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## Copyright (C) 2024 David Legland
## 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
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## The views and conclusions contained in the software and documentation are
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function b = isPointInTriangle(point, p1, p2, p3)
%ISPOINTINTRIANGLE Test if a point is located inside a triangle.
%
% B = isPointInTriangle(POINT, V1, V2, V3)
% POINT is a 1-by-2 row vector containing coordinates of the test point,
% V1, V2 and V3 are 1-by-2 row vectors containing coordinates of triangle
% vertices. The function returns 1 is the point is inside or on the
% boundary of the triangle, and 0 otherwise.
%
% B = isPointInTriangle(POINT, VERTICES)
% Specifiy the coordinates of vertices as a 3-by-2 array.
%
% If POINT contains more than one row, the result B has as many rows as
% the input POINT.
%
%
% Example
% % vertices of the triangle
% p1 = [0 0];
% p2 = [10 0];
% p3 = [5 10];
% tri = [p1;p2;p3];
% % check if points are inside
% isPointInTriangle([0 0], tri)
% ans =
% 1
% isPointInTriangle([5 5], tri)
% ans =
% 1
% isPointInTriangle([10 5], tri)
% ans =
% 0
% % check for an array of points
% isPointInTriangle([0 0;1 0;0 1], tri)
% ans =
% 1
% 1
% 0
%
% See also
% polygons2d, isPointInPolygon, isCounterClockwise
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-05-16, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% if triangle vertices are given as a single array, extract vertices
if nargin == 2
p2 = p1(2, :);
p3 = p1(3, :);
p1 = p1(1, :);
end
% check triangle orientation
isDirect = isCounterClockwise(p1, p2, p3);
% check location of point with respect to each side
if isDirect
b12 = isCounterClockwise(p1, p2, point) >= 0;
b23 = isCounterClockwise(p2, p3, point) >= 0;
b31 = isCounterClockwise(p3, p1, point) >= 0;
else
b12 = isCounterClockwise(p1, p2, point) <= 0;
b23 = isCounterClockwise(p2, p3, point) <= 0;
b31 = isCounterClockwise(p3, p1, point) <= 0;
end
% combines the 3 results
b = b12 & b23 & b31;
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