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annotate scripts/geometry/voronoi.m @ 14237:11949c9795a0

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Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Add clf() to all demos using plot features to get reproducibility. Use 64 as input to all colormaps (jet (64)) to get reproducibility. * bicubic.m, cell2mat.m, celldisp.m, cplxpair.m, interp1.m, interp2.m, interpft.m, interpn.m, profile.m, profshow.m, convhull.m, delaunay.m, griddata.m, inpolygon.m, voronoi.m, autumn.m, bone.m, contrast.m, cool.m, copper.m, flag.m, gmap40.m, gray.m, hot.m, hsv.m, image.m, imshow.m, jet.m, ocean.m, pink.m, prism.m, rainbow.m, spring.m, summer.m, white.m, winter.m, condest.m, onenormest.m, axis.m, clabel.m, colorbar.m, comet.m, comet3.m, compass.m, contour.m, contour3.m, contourf.m, cylinder.m, daspect.m, ellipsoid.m, errorbar.m, ezcontour.m, ezcontourf.m, ezmesh.m, ezmeshc.m, ezplot.m, ezplot3.m, ezpolar.m, ezsurf.m, ezsurfc.m, feather.m, fill.m, fplot.m, grid.m, hold.m, isosurface.m, legend.m, loglog.m, loglogerr.m, pareto.m, patch.m, pbaspect.m, pcolor.m, pie.m, pie3.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, rose.m, scatter.m, scatter3.m, semilogx.m, semilogxerr.m, semilogy.m, semilogyerr.m, shading.m, slice.m, sombrero.m, stairs.m, stem.m, stem3.m, subplot.m, surf.m, surfc.m, surfl.m, surfnorm.m, text.m, title.m, trimesh.m, triplot.m, trisurf.m, uigetdir.m, uigetfile.m, uimenu.m, uiputfile.m, waitbar.m, xlim.m, ylim.m, zlim.m, mkpp.m, pchip.m, polyaffine.m, spline.m, bicgstab.m, cgs.m, gplot.m, pcg.m, pcr.m, treeplot.m, strtok.m, demo.m, example.m, rundemos.m, speed.m, test.m, calendar.m, datestr.m, datetick.m, weekday.m: Revamp %!demos to use Octave coding conventions on spacing, etc.
author Rik <octave@nomad.inbox5.com>
date Fri, 20 Jan 2012 12:59:53 -0800
parents 72c96de7a403
children ce2b59a6d0e5
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2000-2012 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 "linespec" is given it is used to set the color and line style of the
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30 ## plot. If an axis graphics handle @var{hax} is supplied then the Voronoi
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31 ## diagram is drawn on the specified axis rather than in a new figure.
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32 ##
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33 ## The @var{options} argument, which must be a string or cell array of strings,
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34 ## contains options passed to the underlying qhull command.
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35 ## See the documentation for the Qhull library for details
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36 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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37 ##
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38 ## If a single output argument is requested then the Voronoi diagram will be
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39 ## plotted and a graphics handle @var{h} to the plot is returned.
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40 ## [@var{vx}, @var{vy}] = voronoi(@dots{}) returns the Voronoi vertices
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41 ## instead of plotting the diagram.
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42 ##
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43 ## @example
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44 ## @group
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45 ## x = rand (10, 1);
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46 ## y = rand (size (x));
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47 ## h = convhull (x, y);
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48 ## [vx, vy] = voronoi (x, y);
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49 ## plot (vx, vy, "-b", x, y, "o", x(h), y(h), "-g")
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50 ## legend ("", "points", "hull");
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51 ## @end group
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52 ## @end example
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53 ##
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54 ## @seealso{voronoin, delaunay, convhull}
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55 ## @end deftypefn
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56
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57 ## Author: Kai Habel <kai.habel@gmx.de>
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58 ## First Release: 20/08/2000
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59
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60 ## 2002-01-04 Paul Kienzle <pkienzle@users.sf.net>
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61 ## * limit the default graph to the input points rather than the whole diagram
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62 ## * provide example
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63 ## * use unique(x,"rows") rather than __unique_rows__
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64
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65 ## 2003-12-14 Rafael Laboissiere <rafael@laboissiere.net>
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66 ## Added optional fourth argument to pass options to the underlying
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67 ## qhull command
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68
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69 function [vx, vy] = voronoi (varargin)
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70
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71 if (nargin < 1)
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72 print_usage ();
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73 endif
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74
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75 narg = 1;
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76 if (isscalar (varargin{1}) && ishandle (varargin{1}))
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77 handl = varargin{1};
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78 if (! strcmp (get (handl, "type"), "axes"))
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79 error ("voronoi: expecting first argument to be an axes object");
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80 endif
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81 narg++;
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82 elseif (nargout < 2)
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83 handl = gca ();
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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 lx = length (x);
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109 ly = length (y);
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110
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111 if (lx != ly)
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112 error ("voronoi: X and Y must be vectors of the same length");
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113 endif
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114
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115 ## Add box to approximate rays to infinity. For Voronoi diagrams the
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116 ## box can (and should) be close to the points themselves. To make the
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117 ## job of finding the exterior edges it should be at least two times the
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118 ## delta below however
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119 xmax = max (x(:));
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120 xmin = min (x(:));
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121 ymax = max (y(:));
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122 ymin = min (y(:));
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123 xdelta = xmax - xmin;
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124 ydelta = ymax - ymin;
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125 scale = 2;
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126
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127 xbox = [xmin - scale * xdelta; xmin - scale * xdelta; ...
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128 xmax + scale * xdelta; xmax + scale * xdelta];
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129 ybox = [xmin - scale * xdelta; xmax + scale * xdelta; ...
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130 xmax + scale * xdelta; xmin - scale * xdelta];
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131
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132 [p, c, infi] = __voronoi__ ("voronoi",
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133 [[x(:) ; xbox(:)], [y(:); ybox(:)]],
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134 opts{:});
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135
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136 idx = find (! infi);
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137 ll = length (idx);
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138 c = c(idx).';
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139 k = sum (cellfun ("length", c));
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140 edges = cell2mat (cellfun (@(x) [x ; [x(end), x(1:end-1)]], c,
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141 "uniformoutput", false));
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142
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143 ## Identify the unique edges of the Voronoi diagram
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144 edges = sortrows (sort (edges).').';
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145 edges = edges (:, [(edges(1, 1: end - 1) != edges(1, 2 : end) | ...
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146 edges(2, 1 :end - 1) != edges(2, 2 : end)), true]);
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147
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148 ## Eliminate the edges of the diagram representing the box
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149 poutside = (1 : rows(p)) ...
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150 (p (:, 1) < xmin - xdelta | p (:, 1) > xmax + xdelta | ...
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151 p (:, 2) < ymin - ydelta | p (:, 2) > ymax + ydelta);
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152 edgeoutside = ismember (edges (1, :), poutside) & ...
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153 ismember (edges (2, :), poutside);
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154 edges (:, edgeoutside) = [];
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155
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156 ## Get points of the diagram
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157 Vvx = reshape (p(edges, 1), size (edges));
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158 Vvy = reshape (p(edges, 2), size (edges));
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159
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160 if (nargout < 2)
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161 lim = [xmin, xmax, ymin, ymax];
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162 h = plot (handl, Vvx, Vvy, linespec{:}, x, y, '+');
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163 axis (lim + 0.1 * [[-1, 1] * (lim (2) - lim (1)), ...
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164 [-1, 1] * (lim (4) - lim (3))]);
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165 if (nargout == 1)
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166 vx = h;
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167 endif
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168 else
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169 vx = Vvx;
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170 vy = Vvy;
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171 endif
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172
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173 endfunction
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174
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175
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176 %!demo
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177 %! voronoi (rand (10,1), rand (10,1));
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178
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179 %!testif HAVE_QHULL
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180 %! phi = linspace (-pi, 3/4*pi, 8);
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181 %! [x,y] = pol2cart (phi, 1);
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182 %! [vx,vy] = voronoi (x,y);
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183 %! assert(vx(2,:), zeros (1, columns (vx)), eps);
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184 %! assert(vy(2,:), zeros (1, columns (vy)), eps);
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185
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186 %% FIXME: Need input validation tests
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187