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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 centroids = meshFaceCentroids(varargin)
%MESHFACECENTROIDS Compute centroids of faces in a mesh.
%
% CENTROIDS = meshFaceCentroids(VERTICES, FACES)
% VERTICES is a set of 3D points (as a N-by-3 array), and FACES is
% either a N-by-3 index array or a cell array of indices. The function
% computes the centroid of each face, and returns a Nf-by-3 array
% containing their coordinates.
%
% Example
% [v, e, f] = createIcosahedron;
% normals1 = meshFaceNormals(v, f);
% centros1 = meshFaceCentroids(v, f);
% figure; hold on; axis equal; view(3);
% drawMesh(v, f);
% drawVector3d(centros1, normals1);
%
%
% See also
% meshes3d, drawMesh, meshFaceNormals, meshFaceAreas, convhull
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-07-05
% Copyright 2006-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% parse input data
[vertices, faces] = parseMeshData(varargin{:});
if isnumeric(faces)
% trimesh or quadmesh
nf = size(faces, 1);
centroids = zeros(nf, size(vertices, 2));
if size(vertices, 2) == 2
% planar case
for f = 1:nf
centroids(f,:) = polygonCentroid(vertices(faces(f,:), :));
end
else
% 3D case
if size(faces, 2) == 3
% For triangular meshes, uses accelerated method
% (taken from https://github.com/alecjacobson/gptoolbox)
for ff = 1:3
centroids = centroids + 1/3 * vertices(faces(:,ff),:);
end
else
% for quad (or larger) meshes, use slower but more precise method
for f = 1:nf
centroids(f,:) = polygonCentroid3d(vertices(faces(f,:), :));
end
end
end
else
% mesh with faces stored as cell array
nf = length(faces);
centroids = zeros(nf, size(vertices, 2));
if size(vertices, 2) == 2
% planar case
for f = 1:nf
centroids(f,:) = polygonCentroid(vertices(faces{f}, :));
end
else
% 3D case
for f = 1:nf
centroids(f,:) = polygonCentroid3d(vertices(faces{f}, :));
end
end
end
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