -## @code{streamtube} can be called with a cell array containing pre-computed -## streamline data. To do this, @var{vertices} must be created with the -## @code{stream3} function. This option is useful if you need to alter the -## integrator step size or the maximum number of vertices of the streamline. -## -## If the first argument @var{hax} is an axes handle, then plot into this axes, -## rather than the current axes returned by @code{gca}. -## -## The optional return value @var{h} is a graphics handle to the patch plot -## objects created for each streamtube. -## -## Example: -## -## @example -## @group -## [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3:0.1:0); -## u = -x / 10 - y; -## v = x - y / 10; -## w = - ones (size (x)) / 10; -## streamtube (x, y, z, u, v, w, 1, 0, 0); -## @end group -## @end example -## -## @seealso{stream3, streamline} -## @end deftypefn - -## Reference: -## -## @inproceedings{ -## title = {Visualization of 3-D vector fields - Variations on a stream}, -## author = {Dave Darmofal and Robert Haimes}, -## year = {1992} -## } - -function h = streamtube (varargin) - - [hax, varargin, nargin] = __plt_get_axis_arg__ ("streamtube", varargin{:}); - - options = []; - xyz = []; - switch (nargin) - case 0 - print_usage (); - case 6 - [u, v, w, spx, spy, spz] = varargin{:}; - [m, n, p] = size (u); - [x, y, z] = meshgrid (1:n, 1:m, 1:p); - case 7 - if (iscell (varargin{1})) - [xyz, x, y, z, u, v, w] = varargin{:}; - else - [u, v, w, spx, spy, spz, options] = varargin{:}; - [m, n, p] = size (u); - [x, y, z] = meshgrid (1:n, 1:m, 1:p); - endif - case 8 - [xyz, x, y, z, u, v, w, options] = varargin{:}; - case 9 - [x, y, z, u, v, w, spx, spy, spz] = varargin{:}; - case 10 - [x, y, z, u, v, w, spx, spy, spz, options] = varargin{:}; - otherwise - error ("streamtube: invalid number of inputs"); - endswitch - - scale = 1; - num_poly = 20; - if (! isempty (options)) - switch (numel (options)) - case 1 - scale = options(1); - case 2 - scale = options(1); - num_poly = options(2); - otherwise - error ("streamtube: invalid number of OPTIONS elements"); - endswitch - - if (! isreal (scale) || scale <= 0) - error ("streamtube: SCALE must be a real scalar > 0"); - endif - if (! isreal (num_poly) || num_poly < 3) - error ("streamtube: number of polygons N must be greater than 2"); - endif - num_poly = fix (num_poly); - endif - - if (isempty (hax)) - hax = gca (); - else - hax = hax(1); - endif - - if (isempty (xyz)) - xyz = stream3 (x, y, z, u, v, w, spx, spy, spz, 0.2); - endif - - div = divergence (x, y, z, u, v, w); - - ## Determine start radius - mxx = mnx = mxy = mny = mxz = mnz = []; - j = 1; - for i = 1 : length (xyz) - sl = xyz{i}; - if (! isempty (sl)) - slx = sl(:, 1); sly = sl(:, 2); slz = sl(:, 3); - mxx(j) = max (slx(:)); mnx(j) = min (slx(:)); - mxy(j) = max (sly(:)); mny(j) = min (sly(:)); - mxz(j) = max (slz(:)); mnz(j) = min (slz(:)); - j += 1; - endif - endfor - dx = max (mxx) - min (mnx); - dy = max (mxy) - min (mny); - dz = max (mxz) - min (mnz); - rstart = scale * sqrt (dx*dx + dy*dy + dz*dz) / 25; - - h = []; - for i = 1 : length (xyz) - sl = xyz{i}; - num_vertices = rows (sl); - if (! isempty (sl) && num_vertices > 2) - - usl = interp3 (x, y, z, u, sl(:, 1), sl(:, 2), sl(:, 3)); - vsl = interp3 (x, y, z, v, sl(:, 1), sl(:, 2), sl(:, 3)); - wsl = interp3 (x, y, z, w, sl(:, 1), sl(:, 2), sl(:, 3)); - vv = sqrt (usl.*usl + vsl.*vsl + wsl.*wsl); - - div_sl = interp3 (x, y, z, div, sl(:, 1), sl(:, 2), sl(:, 3)); - is_singular_div = find (isnan (div_sl), 1, "first"); - - if (! isempty (is_singular_div)) - max_vertices = is_singular_div - 1; - else - max_vertices = num_vertices; - endif - - if (max_vertices > 2) - - htmp = plottube (hax, sl, div_sl, vv, max_vertices, ... - rstart, num_poly); - h = [h; htmp]; - - endif - endif - endfor - -endfunction - -function h = plottube (hax, sl, div_sl, vv, max_vertices, rstart, num_poly) - - phi = linspace (0, 2*pi, num_poly); - cp = cos (phi); - sp = sin (phi); - - X0 = sl(1, :); - X1 = sl(2, :); - - ## 1st rotation axis - R = X1 - X0; - RE = R / norm (R); - - ## Initial radius - vold = vv(1); - vact = vv(2); - ract = rstart * exp (0.5 * div_sl(2) * norm (R) / vact) * sqrt (vold / vact); - vold = vact; - rold = ract; - - ## Guide point and its rotation to create a segment - N = get_normal1 (R); - K = ract * N; - XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_poly); - - px = zeros (num_poly, max_vertices - 1); - py = zeros (num_poly, max_vertices - 1); - pz = zeros (num_poly, max_vertices - 1); - pc = zeros (num_poly, max_vertices - 1); - - px(:, 1) = XS(1, :).'; - py(:, 1) = XS(2, :).'; - pz(:, 1) = XS(3, :).'; - pc(:, 1) = vact * ones (num_poly, 1); - - for i = 3 : max_vertices - - KK = K; - X0 = X1; - X1 = sl(i, :); - R = X1 - X0; - RE = R / norm (R); - - ## Tube radius - vact = vv(i); - ract = rold * exp (0.5 * div_sl(i) * norm (R) / vact) * sqrt (vold / vact); - vold = vact; - rold = ract; - - ## Project K onto RE and get the difference in order to calculate the next - ## guiding point - Kp = KK - RE * dot (KK, RE); - K = ract * Kp / norm (Kp); - - ## Rotate the guiding point around R and collect patch vertices - XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_poly); - - px(:, i - 1) = XS(1, :).'; - py(:, i - 1) = XS(2, :).'; - pz(:, i - 1) = XS(3, :).'; - pc(:, i - 1) = vact * ones (num_poly, 1); - - endfor - - h = surface (hax, px, py, pz, pc); - -endfunction - -## Arbitrary N normal to X -function N = get_normal1 (X) - - if ((X(3) == 0) && (X(1) == -X(2))) - N = [- X(2) - X(3), X(1), X(1)]; - else - N = [X(3), X(3), - X(1) - X(2)]; - endif - - N /= norm (N); - -endfunction - -## Rotate X around U where |U| = 1 -## cp = cos (angle), sp = sin (angle) -function Y = rotation (X, U, cp, sp) - - ux = U(1); - uy = U(2); - uz = U(3); - - Y(1, :) = X(1) * (cp + ux * ux * (1 - cp)) + ... - X(2) * (ux * uy * (1 - cp) - uz * sp) + ... - X(3) * (ux * uz * (1 - cp) + uy * sp); - - Y(2, :) = X(1) * (uy * ux * (1 - cp) + uz * sp) + ... - X(2) * (cp + uy * uy * (1 - cp)) + ... - X(3) * (uy * uz * (1 - cp) - ux * sp); - - Y(3, :) = X(1) * (uz * ux * (1 - cp) - uy * sp) + ... - X(2) * (uz * uy * (1 - cp) + ux * sp) + ... - X(3) * (cp + uz * uz * (1 - cp)); - -endfunction - - -%!demo -%! clf; -%! [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3.5:0.1:0); -%! a = 0.1; -%! b = 0.1; -%! u = - a * x - y; -%! v = x - a * y; -%! w = - b * ones (size (x)); -%! sx = 1.0; -%! sy = 0.0; -%! sz = 0.0; -%! streamtube (x, y, z, u, v, w, sx, sy, sz, [1.2, 30]); -%! colormap (jet); -%! shading interp; -%! view ([-47, 24]); -%! camlight (); -%! lighting gouraud; -%! grid on; -%! view (3); -%! axis equal; -%! set (gca, "cameraviewanglemode", "manual"); -%! title ("Spiral Sink"); - -%!demo -%! clf; -%! [x, y, z] = meshgrid (-2:0.5:2); -%! t = sqrt (1.0./(x.^2 + y.^2 + z.^2)).^3; -%! u = - x.*t; -%! v = - y.*t; -%! w = - z.*t; -%! [sx, sy, sz] = meshgrid (-2:4:2); -%! xyz = stream3 (x, y, z, u, v, w, sx, sy, sz, [0.1, 60]); -%! streamtube (xyz, x, y, z, u, v, w, [2, 50]); -%! colormap (jet); -%! shading interp; -%! view ([-47, 24]); -%! camlight (); -%! lighting gouraud; -%! grid on; -%! view (3); -%! axis equal; -%! set (gca, "cameraviewanglemode", "manual"); -%! title ("Integration Towards Sink"); - -## Test input validation -%!error streamtube () -%!error <invalid number of inputs> streamtube (1) -%!error <invalid number of inputs> streamtube (1,2) -%!error <invalid number of inputs> streamtube (1,2,3) -%!error <invalid number of inputs> streamtube (1,2,3,4) -%!error <invalid number of inputs> streamtube (1,2,3,4,5) -%!error <invalid number of OPTIONS> streamtube (1,2,3,4,5,6, [1,2,3]) -%!error <SCALE must be a real scalar . 0> streamtube (1,2,3,4,5,6, [1i]) -%!error <SCALE must be a real scalar . 0> streamtube (1,2,3,4,5,6, [0]) -%!error <N must be greater than 2> streamtube (1,2,3,4,5,6, [1, 1i]) -%!error <N must be greater than 2> streamtube (1,2,3,4,5,6, [1, 2])