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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 vol = meshVolume(varargin)
%MESHVOLUME (Signed) volume of the space enclosed by a polygonal mesh.
%
% V = meshVolume(VERTS, FACES)
% Computes the volume of the space enclosed by the polygonal mesh
% represented by vertices VERTS (as a Nv-by-3 array of cooridnates) and
% the array of faces FACES (either as a Nf-by-3 array of vertex indices,
% or as a cell array of arrays of vertex indices).
%
% The volume is computed as the sum of the signed volumes of tetrahedra
% formed by triangular faces and the centroid of the mesh. Faces need to
% be oriented such that normal points outwards the mesh. See:
% http://stackoverflow.com/questions/1838401/general-formula-to-calculate-polyhedron-volume
%
% Example
% % computes the volume of a unit cube (should be equal to 1...)
% [v f] = createCube;
% meshVolume(v, f)
% ans =
% 1
%
% See also
% meshes3d, meshSurfaceArea, tetrahedronVolume, meshComplement
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-10-01, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
% parse input
[vertices, faces] = parseMeshData(varargin{:});
% ensure mesh has triangle faces
faces = triangulateFaces(faces);
% initialize an array of volume
nFaces = size(faces, 1);
vols = zeros(nFaces, 1);
% Shift all vertices to the mesh centroid
vertices = bsxfun(@minus, vertices, mean(vertices,1));
% compute volume of each tetraedron
for i = 1:nFaces
% consider the tetrahedron formed by face and mesh centroid
tetra = vertices(faces(i, :), :);
% volume of current tetrahedron
vols(i) = det(tetra) / 6;
end
vol = sum(vols);
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