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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 = meshSurfaceArea(varargin)
%MESHSURFACEAREA Surface area of a polyhedral mesh.
%
% S = meshSurfaceArea(V, F)
% S = meshSurfaceArea(V, E, F)
% Computes the surface area of the mesh specified by vertex array V and
% face array F. Vertex array is a NV-by-3 array of coordinates.
% Face array can be a NF-by-3 or NF-by-4 numeric array, or a Nf-by-1 cell
% array, containing vertex indices of each face.
%
% This functions iterates on faces, extract vertices of the current face,
% and computes the sum of face areas.
%
% This function assumes faces are coplanar and convex. If faces are all
% triangular, the function "trimeshSurfaceArea" should be more efficient.
%
%
% Example
% % compute the surface of a unit cube (should be equal to 6)
% [v f] = createCube;
% meshSurfaceArea(v, f)
% ans =
% 6
%
% See also
% meshes3d, trimeshSurfaceArea, meshVolume, meshFaceAreas,
% meshFacePolygons, polygonArea3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-10-13, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
% parse input arguments
[vertices, faces] = parseMeshData(varargin{:});
% pre-compute normals
normals = normalizeVector3d(meshFaceNormals(vertices, faces));
% init accumulator
area = 0;
if isnumeric(faces)
% iterate on faces in a numeric array
for i = 1:size(faces, 1)
poly = vertices(faces(i, :), :);
area = area + polyArea3d(poly, normals(i,:));
end
else
% iterate on faces in a cell array
for i = 1:length(faces)
poly = vertices(faces{i}, :);
area = area + polyArea3d(poly, normals(i,:));
end
end
function a = polyArea3d(v, normal)
nv = size(v, 1);
v0 = repmat(v(1,:), nv, 1);
products = sum(cross(v-v0, v([2:end 1], :)-v0, 2), 1);
a = abs(dot(products, normal, 2))/2;
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