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annotate scripts/geometry/voronoi.m @ 18633:3f2a95a4b98d draft lyh-review

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jit compiler: use existing int functions
author Stefan Mahr <dac922@gmx.de>
date Sun, 24 Nov 2013 22:46:32 +0100
parents 5646f999245d
children 0e1f5a750d00
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d63878346099 maint: Update copyright notices for release.
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1 ## Copyright (C) 2000-2013 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} {} voronoi (@var{x}, @var{y})
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21 ## @deftypefnx {Function File} {} voronoi (@var{x}, @var{y}, @var{options})
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22 ## @deftypefnx {Function File} {} voronoi (@dots{}, "linespec")
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23 ## @deftypefnx {Function File} {} voronoi (@var{hax}, @dots{})
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24 ## @deftypefnx {Function File} {@var{h} =} voronoi (@dots{})
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25 ## @deftypefnx {Function File} {[@var{vx}, @var{vy}] =} voronoi (@dots{})
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26 ## Plot the Voronoi diagram of points @code{(@var{x}, @var{y})}.
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27 ## The Voronoi facets with points at infinity are not drawn.
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28 ##
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29 ## If @qcode{"linespec"} is given it is used to set the color and line style
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30 ## of the plot. If an axis graphics handle @var{hax} is supplied then the
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31 ## Voronoi diagram is drawn on the specified axis rather than in a new
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32 ## figure.
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33 ##
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34 ## The @var{options} argument, which must be a string or cell array of strings,
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35 ## contains options passed to the underlying qhull command.
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36 ## See the documentation for the Qhull library for details
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37 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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38 ##
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39 ## If a single output argument is requested then the Voronoi diagram will be
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40 ## plotted and a graphics handle @var{h} to the plot is returned.
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41 ## [@var{vx}, @var{vy}] = voronoi (@dots{}) returns the Voronoi vertices
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42 ## instead of plotting the diagram.
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43 ##
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44 ## @example
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45 ## @group
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46 ## x = rand (10, 1);
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47 ## y = rand (size (x));
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48 ## h = convhull (x, y);
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49 ## [vx, vy] = voronoi (x, y);
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50 ## plot (vx, vy, "-b", x, y, "o", x(h), y(h), "-g");
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51 ## legend ("", "points", "hull");
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52 ## @end group
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53 ## @end example
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54 ##
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55 ## @seealso{voronoin, delaunay, convhull}
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56 ## @end deftypefn
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57
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58 ## Author: Kai Habel <kai.habel@gmx.de>
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59 ## First Release: 20/08/2000
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60
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61 ## 2002-01-04 Paul Kienzle <pkienzle@users.sf.net>
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62 ## * limit the default graph to the input points rather than the whole diagram
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63 ## * provide example
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64 ## * use unique(x,"rows") rather than __unique_rows__
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65
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66 ## 2003-12-14 Rafael Laboissiere <rafael@laboissiere.net>
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67 ## Added optional fourth argument to pass options to the underlying
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68 ## qhull command
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69
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70 function [vx, vy] = voronoi (varargin)
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71
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72 if (nargin < 1)
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73 print_usage ();
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74 endif
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75
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76 narg = 1;
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77 hax = NaN;
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78 if (isscalar (varargin{1}) && ishandle (varargin{1}))
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79 hax = varargin{1};
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80 if (! isaxes (hax))
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81 error ("voronoi: HAX argument must be an axes object");
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82 endif
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83 narg++;
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84 endif
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85
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86 if (nargin < 1 + narg || nargin > 3 + narg)
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87 print_usage ();
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88 endif
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89
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90 x = varargin{narg++};
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91 y = varargin{narg++};
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92
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93 opts = {};
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94 if (narg <= nargin)
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95 if (iscell (varargin{narg}))
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96 opts = varargin(narg++);
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97 elseif (isnumeric (varargin{narg}))
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98 ## Accept, but ignore, the triangulation
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99 narg++;
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100 endif
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101 endif
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102
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103 linespec = {"b"};
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104 if (narg <= nargin && ischar (varargin{narg}))
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105 linespec = varargin(narg);
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106 endif
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107
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108 if (length (x) != length (y))
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109 error ("voronoi: X and Y must be vectors of the same length");
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110 elseif (length (x) < 2)
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111 error ("voronoi: minimum of 2 points needed");
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112 endif
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113
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114 ## Add box to approximate rays to infinity. For Voronoi diagrams the
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115 ## box can (and should) be close to the points themselves. To make the
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116 ## job of finding the exterior edges it should be at least two times the
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117 ## delta below however
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118 xmax = max (x(:));
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119 xmin = min (x(:));
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120 ymax = max (y(:));
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121 ymin = min (y(:));
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122 xdelta = xmax - xmin;
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123 ydelta = ymax - ymin;
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124 scale = 2;
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125
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126 xbox = [xmin - scale * xdelta; xmin - scale * xdelta; ...
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127 xmax + scale * xdelta; xmax + scale * xdelta];
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128 ybox = [ymin - scale * ydelta; ymax + scale * ydelta; ...
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129 ymax + scale * ydelta; ymin - scale * ydelta];
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130
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131 [p, c, infi] = __voronoi__ ("voronoi",
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132 [[x(:) ; xbox(:)], [y(:); ybox(:)]],
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133 opts{:});
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134
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135 c = c(! infi).';
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136 ## Delete null entries which cause problems in next cellfun function
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137 c(cellfun ("isempty", c)) = [];
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138 edges = cell2mat (cellfun (@(x) [x ; [x(end), x(1:end-1)]], c,
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139 "uniformoutput", false));
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140
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141 ## Identify the unique edges of the Voronoi diagram
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142 edges = sortrows (sort (edges).').';
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143 edges = edges(:, [(edges(1, 1 :end - 1) != edges(1, 2 : end) | ...
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144 edges(2, 1 :end - 1) != edges(2, 2 : end)), true]);
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145
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146 if (numel (x) > 2)
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147 ## Eliminate the edges of the diagram representing the box
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148 poutside = (1:rows (p)) ...
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149 (p(:, 1) < xmin - xdelta | p(:, 1) > xmax + xdelta | ...
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150 p(:, 2) < ymin - ydelta | p(:, 2) > ymax + ydelta);
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151 edgeoutside = ismember (edges(1, :), poutside) & ...
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152 ismember (edges(2, :), poutside);
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153 edges(:, edgeoutside) = [];
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154 else
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155 ## look for the edge between the two given points
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156 for edge = edges(1:2,:)
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157 if (det ([[[1;1],p(edge,1:2)];1,x(1),y(1)])
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158 * det ([[[1;1],p(edge,1:2)];1,x(2),y(2)]) < 0)
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159 edges = edge;
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160 break;
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161 endif
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162 endfor
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163 ## Use larger plot limits to make it more likely single bisector is shown.
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164 xdelta = ydelta = max (xdelta, ydelta);
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165 endif
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166
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167 ## Get points of the diagram
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168 Vvx = reshape (p(edges, 1), size (edges));
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169 Vvy = reshape (p(edges, 2), size (edges));
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170
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c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
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171 if (nargout < 2)
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Rik <rik@octave.org>
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172 if (isnan (hax))
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173 hax = gca ();
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174 endif
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175 h = plot (hax, Vvx, Vvy, linespec{:}, x, y, '+');
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176 lim = [xmin, xmax, ymin, ymax];
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177 axis (lim + 0.1 * [[-1, 1] * xdelta, [-1, 1] * ydelta]);
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178 if (nargout == 1)
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179 vx = h;
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180 endif
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181 else
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182 vx = Vvx;
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183 vy = Vvy;
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184 endif
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185
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186 endfunction
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187
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188
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189 %!demo
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190 %! voronoi (rand (10,1), rand (10,1));
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191
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192 %!testif HAVE_QHULL
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193 %! phi = linspace (-pi, 3/4*pi, 8);
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194 %! [x,y] = pol2cart (phi, 1);
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195 %! [vx,vy] = voronoi (x,y);
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196 %! assert (vx(2,:), zeros (1, columns (vx)), eps);
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197 %! assert (vy(2,:), zeros (1, columns (vy)), eps);
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198
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199 %!testif HAVE_QHULL
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200 %! ## Special case of just 2 points
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201 %! x = [0 1]; y = [1 0];
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202 %! [vx, vy] = voronoi (x,y);
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203 %! assert (vx, [-0.7; 1.7], eps);
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204 %! assert (vy, [-0.7; 1.7], eps);
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205
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206 %% Input validation tests
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207 %!error voronoi ()
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208 %!error voronoi (ones (3,1))
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209 %!error voronoi (ones (3,1), ones (3,1), "bogus1", "bogus2", "bogus3")
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210 %!error <HAX argument must be an axes object> voronoi (0, ones (3,1), ones (3,1))
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211 %!error <X and Y must be vectors of the same length> voronoi (ones (3,1), ones (4,1))
18202
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212 %!error <minimum of 2 points needed> voronoi (2.5, 3.5)
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diff changeset
213