Mercurial > octave
annotate scripts/geometry/inpolygon.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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27919
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update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2006-2020 The Octave Project Developers |
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2 ## |
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution |
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4 ## or <https://octave.org/COPYRIGHT.html/>. |
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5 ## |
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6 ## and Søren Hauberg |
6847 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
6847 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
6847 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
6847 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
6847 | 23 |
24 ## -*- texinfo -*- | |
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25 ## @deftypefn {} {@var{in} =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv}) |
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26 ## @deftypefnx {} {[@var{in}, @var{on}] =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv}) |
6847 | 27 ## |
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28 ## For a polygon defined by vertex points @code{(@var{xv}, @var{yv})}, return |
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29 ## true if the points @code{(@var{x}, @var{y})} are inside (or on the boundary) |
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30 ## of the polygon; Otherwise, return false. |
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31 ## |
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32 ## The input variables @var{x} and @var{y}, must have the same dimension. |
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33 ## |
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34 ## The optional output @var{on} returns true if the points are exactly on the |
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35 ## polygon edge, and false otherwise. |
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36 ## @seealso{delaunay} |
6847 | 37 ## @end deftypefn |
38 | |
39 ## Author: Frederick (Rick) A Niles <niles@rickniles.com> | |
40 ## Created: 14 November 2006 | |
41 | |
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42 ## Vectorized by Søren Hauberg <soren@hauberg.org> |
6847 | 43 |
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44 ## The method for determining if a point is in a polygon is based on |
6847 | 45 ## the algorithm shown on |
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46 ## http://local.wasp.uwa.edu.au/~pbourke/geometry/insidepoly/ |
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47 ## and is credited to Randolph Franklin. |
6847 | 48 |
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49 function [in, on] = inpolygon (x, y, xv, yv) |
6847 | 50 |
7125 | 51 if (nargin != 4) |
52 print_usage (); | |
53 endif | |
54 | |
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55 if (! (isreal (x) && isreal (y) && isnumeric (x) && isnumeric (y) |
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56 && size_equal (x, y))) |
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57 error ("inpolygon: X and Y must be real arrays of the same size"); |
7125 | 58 elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv) |
10549 | 59 && size_equal (xv, yv))) |
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60 error ("inpolygon: XV and YV must be real vectors of the same size"); |
6847 | 61 endif |
62 | |
7125 | 63 npol = length (xv); |
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64 |
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65 in = on = false (size (x)); |
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66 |
6847 | 67 j = npol; |
68 for i = 1 : npol | |
69 delta_xv = xv(j) - xv(i); | |
70 delta_yv = yv(j) - yv(i); | |
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71 ## distance = [distance from (x,y) to edge] * length(edge) |
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72 distance = delta_xv .* (y - yv(i)) - (x - xv(i)) .* delta_yv; |
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73 |
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74 ## is y between the y-values of edge i,j AND (x,y) on the left of the edge? |
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75 idx1 = (((yv(i) <= y & y < yv(j)) | (yv(j) <= y & y < yv(i))) |
10549 | 76 & 0 < distance.*delta_yv); |
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77 in(idx1) = ! in(idx1); |
6847 | 78 |
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79 ## Check if (x,y) are actually on the boundary of the polygon. |
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80 idx2 = (((yv(i) <= y & y <= yv(j)) | (yv(j) <= y & y <= yv(i))) |
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81 & ((xv(i) <= x & x <= xv(j)) | (xv(j) <= x & x <= xv(i))) |
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82 & (0 == distance | ! delta_xv)); |
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83 on(idx2) = true; |
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84 |
6847 | 85 j = i; |
86 endfor | |
7125 | 87 |
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88 ## Matlab definition include both in polygon and on polygon points. |
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89 in |= on; |
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90 |
6847 | 91 endfunction |
92 | |
93 | |
94 %!demo | |
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95 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ... |
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96 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ... |
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97 %! 0.05840 ]; |
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98 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ... |
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99 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ... |
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100 %! 0.60628 ]; |
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101 %! xa = [0:0.1:2.3]; |
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102 %! ya = [0:0.1:1.4]; |
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103 %! [x,y] = meshgrid (xa, ya); |
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104 %! [in,on] = inpolygon (x, y, xv, yv); |
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105 %! inside = in & ! on; |
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106 %! |
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107 %! clf; |
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108 %! plot (xv, yv); |
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109 %! hold on; |
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110 %! plot (x(inside), y(inside), "@g"); |
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111 %! plot (x(! in), y(! in), "@m"); |
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112 %! plot (x(on), y(on), "@b"); |
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113 %! hold off; |
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114 %! disp ("Green points are inside polygon, magenta are outside,"); |
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115 %! disp ("and blue are on boundary."); |
6847 | 116 |
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117 %!demo |
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118 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ... |
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119 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ... |
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120 %! 0.05840, 0.73295, 1.28913, 1.74221, 1.16023, ... |
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121 %! 0.73295, 0.05840 ]; |
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122 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ... |
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123 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ... |
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124 %! 0.60628, 0.82096, 0.67155, 0.96114, 1.14833, ... |
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125 %! 0.82096, 0.60628]; |
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126 %! xa = [0:0.1:2.3]; |
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127 %! ya = [0:0.1:1.4]; |
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128 %! [x, y] = meshgrid (xa, ya); |
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129 %! [in, on] = inpolygon (x, y, xv, yv); |
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130 %! inside = in & ! on; |
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131 %! |
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132 %! clf; |
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133 %! plot (xv, yv); |
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134 %! hold on; |
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135 %! plot (x(inside), y(inside), "@g"); |
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136 %! plot (x(! in), y(! in), "@m"); |
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137 %! plot (x(on), y(on), "@b"); |
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138 %! hold off; |
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139 %! disp ("Green points are inside polygon, magenta are outside,"); |
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140 %! disp ("and blue are on boundary."); |
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141 |
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142 %!test |
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143 %! [in, on] = inpolygon ([1, 0, 2], [1, 0, 0], [-1, -1, 1, 1], [-1, 1, 1, -1]); |
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144 %! assert (in, [true, true, false]); |
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145 %! assert (on, [true, false, false]); |
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146 |
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147 ## 3D array input |
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148 %!test |
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149 %! x = zeros (2, 2, 2); |
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150 %! x(1, 1, 1) = 1; |
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151 %! x(2, 2, 2) = 2; |
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152 %! y = zeros (2, 2, 2); |
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153 %! y(1, 1, 1) = 1; |
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154 %! y(2, 2, 2) = -1; |
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155 %! [in, on] = inpolygon (x, y, [-1, -1, 1, 1], [-1, 1, 1, -1]); |
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156 %! IN = true (2, 2, 2); |
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157 %! IN(2, 2, 2) = false; |
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158 %! ON = false (2, 2, 2); |
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159 %! ON(1, 1, 1) = true; |
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160 %! assert (in, IN); |
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161 %! assert (on, ON); |
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162 |
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163 ## Test input validation |
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164 %!error inpolygon () |
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165 %!error inpolygon (1, 2) |
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166 %!error inpolygon (1, 2, 3) |
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167 %!error inpolygon (1, 2, 3, 4, 5) |
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168 %!error <X and Y must be real> inpolygon (1i, 1, [3, 4], [5, 6]) |
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169 %!error <X and Y must be real> inpolygon (1, {1}, [3, 4], [5, 6]) |
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170 %!error <X and Y must be .* the same size> inpolygon (1, [1,2], [3, 4], [5, 6]) |
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171 %!error <X and Y must be .* the same size> inpolygon (1, ones (1,1,2), [3, 4], [5, 6]) |
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172 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3i, 4], [5, 6]) |
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173 %!error <XV and YV must be real vectors> inpolygon (1, 1, [3, 4], {5, 6}) |
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174 %!error <XV and YV must .* the same size> inpolygon ([1,2], [3, 4], [5, 6], 1) |