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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 = polygonArea(poly, varargin)
%POLYGONAREA Compute the signed area of a polygon.
%
% A = polygonArea(POINTS);
% Compute area of a polygon defined by POINTS. POINTS is a N-by-2 array
% of double containing coordinates of vertices.
%
% Vertices of the polygon are supposed to be oriented Counter-Clockwise
% (CCW). In this case, the signed area is positive.
% If vertices are oriented Clockwise (CW), the signed area is negative.
%
% If polygon is self-crossing, the result is undefined.
%
% Examples
% % compute area of a simple shape
% poly = [10 10;30 10;30 20;10 20];
% area = polygonArea(poly)
% area =
% 200
%
% % compute area of CW polygon
% area2 = polygonArea(poly(end:-1:1, :))
% area2 =
% -200
%
% % Computes area of a paper hen
% x = [0 10 20 0 -10 -20 -10 -10 0];
% y = [0 0 10 10 20 10 10 0 -10];
% poly = [x' y'];
% area = polygonArea(poly)
% area =
% 400
%
% % Area of unit square with 25% hole
% pccw = [0 0; 1 0; 1 1; 0 1];
% pcw = pccw([1 4 3 2], :) * .5 + .25;
% polygonArea ([pccw; nan(1,2); pcw])
% ans =
% 0.75
%
% References
% algo adapted from P. Bourke web page
% http://paulbourke.net/geometry/polygonmesh/
%
% See also
% polygons2d, polygonCentroid, polygonSecondAreaMoments, triangleArea
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-05-05
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
%% Process special cases
% in case of polygon sets, computes the sum of polygon areas
if iscell(poly)
area = 0;
for i = 1:length(poly)
area = area + polygonArea(poly{i});
end
return;
end
% check there are enough points
if size(poly, 1) < 2
area = 0;
return;
end
% case of polygons with holes -> computes the sum of areas
if any(isnan(poly))
area = sum(polygonArea(splitPolygons(poly)));
return;
end
%% Process single polygons or single rings
% extract coordinates
if nargin == 1
% polygon given as N-by-2 array
px = poly(:, 1);
py = poly(:, 2);
elseif nargin == 2
% poylgon given as two N-by-1 arrays
px = poly;
py = varargin{1};
end
% indices of next vertices
N = length(px);
iNext = [2:N 1];
% compute area (vectorized version)
area = sum(px .* py(iNext) - px(iNext) .* py) / 2;
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