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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 alpha = meshDihedralAngles(vertices, edges, faces)
%MESHDIHEDRALANGLES Dihedral at edges of a polyhedal mesh.
%
% ALPHA = meshDihedralAngles(V, E, F)
% where V, E and F represent vertices, edges and faces of a mesh,
% computes the dihedral angle between the two adjacent faces of each edge
% in the mesh. ALPHA is a column array with as many rows as the number of
% edges. The i-th element of ALPHA corresponds to the i-th edge.
%
% Note: the function assumes that the faces are correctly oriented. The
% face vertices should be indexed counter-clockwise when considering the
% supporting plane of the face, with the outer normal oriented outwards
% of the mesh.
%
% Example
% [v, e, f] = createCube;
% rad2deg(meshDihedralAngles(v, e, f))
% ans =
% 90
% 90
% 90
% 90
% 90
% 90
% 90
% 90
% 90
% 90
% 90
% 90
%
% See also
% meshes3d, polyhedronMeanBreadth, trimeshMeanBreadth, dihedralAngle, meshEdgeFaces
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-10-04, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
% compute normal of each face
normals = meshFaceNormals(vertices, faces);
% indices of faces adjacent to each edge
edgeFaces = meshEdgeFaces(vertices, edges, faces);
% allocate memory for resulting angles
Ne = size(edges, 1);
alpha = zeros(Ne, 1);
% iterate over edges
for i = 1:Ne
% indices of adjacent faces
indFace1 = edgeFaces(i, 1);
indFace2 = edgeFaces(i, 2);
% normal vector of adjacent faces
normal1 = normals(indFace1, :);
normal2 = normals(indFace2, :);
% compute dihedral angle of two vectors
alpha(i) = vectorAngle3d(normal1, normal2);
end
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