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annotate scripts/geometry/delaunay.m @ 20654:b65888ec820e draft default tip gccjit

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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents 9fc020886ae9
children
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1 ## Copyright (C) 1999-2015 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} {@var{tri} =} delaunay (@var{x}, @var{y})
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21 ## @deftypefnx {Function File} {@var{tetr} =} delaunay (@var{x}, @var{y}, @var{z})
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22 ## @deftypefnx {Function File} {@var{tri} =} delaunay (@var{x})
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23 ## @deftypefnx {Function File} {@var{tri} =} delaunay (@dots{}, @var{options})
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24 ## Compute the Delaunay triangulation for a 2-D or 3-D set of points.
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25 ##
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26 ## For 2-D sets, the return value @var{tri} is a set of triangles which
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27 ## satisfies the Delaunay circum-circle criterion, i.e., only a single data
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28 ## point from [@var{x}, @var{y}] is within the circum-circle of the defining
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29 ## triangle. The set of triangles @var{tri} is a matrix of size [n, 3]. Each
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30 ## row defines a triangle and the three columns are the three vertices of the
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31 ## triangle. The value of @code{@var{tri}(i,j)} is an index into @var{x} and
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32 ## @var{y} for the location of the j-th vertex of the i-th triangle.
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33 ##
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34 ## For 3-D sets, the return value @var{tetr} is a set of tetrahedrons which
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35 ## satisfies the Delaunay circum-circle criterion, i.e., only a single data
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36 ## point from [@var{x}, @var{y}, @var{z}] is within the circum-circle of the
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37 ## defining tetrahedron. The set of tetrahedrons is a matrix of size [n, 4].
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38 ## Each row defines a tetrahedron and the four columns are the four vertices of
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39 ## the tetrahedron. The value of @code{@var{tetr}(i,j)} is an index into
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40 ## @var{x}, @var{y}, @var{z} for the location of the j-th vertex of the i-th
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41 ## tetrahedron.
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42 ##
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43 ## The input @var{x} may also be a matrix with two or three columns where the
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44 ## first column contains x-data, the second y-data, and the optional third
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45 ## column contains z-data.
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46 ##
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47 ## The optional last argument, which must be a string or cell array of strings,
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48 ## contains options passed to the underlying qhull command.
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49 ## See the documentation for the Qhull library for details
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50 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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51 ## The default options are @code{@{"Qt", "Qbb", "Qc", "Qz"@}}.
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52 ##
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53 ## If @var{options} is not present or @code{[]} then the default arguments are
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54 ## used. Otherwise, @var{options} replaces the default argument list.
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55 ## To append user options to the defaults it is necessary to repeat the
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56 ## default arguments in @var{options}. Use a null string to pass no arguments.
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57 ##
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58 ## @example
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59 ## @group
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60 ## x = rand (1, 10);
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61 ## y = rand (1, 10);
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62 ## tri = delaunay (x, y);
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63 ## triplot (tri, x, y);
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64 ## hold on;
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65 ## plot (x, y, "r*");
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66 ## axis ([0,1,0,1]);
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67 ## @end group
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68 ## @end example
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69 ## @seealso{delaunayn, convhull, voronoi, triplot, trimesh, tetramesh, trisurf}
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70 ## @end deftypefn
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71
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72 ## Author: Kai Habel <kai.habel@gmx.de>
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73
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74 function tri = delaunay (varargin)
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75
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76 if (nargin < 1 || nargin > 4)
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77 print_usage ();
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78 endif
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79
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80 z = [];
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81 options = [];
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82
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83 switch (nargin)
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84
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85 case 1
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86 if (! ismatrix (varargin{1})
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87 || (columns (varargin{1}) != 2 && columns (varargin{1}) != 3))
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88 error ("delaunay: X must be a matrix with 2 or 3 columns");
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89 else
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90 x = varargin{1}(:,1);
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91 y = varargin{1}(:,2);
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92 if (columns (varargin{1}) == 3)
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93 z = varargin{1}(:,3);
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94 endif
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95 endif
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96
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97 case 2
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98 if (isnumeric (varargin{2}))
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99 x = varargin{1};
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100 y = varargin{2};
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101 elseif (! (ischar (varargin{2}) || iscellstr (varargin{2})))
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102 error ("delaunay: OPTIONS must be a string or cell array of strings");
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103 else
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104 options = varargin{2};
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105 ncols = columns (varargin{1});
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106
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107 if (! ismatrix (varargin{1}) || (ncols != 2 && ncols != 3))
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108 error ("delaunay: X must be a matrix with 2 or 3 columns");
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109 else
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110 x = varargin{1}(:,1);
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111 y = varargin{1}(:,2);
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112 if (ncols == 3)
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113 z = varargin{1}(:,3);
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114 endif
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115 endif
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116 endif
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117
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118 case 3
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119 if (isnumeric (varargin{3}))
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120 x = varargin{1};
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121 y = varargin{2};
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122 z = varargin{3};
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123 elseif (! (ischar (varargin{3}) || iscellstr (varargin{3})))
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124 error ("delaunay: OPTIONS must be a string or cell array of strings");
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125 else
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126 x = varargin{1};
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127 y = varargin{2};
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128 options = varargin{3};
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129 endif
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130
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131 case 4
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132 x = varargin{1};
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133 y = varargin{2};
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134 z = varargin{3};
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135 options = varargin{4};
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136
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137 if (! (ischar (options) || iscellstr (options)))
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138 error ("delaunay: OPTIONS must be a string or cell array of strings");
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139 endif
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140
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141 endswitch
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142
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143 if (isempty (z))
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144 if (! size_equal (x, y))
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145 error ("delaunay: X and Y must be the same size");
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146 endif
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147 tri = delaunayn ([x(:), y(:)], options);
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148 else
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149 if (! size_equal (x, y, z))
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150 error ("delaunay: X, Y, and Z must be the same size");
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151 endif
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152 tri = delaunayn ([x(:), y(:), z(:)], options);
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153 endif
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154
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155 endfunction
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156
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157
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158 %!demo
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159 %! old_state = rand ("state");
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160 %! restore_state = onCleanup (@() rand ("state", old_state));
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161 %! rand ("state", 1);
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162 %! x = rand (1,10);
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163 %! y = rand (1,10);
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164 %! tri = delaunay (x,y);
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165 %! clf;
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166 %! triplot (tri, x, y);
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167 %! hold on;
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168 %! plot (x, y, "r*");
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169 %! axis ([0,1,0,1]);
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170
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171 %!testif HAVE_QHULL
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172 %! x = [-1, 0, 1, 0];
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173 %! y = [0, 1, 0, -1];
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174 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;2,3,4]);
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175
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176 %!testif HAVE_QHULL
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177 %! x = [-1, 0, 1, 0];
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178 %! y = [0, 1, 0, -1];
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179 %! assert (sortrows (sort (delaunay ([x(:) y(:)]), 2)), [1,2,4;2,3,4]);
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180
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181 %!testif HAVE_QHULL
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182 %! x = [-1, 0, 1, 0, 0];
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183 %! y = [0, 1, 0, -1, 0];
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184 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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185
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186 %!testif HAVE_QHULL
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187 %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
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188 %! assert (sortrows (sort (delaunay (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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189
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190 %!testif HAVE_QHULL
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191 %! x = [1 5 2; 5 6 7];
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192 %! y = [5 7 8; 1 2 3];
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193 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;1,3,4;1,3,5;3,4,6]);
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194
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195 ## Test 3-D input
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196 %!testif HAVE_QHULL
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197 %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1];
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198 %! assert (sortrows (sort (delaunay (x, y, z), 2)), [1,2,3,4;1,2,4,5])
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199
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200 ## Input validation tests
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201 %!error delaunay ()
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202 %!error delaunay (1,2,3,4,5)
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203 %!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4))
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204 %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), struct())
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205 %!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4), "")
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206 %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), struct())
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207 %!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), ones (2,2), struct())
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208 %!error <X and Y must be the same size> delaunay (1, [1 2])
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209 %!error <X, Y, and Z must be the same size> delaunay (1, [1 2], [1 2])
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210