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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 = polygonArea3d(poly, varargin)
%POLYGONAREA3D Area of a 3D polygon.
%
% AREA = polygonArea3d(POLY)
% POLY is given as a N-by-3 array of vertex coordinates. The resulting
% area is positive.
% Works also for polygons given as a cell array of polygons.
%
% Example
% % area of a simple 3D square
% poly = [10 30 20;20 30 20;20 40 20;10 40 20];
% polygonArea3d(poly)
% ans =
% 100
%
% % Area of a 3D mesh
% [v f] = createCubeOctahedron;
% polygons = meshFacePolygons(v, f);
% areas = polygonArea3d(polygons);
% sum(areas)
% ans =
% 18.9282
%
% See also
% polygons3d, triangleArea3d, polygonArea, polygonCentroid3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-02-24, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
% Check multiple polygons
if iscell(poly) || sum(sum(isnan(poly))) > 0
% split the polygons into a cell array
polygons = splitPolygons3d(poly);
nPolys = length(polygons);
% compute area of each polygon
area = zeros(nPolys, 1);
for i = 1:nPolys
area(i) = polygonArea3d(polygons{i});
end
return;
end
% put the first vertex at origin (reducing computation errors for polygons
% far from origin)
v0 = poly(1, :);
poly = bsxfun(@minus, poly, v0);
% indices of next vertices
N = size(poly, 1);
iNext = [2:N 1];
% compute cross-product of each elementary triangle formed by origin and
% two consecutive vertices
cp = cross(poly, poly(iNext,:), 2);
% choose one of the triangles as reference for the normal direction
vn = vectorNorm3d(cp);
[tmp, ind] = max(vn); %#ok<ASGLU>
cpRef = cp(ind,:);
% compute the sign of the area of each triangle
% (need to compute the sign explicitely, as the norm of the cross product
% does not keep orientation within supporting plane)
sign_i = sign(dot(cp, repmat(cpRef, N, 1), 2));
% compute area of each triangle, using sign correction
area_i = vectorNorm3d(cp) .* sign_i;
% sum up individual triangles area
area = sum(area_i) / 2;
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