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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 01de0045b2e3
children 66456820ff59
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2007-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{T} =} delaunayn (@var{pts})
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28 ## @deftypefnx {} {@var{T} =} delaunayn (@var{pts}, @var{options})
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29 ## Compute the Delaunay triangulation for an N-dimensional set of points.
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30 ##
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31 ## The Delaunay triangulation is a tessellation of the convex hull of a set of
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32 ## points such that no N-sphere defined by the N-triangles contains any other
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33 ## points from the set.
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34 ##
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35 ## The input matrix @var{pts} of size [n, dim] contains n points in a space of
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36 ## dimension dim. The return matrix @var{T} has size [m, dim+1]. Each row of
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37 ## @var{T} contains a set of indices back into the original set of points
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38 ## @var{pts} which describes a simplex of dimension dim. For example, a 2-D
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39 ## simplex is a triangle and 3-D simplex is a tetrahedron.
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40 ##
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41 ## An optional second argument, which must be a string or cell array of
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42 ## strings, contains options passed to the underlying qhull command. See the
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43 ## documentation for the Qhull library for details
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44 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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45 ## The default options depend on the dimension of the input:
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46 ##
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47 ## @itemize
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48 ## @item 2-D and 3-D: @var{options} = @code{@{"Qt", "Qbb", "Qc"@}}
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49 ##
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50 ## @item 4-D and higher: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qx"@}}
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51 ## @end itemize
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52 ##
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53 ## If Qhull fails for 2-D input the triangulation is attempted again with
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54 ## the options @code{@{"Qt", "Qbb", "Qc", "Qz"@}} which may result in
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55 ## reduced accuracy.
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56 ##
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57 ## If @var{options} is not present or @code{[]} then the default arguments are
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58 ## used. Otherwise, @var{options} replaces the default argument list.
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59 ## To append user options to the defaults it is necessary to repeat the
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60 ## default arguments in @var{options}. Use a null string to pass no arguments.
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61 ##
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62 ## @seealso{delaunay, convhulln, voronoin, trimesh, tetramesh}
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63 ## @end deftypefn
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64
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65 function T = delaunayn (pts, varargin)
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66
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67 if (nargin < 1)
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68 print_usage ();
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69 endif
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70
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71 if (isempty (varargin) || isempty (varargin{1}))
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72 try
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73 T = __delaunayn__ (pts);
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74 catch
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75 if (columns (pts) <= 2)
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76 T = __delaunayn__ (pts, "Qt Qbb Qc Qz");
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77 endif
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78 end_try_catch
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79 else
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80 T = __delaunayn__ (pts, varargin{:});
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81 endif
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82
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83 if (isa (pts, "single"))
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84 tol = 1e3 * eps ("single");
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85 else
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86 tol = 1e3 * eps;
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87 endif
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88
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89 ## Try to remove the zero volume simplices. The volume of the i-th simplex is
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90 ## given by abs(det(pts(T(i,1:end-1),:)-pts(T(i,2:end),:)))/factorial(ndim+1)
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91 ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a
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92 ## relative volume less than some arbitrary criteria is rejected. The
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93 ## criteria we use is the volume of the simplex corresponding to an
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94 ## orthogonal simplex is equal edge length all equal to the edge length of
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95 ## the original simplex. If the relative volume is 1e3*eps then the simplex
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96 ## is rejected. Note division of the two volumes means that the factor
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97 ## factorial(ndim+1) is dropped.
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98 [nt, nd] = size (T);
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99 if (nd == 3)
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100 ## 2-D case
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101 np = rows (pts);
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102 ptsz = [pts, zeros(np, 1)];
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103 p1 = ptsz(T(:,1), :);
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104 p2 = ptsz(T(:,2), :);
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105 p3 = ptsz(T(:,3), :);
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106 p12 = p1 - p2;
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107 p23 = p2 - p3;
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108 det = cross (p12, p23, 2);
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109 idx = abs (det (:,3) ./ sqrt (sumsq (p12, 2))) < tol & ...
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110 abs (det (:,3) ./ sqrt (sumsq (p23, 2))) < tol;
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111 else
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112 ## FIXME: Vectorize this for loop or convert delaunayn to .oct function
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113 idx = [];
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114 for i = 1:nt
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115 X = pts(T(i,1:end-1),:) - pts(T(i,2:end),:);
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116 if (abs (det (X)) / sqrt (sumsq (X, 2)) < tol)
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117 idx(end+1) = i;
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118 endif
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119 endfor
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120 endif
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121 T(idx,:) = [];
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122
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9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman]
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123 endfunction
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124
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125
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126 %!testif HAVE_QHULL
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127 %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
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128 %! assert (sortrows (sort (delaunayn (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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129
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130 ## Test 3-D input
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131 %!testif HAVE_QHULL
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132 %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1];
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133 %! assert (sortrows (sort (delaunayn ([x(:) y(:) z(:)]), 2)),
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134 %! [1,2,3,4;1,2,4,5]);
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135
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136 ## FIXME: Need tests for delaunayn
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137
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138 ## Input validation tests
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139 %!error <Invalid call> delaunayn ()