Mercurial > octave
view scripts/geometry/delaunay.m @ 28912:0de38a6ef693
maint: Use Octave convention of space after function name in scripts dir.
* cplxpair.m, gradient.m, integral.m, integral3.m, interp2.m, interpft.m,
num2str.m, pol2cart.m, quad2d.m, quadgk.m, quadl.m, repelem.m, sph2cart.m,
convhull.m, delaunay.m, delaunayn.m, movegui.m, print_usage.m,
__strip_html_tags__.m, colormap.m, gray2ind.m, imformats.m, importdata.m,
javachk.m, condest.m, isbanded.m, krylov.m, lscov.m, rref.m, inputParser.m,
publish.m, symvar.m, validateattributes.m, ode15i.m, ode15s.m, ode23.m,
ode23s.m, ode45.m, fminbnd.m, fminsearch.m, glpk.m, qp.m, get_forge_pkg.m,
installed_packages.m, annotation.m, axis.m, camorbit.m, campos.m, camva.m,
camzoom.m, daspect.m, legend.m, pbaspect.m, __gnuplot_legend__.m, light.m,
patch.m, plotyy.m, __pie__.m, reducepatch.m, ribbon.m, streamline.m, trisurf.m,
figure.m, ndgrid.m, __gnuplot_draw_axes__.m, __opengl_print__.m, padecoef.m,
polygcd.m, ppval.m, spline.m, union.m, bicg.m, bicgstab.m, cgs.m, eigs.m,
gmres.m, pcg.m, pcr.m, __alltohandles__.m, __sprand__.m, qmr.m, tfqmr.m,
betaincinv.m, cosint.m, gammainc.m, discrete_cdf.m, discrete_inv.m,
discrete_rnd.m, base2dec.m, strtok.m, compare_plot_demos.m,
html_compare_plot_demos.m, speed.m, test.m, weboptions.m, webread.m, webwrite.m:
Use Octave convention of space after function name and before '(' in scripts
directory.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 13 Oct 2020 18:17:29 -0700 |
parents | 90fea9cc9caa |
children | 7854d5752dd2 |
line wrap: on
line source
######################################################################## ## ## Copyright (C) 1999-2020 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 {} {@var{tri} =} delaunay (@var{x}, @var{y}) ## @deftypefnx {} {@var{tetr} =} delaunay (@var{x}, @var{y}, @var{z}) ## @deftypefnx {} {@var{tri} =} delaunay (@var{x}) ## @deftypefnx {} {@var{tri} =} delaunay (@dots{}, @var{options}) ## Compute the Delaunay triangulation for a 2-D or 3-D set of points. ## ## For 2-D sets, the return value @var{tri} is a set of triangles which ## satisfies the Delaunay circum-circle criterion, i.e., no data point from ## [@var{x}, @var{y}] is within the circum-circle of the defining triangle. ## The set of triangles @var{tri} is a matrix of size [n, 3]. Each row defines ## a triangle and the three columns are the three vertices of the triangle. ## The value of @code{@var{tri}(i,j)} is an index into @var{x} and @var{y} for ## the location of the j-th vertex of the i-th triangle. ## ## For 3-D sets, the return value @var{tetr} is a set of tetrahedrons which ## satisfies the Delaunay circum-circle criterion, i.e., no data point from ## [@var{x}, @var{y}, @var{z}] is within the circum-circle of the defining ## tetrahedron. The set of tetrahedrons is a matrix of size [n, 4]. Each row ## defines a tetrahedron and the four columns are the four vertices of the ## tetrahedron. The value of @code{@var{tetr}(i,j)} is an index into @var{x}, ## @var{y}, @var{z} for the location of the j-th vertex of the i-th ## tetrahedron. ## ## The input @var{x} may also be a matrix with two or three columns where the ## first column contains x-data, the second y-data, and the optional third ## column contains z-data. ## ## An optional final argument, which must be a string or cell array of strings, ## contains options passed to the underlying qhull command. ## See the documentation for the Qhull library for details ## @url{http://www.qhull.org/html/qh-quick.htm#options}. ## The default options are @code{@{"Qt", "Qbb", "Qc"@}}. ## If Qhull fails for 2-D input the triangulation is attempted again with ## the options @code{@{"Qt", "Qbb", "Qc", "Qz"@}} which may result in ## reduced accuracy. ## ## If @var{options} is not present or @code{[]} then the default arguments are ## used. Otherwise, @var{options} replaces the default argument list. ## To append user options to the defaults it is necessary to repeat the ## default arguments in @var{options}. Use a null string to pass no arguments. ## ## @example ## @group ## x = rand (1, 10); ## y = rand (1, 10); ## tri = delaunay (x, y); ## triplot (tri, x, y); ## hold on; ## plot (x, y, "r*"); ## axis ([0,1,0,1]); ## @end group ## @end example ## @seealso{delaunayn, convhull, voronoi, triplot, trimesh, tetramesh, trisurf} ## @end deftypefn function tri = delaunay (varargin) if (nargin < 1 || nargin > 4) print_usage (); endif z = []; options = []; switch (nargin) case 1 if (! ismatrix (varargin{1}) || (columns (varargin{1}) != 2 && columns (varargin{1}) != 3)) error ("delaunay: X must be a matrix with 2 or 3 columns"); else x = varargin{1}(:,1); y = varargin{1}(:,2); if (columns (varargin{1}) == 3) z = varargin{1}(:,3); endif endif case 2 if (isnumeric (varargin{2})) x = varargin{1}; y = varargin{2}; elseif (! (ischar (varargin{2}) || iscellstr (varargin{2}))) error ("delaunay: OPTIONS must be a string or cell array of strings"); else options = varargin{2}; ncols = columns (varargin{1}); if (! ismatrix (varargin{1}) || (ncols != 2 && ncols != 3)) error ("delaunay: X must be a matrix with 2 or 3 columns"); else x = varargin{1}(:,1); y = varargin{1}(:,2); if (ncols == 3) z = varargin{1}(:,3); endif endif endif case 3 if (isnumeric (varargin{3})) x = varargin{1}; y = varargin{2}; z = varargin{3}; elseif (! (ischar (varargin{3}) || iscellstr (varargin{3}))) error ("delaunay: OPTIONS must be a string or cell array of strings"); else x = varargin{1}; y = varargin{2}; options = varargin{3}; endif case 4 x = varargin{1}; y = varargin{2}; z = varargin{3}; options = varargin{4}; if (! (ischar (options) || iscellstr (options))) error ("delaunay: OPTIONS must be a string or cell array of strings"); endif endswitch if (isempty (z)) x = x(:); y = y(:); if (! size_equal (x, y)) error ("delaunay: X and Y must be the same size"); endif tri = delaunayn ([x, y], options); else x = x(:); y = y(:); z = z(:); if (! size_equal (x, y, z)) error ("delaunay: X, Y, and Z must be the same size"); endif tri = delaunayn ([x, y, z], options); endif endfunction %!demo %! old_state = rand ("state"); %! restore_state = onCleanup (@() rand ("state", old_state)); %! rand ("state", 1); %! x = rand (1,10); %! y = rand (1,10); %! tri = delaunay (x,y); %! clf; %! triplot (tri, x, y); %! hold on; %! plot (x, y, "r*"); %! axis ([0,1,0,1]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0]; %! y = [0, 1, 0, -1]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;2,3,4]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0]; %! y = [0, 1, 0, -1]; %! mat = [x(:), y(:)]; %! assert (sortrows (sort (delaunay (mat), 2)), [1,2,4;2,3,4]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0, 0]; %! y = [0, 1, 0, -1, 0]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]); %!testif HAVE_QHULL %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0]; %! assert (sortrows (sort (delaunay (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]); %!testif HAVE_QHULL %! x = [1 5 2; 5 6 7]; %! y = [5 7 8; 1 2 3]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;1,3,4;1,3,5;3,4,6]); ## Test 3-D input %!testif HAVE_QHULL %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1]; %! assert (sortrows (sort (delaunay (x, y, z), 2)), [1,2,3,4;1,2,4,5]); ## Input validation tests %!error <Invalid call> delaunay () %!error <Invalid call> delaunay (1,2,3,4,5) %!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4)) %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), struct ()) %!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4), "") %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), struct ()) %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), ones (2,2), struct ()) %!error <X and Y must be the same size> delaunay (1, [1 2]) %!error <X, Y, and Z must be the same size> delaunay (1, [1 2], [1 2])