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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 = tetrahedronVolume(vertices, varargin)
%TETRAHEDRONVOLUME Signed volume of a tetrahedron.
%
% VOL = tetrahedronVolume(TETRA)
% Comptues the siged volume of the tetrahedron TETRA defined by a 4-by-4
% array representing the polyhedron vertices.
%
% Example
% vi = [0 0 0;1 0 0;0 1 0;0 0 1];
% tetrahedronVolume(vi)
% ans =
% 0.1667
%
% [V F] = createTetrahedron;
% tetrahedronVolume(V)
% ans =
% -.3333
%
% See also
% meshes3d, createTetrahedron, meshVolume
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-04-05, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
if nargin == 2
tetras = varargin{1};
nTetras = size(tetras, 1);
vol = zeros(nTetras, 1);
for i = 1:nTetras
tetra = tetras(i,:);
vol(i) = det(bsxfun(@minus, vertices(tetra(2:4),:), vertices(tetra(1),:))) / 6;
end
return;
end
% control on inputs
if nargin == 4
vertices = [vertices ; varargin{1} ; varargin{2} ; varargin{3}];
end
if size(vertices, 1) < 4
error('Input vertex array requires at least 4 vertices');
end
% compute volume of tetrahedron, using first vertex as origin
vol = det(vertices(2:4,:) - vertices([1 1 1],:)) / 6;
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