Mercurial > octave
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> |
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date | Sat, 25 Apr 2015 20:50:36 -0700 |
parents | 9fc020886ae9 |
children | 7503499a252b |
rev | line source |
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1 ## Copyright (C) 2006-2015 Frederick (Rick) A Niles |
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2 ## and Søren Hauberg |
6847 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
6847 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
6847 | 19 |
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}) |
6847 | 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} |
6847 | 32 ## @end deftypefn |
33 | |
34 ## Author: Frederick (Rick) A Niles <niles@rickniles.com> | |
35 ## Created: 14 November 2006 | |
36 | |
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37 ## Vectorized by Søren Hauberg <soren@hauberg.org> |
6847 | 38 |
39 ## The method for determining if a point is in in a polygon is based on | |
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. |
6847 | 43 |
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44 function [in, on] = inpolygon (x, y, xv, yv) |
6847 | 45 |
7125 | 46 if (nargin != 4) |
47 print_usage (); | |
48 endif | |
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"); |
7125 | 53 elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv) |
10549 | 54 && size_equal (xv, yv))) |
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55 error ("inpolygon: XV and YV must be real vectors of the same size"); |
6847 | 56 endif |
57 | |
7125 | 58 npol = length (xv); |
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59 |
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60 in = on = false (size (x)); |
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61 |
6847 | 62 j = npol; |
63 for i = 1 : npol | |
64 delta_xv = xv(j) - xv(i); | |
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))) |
10549 | 71 & 0 < distance.*delta_yv); |
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72 in(idx1) = ! in(idx1); |
6847 | 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 |
6847 | 80 j = i; |
81 endfor | |
7125 | 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 |
6847 | 86 endfunction |
87 | |
88 | |
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."); |
6847 | 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 %! |
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127 %! clf; |
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128 %! plot (xv, yv); |
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129 %! hold on; |
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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."); |
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136 |
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137 %!test |
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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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139 %! assert (in, [true, true, false]); |
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140 %! assert (on, [true, false, false]); |
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141 |
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maint: Clean up m-files to follow Octave coding conventions.
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142 ## Test input validation |
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143 %!error inpolygon () |
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144 %!error inpolygon (1, 2) |
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145 %!error inpolygon (1, 2, 3) |
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bef9086a6725
inpolygon.m: Overhaul function and fix bug #40970.
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146 %!error inpolygon (1, 2, 3, 4, 5) |
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147 %!error <X and Y must be real matrices> inpolygon (1i, 1, [3, 4], [5, 6]) |
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148 %!error <X and Y must be real matrices> inpolygon (1, {1}, [3, 4], [5, 6]) |
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149 %!error <X and Y must be .* the same size> inpolygon (1, [1,2], [3, 4], [5, 6]) |
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150 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3i, 4], [5, 6]) |
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151 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3, 4], {5, 6}) |
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152 %!error <XV and YV must .* the same size> inpolygon ([1,2], [3, 4], [5, 6], 1) |
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153 |