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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 areas = meshFaceAreas(vertices, faces)
%MESHFACEAREAS Surface area of each face of a mesh.
%
% areas = meshFaceAreas(vertices, faces)
%
% Example
% [v, f] = createOctahedron;
% meshFaceAreas(v, f)'
% ans =
% 1.7321 1.7321 1.7321 1.7321 1.7321 1.7321 1.7321 1.7321
%
% See also
% meshes3d, meshSurfaceArea, meshFaceCentroids
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2018-06-21, using Matlab 9.4.0.813654 (R2018a)
% Copyright 2018-2023 INRA - Cepia Software Platform
if isnumeric(faces)
% trimesh or quadmesh
nf = size(faces, 1);
areas = zeros(nf, 1);
if size(vertices, 2) == 2
% planar case
for f = 1:nf
areas(f,:) = polygonArea(vertices(faces(f,:), :));
end
else
% 3D case
if size(faces, 2) == 3
% For triangular meshes, uses accelerated method
v1 = vertices(faces(:,1), :);
v12 = vertices(faces(:,2), :) - v1;
v13 = vertices(faces(:,3), :) - v1;
areas = vectorNorm3d(crossProduct3d(v12, v13))/2;
else
% for quad (or larger) meshes, use slower but more precise method
for f = 1:nf
areas(f) = polygonArea3d(vertices(faces(f,:), :));
end
end
end
else
% mesh with faces stored as cell array
nf = length(faces);
areas = zeros(nf, 1);
if size(vertices, 2) == 2
% planar case
for f = 1:nf
areas(f) = polygonArea(vertices(faces{f}, :));
end
else
% 3D case
for f = 1:nf
areas(f) = polygonArea3d(vertices(faces{f}, :));
end
end
end
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