annotate scripts/geometry/inpolygon.m @ 31706:597f3ee61a48 stable

update Octave Project Developers copyright for the new year
author John W. Eaton <jwe@octave.org>
date Fri, 06 Jan 2023 13:11:27 -0500
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2006-2023 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## or <https://octave.org/copyright/>.
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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 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{in} =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv})
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28 ## @deftypefnx {} {[@var{in}, @var{on}] =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv})
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29 ##
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30 ## For a polygon defined by vertex points @code{(@var{xv}, @var{yv})}, return
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31 ## true if the points @code{(@var{x}, @var{y})} are inside (or on the boundary)
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32 ## of the polygon; Otherwise, return false.
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33 ##
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34 ## The input variables @var{x} and @var{y}, must have the same dimension.
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35 ##
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36 ## The optional output @var{on} returns true if the points are exactly on the
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37 ## polygon edge, and false otherwise.
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38 ## @seealso{delaunay}
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39 ## @end deftypefn
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40
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41 ## Algorithm: The method for determining if a point is in a polygon is based on
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42 ## the algorithm shown on
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43 ## http://local.wasp.uwa.edu.au/~pbourke/geometry/insidepoly/
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44 ## and is credited to Randolph Franklin.
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45
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46 function [in, on] = inpolygon (x, y, xv, yv)
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47
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48 if (nargin != 4)
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49 print_usage ();
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50 endif
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51
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52 if (! (isreal (x) && isreal (y) && isnumeric (x) && isnumeric (y)
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53 && size_equal (x, y)))
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54 error ("inpolygon: X and Y must be real arrays of the same size");
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55 elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv)
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56 && size_equal (xv, yv)))
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57 error ("inpolygon: XV and YV must be real vectors of the same size");
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58 endif
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59
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60 npol = length (xv);
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61
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62 in = on = false (size (x));
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63
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64 j = npol;
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65 for i = 1 : npol
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66 delta_xv = xv(j) - xv(i);
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67 delta_yv = yv(j) - yv(i);
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68 ## distance = [distance from (x,y) to edge] * length(edge)
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69 distance = delta_xv .* (y - yv(i)) - (x - xv(i)) .* delta_yv;
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70
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71 ## is y between the y-values of edge i,j AND (x,y) on the left of the edge?
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72 idx1 = (((yv(i) <= y & y < yv(j)) | (yv(j) <= y & y < yv(i)))
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73 & 0 < distance.*delta_yv);
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74 in(idx1) = ! in(idx1);
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75
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76 ## Check if (x,y) are actually on the boundary of the polygon.
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77 idx2 = (((yv(i) <= y & y <= yv(j)) | (yv(j) <= y & y <= yv(i)))
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78 & ((xv(i) <= x & x <= xv(j)) | (xv(j) <= x & x <= xv(i)))
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79 & (0 == distance | ! delta_xv));
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80 on(idx2) = true;
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81
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82 j = i;
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83 endfor
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84
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85 ## Matlab definition include both in polygon and on polygon points.
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86 in |= on;
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87
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88 endfunction
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89
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90
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91 %!demo
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92 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
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93 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
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94 %! 0.05840 ];
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95 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
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96 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
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97 %! 0.60628 ];
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98 %! xa = [0:0.1:2.3];
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99 %! ya = [0:0.1:1.4];
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100 %! [x,y] = meshgrid (xa, ya);
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101 %! [in,on] = inpolygon (x, y, xv, yv);
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102 %! inside = in & ! on;
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103 %!
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104 %! clf;
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105 %! plot (xv, yv);
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106 %! hold on;
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107 %! plot (x(inside), y(inside), "@g");
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108 %! plot (x(! in), y(! in), "@m");
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109 %! plot (x(on), y(on), "@b");
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110 %! hold off;
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111 %! disp ("Green points are inside polygon, magenta are outside,");
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112 %! disp ("and blue are on boundary.");
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113
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114 %!demo
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115 %! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
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116 %! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
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117 %! 0.05840, 0.73295, 1.28913, 1.74221, 1.16023, ...
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118 %! 0.73295, 0.05840 ];
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119 %! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
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120 %! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
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121 %! 0.60628, 0.82096, 0.67155, 0.96114, 1.14833, ...
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122 %! 0.82096, 0.60628];
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123 %! xa = [0:0.1:2.3];
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124 %! ya = [0:0.1:1.4];
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125 %! [x, y] = meshgrid (xa, ya);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
126 %! [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
diff changeset
127 %! inside = in & ! on;
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
128 %!
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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129 %! clf;
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Rik <octave@nomad.inbox5.com>
parents: 14222
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130 %! plot (xv, yv);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
131 %! hold on;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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132 %! plot (x(inside), y(inside), "@g");
20955
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Rik <rik@octave.org>
parents: 20852
diff changeset
133 %! plot (x(! in), y(! in), "@m");
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
134 %! 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
135 %! 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
136 %! 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
137 %! disp ("and blue are on boundary.");
13057
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
138
85c77dd2e85b codesprint: tests for inpolygon
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
139 %!test
20133
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
140 %! [in, on] = inpolygon ([1, 0, 2], [1, 0, 0], [-1, -1, 1, 1], [-1, 1, 1, -1]);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
141 %! assert (in, [true, true, false]);
bef9086a6725 inpolygon.m: Overhaul function and fix bug #40970.
Rik <rik@octave.org>
parents: 19833
diff changeset
142 %! assert (on, [true, false, false]);
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
143
31253
a40c0b7aa376 maint: changes to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 30564
diff changeset
144 ## 3-D array input
21222
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
145 %!test
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
146 %! x = 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
147 %! x(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
148 %! x(2, 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
149 %! 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
150 %! 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
151 %! 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
152 %! [in, on] = inpolygon (x, y, [-1, -1, 1, 1], [-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
153 %! 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
154 %! 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
155 %! 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
156 %! 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
157 %! 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
158 %! assert (on, ON);
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
159
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
160 ## Test input validation
28896
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 27984
diff changeset
161 %!error <Invalid call> inpolygon ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 27984
diff changeset
162 %!error <Invalid call> inpolygon (1, 2)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 27984
diff changeset
163 %!error <Invalid call> inpolygon (1, 2, 3)
21222
732ec49d1ec5 Fix regressions caused by ismatrix definition change (partial fix bug #47036).
Colin Macdonald <cbm@m.fsf.org>
parents: 20181
diff changeset
164 %!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
165 %!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
166 %!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
167 %!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
168 %!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
169 %!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
170 %!error <XV and YV must .* the same size> inpolygon ([1,2], [3, 4], [5, 6], 1)