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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
## 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.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function area = triangleArea(pt1, pt2, pt3)
%TRIANGLEAREA Signed area of a triangle.
%
% AREA = triangleArea(P1, P2, P3)
% Computes area of the triangle whose vertices are given by P1, P2 and
% P3. Each vertex is a 1-by-2 row vector.
%
% AREA = triangleArea(PTS)
% Concatenates vertex coordinates in a 3-by-2 array. Each row of the
% array contains coordinates of one vertex.
%
%
% Example
% % Compute area of a Counter-Clockwise (CCW) oriented triangle
% triangleArea([10 10], [30 10], [10 40])
% ans =
% 300
%
% % Compute area of a Clockwise (CW) oriented triangle
% triangleArea([10 40], [30 10], [10 10])
% ans =
% -300
%
% See also
% polygonArea, triangleArea3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-08-23, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% if data is given as one array, split vertices
if nargin == 1
pt2 = pt1(2,:);
pt3 = pt1(3,:);
pt1 = pt1(1,:);
end
% compute individual vectors
v12 = bsxfun(@minus, pt2, pt1);
v13 = bsxfun(@minus, pt3, pt1);
% compute area from cross product
area = (v13(:,2) .* v12(:,1) - v13(:,1) .* v12(:,2)) / 2;
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