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annotate scripts/geometry/delaunay.m @ 18549:43cc202335dc stable release-3-8-1

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Version 3.8.1 released. * configure.ac (OCTAVE_VERSION): Now 3.8.1. (OCTAVE_MINOR_VERSION): Now 1. (OCTAVE_RELEASE_DATE): Set to 2014-03-06. Update copyright date for startup message.
author John W. Eaton <jwe@octave.org>
date Thu, 06 Mar 2014 14:40:35 -0500
parents d63878346099
children ba167badef9f 446c46af4b42
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1 ## Copyright (C) 1999-2013 Kai Habel
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} delaunay (@var{x}, @var{y})
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21 ## @deftypefnx {Function File} {} delaunay (@var{x})
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22 ## @deftypefnx {Function File} {} delaunay (@dots{}, @var{options})
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23 ## @deftypefnx {Function File} {@var{tri} =} delaunay (@dots{})
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24 ## Compute the Delaunay triangulation for a 2-D set of points.
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25 ## The return value @var{tri} is a set of triangles which satisfies the
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26 ## Delaunay circum-circle criterion, i.e., only a single data point from
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27 ## [@var{x}, @var{y}] is within the circum-circle of the defining triangle.
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28 ## The input @var{x} may also be a matrix with two columns where the first
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29 ## column contains x-data and the second y-data.
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30 ##
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31 ## The set of triangles @var{tri} is a matrix of size [n, 3]. Each
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32 ## row defines a triangle and the three columns are the three vertices
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33 ## of the triangle. The value of @code{@var{tri}(i,j)} is an index into
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34 ## @var{x} and @var{y} for the location of the j-th vertex of the i-th
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35 ## triangle.
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36 ##
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37 ## The optional last argument, which must be a string or cell array of strings,
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38 ## contains options passed to the underlying qhull command.
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39 ## See the documentation for the Qhull library for details
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40 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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41 ## The default options are @code{@{"Qt", "Qbb", "Qc", "Qz"@}}.
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42 ##
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43 ## If @var{options} is not present or @code{[]} then the default arguments are
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44 ## used. Otherwise, @var{options} replaces the default argument list.
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45 ## To append user options to the defaults it is necessary to repeat the
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46 ## default arguments in @var{options}. Use a null string to pass no arguments.
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47 ##
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48 ## If no output argument is specified the resulting Delaunay triangulation
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49 ## is plotted along with the original set of points.
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50 ##
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51 ## @example
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52 ## @group
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53 ## x = rand (1, 10);
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54 ## y = rand (1, 10);
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55 ## T = delaunay (x, y);
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56 ## VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
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57 ## VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
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58 ## axis ([0,1,0,1]);
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59 ## plot (VX, VY, "b", x, y, "r*");
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60 ## @end group
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61 ## @end example
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62 ## @seealso{delaunay3, delaunayn, convhull, voronoi, triplot, trimesh, trisurf}
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63 ## @end deftypefn
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64
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65 ## Author: Kai Habel <kai.habel@gmx.de>
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66
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67 function tri = delaunay (varargin)
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68
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69 if (nargin < 1 || nargin > 3)
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70 print_usage ();
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71 endif
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72
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73 options = [];
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74
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75 switch (nargin)
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76
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77 case 1
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78 if (! ismatrix (varargin{1}) || columns (varargin{1}) != 2)
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79 error ("delaunay: X must be a matrix with 2 columns");
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80 else
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81 x = varargin{1}(:,1);
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82 y = varargin{1}(:,2);
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83 endif
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84
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85 case 2
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86 if (isnumeric (varargin{2}))
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87 x = varargin{1};
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88 y = varargin{2};
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89 elseif (ischar (varargin{2}) || iscellstr (varargin{2}))
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90 options = varargin{2};
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91 if (! ismatrix (varargin{1}) && columns (varargin{1}) != 2)
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92 error ("delaunay: X must be a matrix with 2 columns");
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93 else
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94 x = varargin{1}(:,1);
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95 y = varargin{1}(:,2);
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96 endif
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97 else
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98 error ("delaunay: OPTIONS must be a string or cell array of strings");
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99 endif
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100
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101 case 3
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102 x = varargin{1};
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103 y = varargin{2};
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104 options = varargin{3};
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105
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106 if (! (ischar (options) || iscellstr (options)))
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107 error ("delaunay: OPTIONS must be a string or cell array of strings");
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108 endif
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109
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110 endswitch
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111
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112 if (! (isequal(size(x),size(y))))
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113 error ("delaunay: X and Y must be the same size");
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114 endif
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115
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116 T = delaunayn ([x(:), y(:)], options);
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117
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118 if (nargout == 0)
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119 x = x(:).';
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120 y = y(:).';
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121 VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
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122 VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
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123 plot (VX, VY, "b", x, y, "r*");
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124 else
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125 tri = T;
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126 endif
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128 endfunction
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131 %!demo
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132 %! old_state = rand ("state");
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133 %! restore_state = onCleanup (@() rand ("state", old_state));
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134 %! rand ("state", 1);
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135 %! x = rand (1,10);
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136 %! y = rand (1,10);
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137 %! T = delaunay (x,y);
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138 %! VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
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139 %! VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
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11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
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140 %! clf;
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141 %! plot (VX,VY,"b", x,y,"r*");
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142 %! axis ([0,1,0,1]);
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143
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144 %!testif HAVE_QHULL
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145 %! x = [-1, 0, 1, 0];
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146 %! y = [0, 1, 0, -1];
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147 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;2,3,4]);
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148
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149 %!testif HAVE_QHULL
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7c4a6197e020 delaunay.m: Accept a single matrix as input.
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150 %! x = [-1, 0, 1, 0];
7c4a6197e020 delaunay.m: Accept a single matrix as input.
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151 %! y = [0, 1, 0, -1];
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152 %! assert (sortrows (sort (delaunay ([x(:) y(:)]), 2)), [1,2,4;2,3,4]);
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7c4a6197e020 delaunay.m: Accept a single matrix as input.
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154 %!testif HAVE_QHULL
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155 %! x = [-1, 0, 1, 0, 0];
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156 %! y = [0, 1, 0, -1, 0];
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157 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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f72ffae1fcc3 delaunay.m: Fixed matlab compatibility and input check for single matrix (bug #39644)
Andreas Weber <andreas.weber@hs-offenburg.de>
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159 %!testif HAVE_QHULL
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160 %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
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parents: 16932
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161 %! assert (sortrows (sort (delaunay (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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163 %!testif HAVE_QHULL
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164 %! x = [1 5 2; 5 6 7];
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165 %! y = [5 7 8; 1 2 3];
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166 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;1,3,4;1,3,5;3,4,6]);
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168 %% FIXME: Need input validation tests
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169