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>
date Mon, 06 Jan 2020 22:29:51 -0500
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27919
1891570abac8 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
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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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.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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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.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23
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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})
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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}
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37 ## @end deftypefn
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38
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39 ## Author: Frederick (Rick) A Niles <niles@rickniles.com>
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40 ## Created: 14 November 2006
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41
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42 ## Vectorized by Søren Hauberg <soren@hauberg.org>
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43
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44 ## The method for determining if a point is in a polygon is based on
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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.
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48
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49 function [in, on] = inpolygon (x, y, xv, yv)
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50
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51 if (nargin != 4)
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52 print_usage ();
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53 endif
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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");
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58 elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv)
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59 && size_equal (xv, yv)))
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60 error ("inpolygon: XV and YV must be real vectors of the same size");
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61 endif
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62
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63 npol = length (xv);
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64
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65 in = on = false (size (x));
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66
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67 j = npol;
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68 for i = 1 : npol
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69 delta_xv = xv(j) - xv(i);
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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)))
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76 & 0 < distance.*delta_yv);
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77 in(idx1) = ! in(idx1);
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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
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85 j = i;
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86 endfor
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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
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91 endfunction
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92
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93
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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.");
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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];
20133
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128 %! [x, y] = meshgrid (xa, ya);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
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129 %! [in, on] = inpolygon (x, y, xv, yv);
20955
77f5591878bf maint: Use '! expr' rather than '!expr' to conform to coding guidelines.
Rik <rik@octave.org>
parents: 20852
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130 %! inside = in & ! on;
14237
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131 %!
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Rik <octave@nomad.inbox5.com>
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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");
20955
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Rik <rik@octave.org>
parents: 20852
diff changeset
136 %! plot (x(! in), y(! in), "@m");
14237
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parents: 14222
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137 %! plot (x(on), y(on), "@b");
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
138 %! hold off;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
139 %! disp ("Green points are inside polygon, magenta are outside,");
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
140 %! disp ("and blue are on boundary.");
13057
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
141
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
142 %!test
20133
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Rik <rik@octave.org>
parents: 19833
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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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Rik <rik@octave.org>
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144 %! assert (in, [true, true, false]);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
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145 %! assert (on, [true, false, false]);
14237
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parents: 14222
diff changeset
146
21222
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
147 ## 3D array input
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
148 %!test
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
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149 %! x = zeros (2, 2, 2);
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
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150 %! x(1, 1, 1) = 1;
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
151 %! x(2, 2, 2) = 2;
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
152 %! y = zeros (2, 2, 2);
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
153 %! y(1, 1, 1) = 1;
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
154 %! y(2, 2, 2) = -1;
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
155 %! [in, on] = inpolygon (x, y, [-1, -1, 1, 1], [-1, 1, 1, -1]);
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
156 %! IN = true (2, 2, 2);
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
157 %! IN(2, 2, 2) = false;
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
158 %! ON = false (2, 2, 2);
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
159 %! ON(1, 1, 1) = true;
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
160 %! assert (in, IN);
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
161 %! assert (on, ON);
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
162
19833
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Rik <rik@octave.org>
parents: 19697
diff changeset
163 ## Test input validation
14237
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164 %!error inpolygon ()
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
165 %!error inpolygon (1, 2)
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
166 %!error inpolygon (1, 2, 3)
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
167 %!error inpolygon (1, 2, 3, 4, 5)
21222
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Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
168 %!error <X and Y must be real> inpolygon (1i, 1, [3, 4], [5, 6])
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
169 %!error <X and Y must be real> inpolygon (1, {1}, [3, 4], [5, 6])
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
170 %!error <X and Y must be .* the same size> inpolygon (1, [1,2], [3, 4], [5, 6])
21222
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
171 %!error <X and Y must be .* the same size> inpolygon (1, ones (1,1,2), [3, 4], [5, 6])
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
172 %!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
173 %!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
174 %!error <XV and YV must .* the same size> inpolygon ([1,2], [3, 4], [5, 6], 1)