annotate scripts/geometry/inpolygon.m @ 20133:bef9086a6725

inpolygon.m: Overhaul function and fix bug #40970. * NEWS: Announce changes in inpolygon definition. * inpolygon.m: Use 'in |= on' to include points on the boundary since this is what Matlab does. Rewrite docstring with new definition. Change error() messages to be more explicit. Add more input validation tests.
author Rik <rik@octave.org>
date Sat, 25 Apr 2015 20:50:36 -0700
parents 9fc020886ae9
children 7503499a252b
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1 ## Copyright (C) 2006-2015 Frederick (Rick) A Niles
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2 ## and Søren Hauberg
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{in} =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv})
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22 ## @deftypefnx {Function File} {[@var{in}, @var{on}] =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv})
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23 ##
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24 ## For a polygon defined by vertex points @code{(@var{xv}, @var{yv})}, return
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25 ## true if the points @code{(@var{x}, @var{y})} are inside (or on the boundary)
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26 ## of the polygon; Otherwise, return false.
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27 ##
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28 ## The variables @var{x}, @var{y}, must have the same dimension. The optional
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29 ## output @var{on} returns true if the points are exactly on the polygon
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30 ## edge, and false otherwise.
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31 ## @seealso{delaunay}
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32 ## @end deftypefn
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33
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34 ## Author: Frederick (Rick) A Niles <niles@rickniles.com>
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35 ## Created: 14 November 2006
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36
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37 ## Vectorized by Søren Hauberg <soren@hauberg.org>
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38
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39 ## The method for determining if a point is in in a polygon is based on
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40 ## the algorithm shown on
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41 ## http://local.wasp.uwa.edu.au/~pbourke/geometry/insidepoly/
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42 ## and is credited to Randolph Franklin.
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43
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44 function [in, on] = inpolygon (x, y, xv, yv)
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45
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46 if (nargin != 4)
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47 print_usage ();
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48 endif
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49
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50 if (! (isreal (x) && isreal (y) && ismatrix (y) && ismatrix (y)
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51 && size_equal (x, y)))
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52 error ("inpolygon: X and Y must be real matrices of the same size");
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53 elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv)
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54 && size_equal (xv, yv)))
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55 error ("inpolygon: XV and YV must be real vectors of the same size");
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56 endif
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57
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58 npol = length (xv);
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59
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60 in = on = false (size (x));
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61
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62 j = npol;
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63 for i = 1 : npol
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64 delta_xv = xv(j) - xv(i);
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65 delta_yv = yv(j) - yv(i);
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66 ## distance = [distance from (x,y) to edge] * length(edge)
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67 distance = delta_xv .* (y - yv(i)) - (x - xv(i)) .* delta_yv;
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68
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69 ## is y between the y-values of edge i,j AND (x,y) on the left of the edge?
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70 idx1 = (((yv(i) <= y & y < yv(j)) | (yv(j) <= y & y < yv(i)))
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71 & 0 < distance.*delta_yv);
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72 in(idx1) = ! in(idx1);
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73
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74 ## Check if (x,y) are actually on the boundary of the polygon.
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75 idx2 = (((yv(i) <= y & y <= yv(j)) | (yv(j) <= y & y <= yv(i)))
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76 & ((xv(i) <= x & x <= xv(j)) | (xv(j) <= x & x <= xv(i)))
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77 & (0 == distance | !delta_xv));
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78 on(idx2) = true;
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79
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80 j = i;
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81 endfor
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82
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83 ## Matlab definition include both in polygon and on polygon points.
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84 in |= on;
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85
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86 endfunction
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87
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88
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89 %!demo
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90 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
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91 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
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92 %! 0.05840 ];
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93 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
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94 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
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95 %! 0.60628 ];
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96 %! xa = [0:0.1:2.3];
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97 %! ya = [0:0.1:1.4];
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98 %! [x,y] = meshgrid (xa, ya);
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99 %! [in,on] = inpolygon (x, y, xv, yv);
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100 %! inside = in & !on;
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101 %!
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102 %! clf;
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103 %! plot (xv, yv);
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104 %! hold on;
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105 %! plot (x(inside), y(inside), "@g")
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106 %! plot (x(!in), y(!in), "@m");
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107 %! plot (x(on), y(on), "@b");
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108 %! hold off;
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109 %! disp ("Green points are inside polygon, magenta are outside,");
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110 %! disp ("and blue are on boundary.");
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111
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112 %!demo
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113 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
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114 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
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115 %! 0.05840, 0.73295, 1.28913, 1.74221, 1.16023, ...
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116 %! 0.73295, 0.05840 ];
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117 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
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118 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
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119 %! 0.60628, 0.82096, 0.67155, 0.96114, 1.14833, ...
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120 %! 0.82096, 0.60628];
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121 %! xa = [0:0.1:2.3];
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122 %! ya = [0:0.1:1.4];
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123 %! [x, y] = meshgrid (xa, ya);
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124 %! [in, on] = inpolygon (x, y, xv, yv);
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125 %! inside = in & !on;
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126 %!
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
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127 %! clf;
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128 %! plot (xv, yv);
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129 %! hold on;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
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130 %! plot (x(inside), y(inside), "@g");
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131 %! plot (x(!in), y(!in), "@m");
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132 %! plot (x(on), y(on), "@b");
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133 %! hold off;
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134 %! disp ("Green points are inside polygon, magenta are outside,");
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135 %! disp ("and blue are on boundary.");
13057
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
136
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
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137 %!test
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
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138 %! [in, on] = inpolygon ([1, 0, 2], [1, 0, 0], [-1, -1, 1, 1], [-1, 1, 1, -1]);
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Rik <rik@octave.org>
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139 %! assert (in, [true, true, false]);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
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140 %! assert (on, [true, false, false]);
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141
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
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142 ## Test input validation
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143 %!error inpolygon ()
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
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144 %!error inpolygon (1, 2)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
145 %!error inpolygon (1, 2, 3)
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
146 %!error inpolygon (1, 2, 3, 4, 5)
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
147 %!error <X and Y must be real matrices> inpolygon (1i, 1, [3, 4], [5, 6])
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
148 %!error <X and Y must be real matrices> inpolygon (1, {1}, [3, 4], [5, 6])
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
149 %!error <X and Y must be .* the same size> inpolygon (1, [1,2], [3, 4], [5, 6])
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
150 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3i, 4], [5, 6])
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
151 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3, 4], {5, 6})
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
152 %!error <XV and YV must .* the same size> inpolygon ([1,2], [3, 4], [5, 6], 1)
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153