/usr/share/octave/packages/geometry-1.7.0/geom2d/isCounterClockwise.m is in octave-geometry 1.7.0-1build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 | ## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{ccw} = } isCounterClockwise (@var{p1}, @var{p2}, @var{p3})
## @deftypefnx {Function File} {@var{ccw} = } isCounterClockwise (@var{p1}, @var{p2}, @var{p3},@var{tol})
## Compute relative orientation of 3 points
##
## Computes the orientation of the 3 points. The returns is:
## +1 if the path @var{p1}-> @var{p2}-> @var{p3} turns Counter-Clockwise (i.e., the point @var{p3}
## is located "on the left" of the line @var{p1}- @var{p2})
## -1 if the path turns Clockwise (i.e., the point @var{p3} lies "on the right"
## of the line @var{p1}- @var{p2})
## 0 if the point @var{p3} is located on the line segment [ @var{p1} @var{p2}].
##
## This function can be used in more complicated algorithms: detection of
## line segment intersections, convex hulls, point in triangle...
##
## @var{ccw} = isCounterClockwise( @var{p1}, @var{p2}, @var{p3}, EPS);
## Specifies the threshold used for detecting colinearity of the 3 points.
## Default value is 1e-12 (absolute).
##
## Example
##
## @example
## isCounterClockwise([0 0], [10 0], [10 10])
## ans =
## 1
## isCounterClockwise([0 0], [0 10], [10 10])
## ans =
## -1
## isCounterClockwise([0 0], [10 0], [5 0])
## ans =
## 0
## @end example
##
## @seealso{points2d, isPointOnLine, isPointInTriangle}
## @end deftypefn
function res = isCounterClockwise(p1, p2, p3, varargin)
# get threshold value
eps = 1e-12;
if ~isempty(varargin)
eps = varargin{1};
end
# ensure all data have same size
np = max([size(p1, 1) size(p2, 1) size(p3,1)]);
if np > 1
if size(p1,1) == 1
p1 = repmat(p1, np, 1);
end
if size(p2,1) == 1
p2 = repmat(p2, np, 1);
end
if size(p3,1) == 1
p3 = repmat(p3, np, 1);
end
end
# init with 0
res = zeros(np, 1);
# extract vector coordinates
x0 = p1(:, 1);
y0 = p1(:, 2);
dx1 = p2(:, 1) - x0;
dy1 = p2(:, 2) - y0;
dx2 = p3(:, 1) - x0;
dy2 = p3(:, 2) - y0;
# check non colinear cases
res(dx1 .* dy2 > dy1 .* dx2) = 1;
res(dx1 .* dy2 < dy1 .* dx2) = -1;
# case of colinear points
ind = abs(dx1 .* dy2 - dy1 .* dx2) < eps;
res(ind( (dx1(ind) .* dx2(ind) < 0) | (dy1(ind) .* dy2(ind) < 0) )) = -1;
res(ind( hypot(dx1(ind), dy1(ind)) < hypot(dx2(ind), dy2(ind)) )) = 1;
endfunction
%!shared p0,pu,pd,pl,pr
%! p0 = [2, 3]; # center point
%! pu = [2, 4]; # up point
%! pd = [2, 2]; # down point
%! pl = [1, 3]; # left point
%! pr = [3, 3]; # right point
%!assert (+1, isCounterClockwise(pl, p0, pu));
%!assert (+1, isCounterClockwise(pd, p0, pl));
%!assert (+1, isCounterClockwise(pr, p0, pd));
%!assert (+1, isCounterClockwise(pu, p0, pr));
# turn 90° right => return -1
%!assert (-1, isCounterClockwise(pl, p0, pd));
%!assert (-1, isCounterClockwise(pd, p0, pr));
%!assert (-1, isCounterClockwise(pr, p0, pu));
%!assert (-1, isCounterClockwise(pu, p0, pl));
%!test # turn 90° left => return +1
%! pts1 = [pl;pd;pr;pu;pl;pd;pr;pu];
%! pts2 = [p0;p0;p0;p0;p0;p0;p0;p0];
%! pts3 = [pu;pl;pd;pr;pd;pr;pu;pl];
%! expected = [1;1;1;1;-1;-1;-1;-1];
%! result = isCounterClockwise(pts1, pts2, pts3);
%! assert (result, expected, 1e-6);
# aligned with p0-p1-p2 => return +1
%!assert (+1, isCounterClockwise(pl, p0, pr));
%!assert (+1, isCounterClockwise(pu, p0, pd));
%!assert (+1, isCounterClockwise(pr, p0, pl));
%!assert (+1, isCounterClockwise(pd, p0, pu));
# aligned ]ith p0-p2-p1 => return 0
%!assert (0, isCounterClockwise(pl, pr, p0));
%!assert (0, isCounterClockwise(pu, pd, p0));
%!assert (0, isCounterClockwise(pr, pl, p0));
%!assert (0, isCounterClockwise(pd, pu, p0));
# aligned with p1-p0-p2 => return -1
%!assert (-1, isCounterClockwise(p0, pl, pr));
%!assert (-1, isCounterClockwise(p0, pu, pd));
%!assert (-1, isCounterClockwise(p0, pr, pl));
%!assert (-1, isCounterClockwise(p0, pr, pl));
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