meshDihedralAngles

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

0001 function alpha = meshDihedralAngles(vertices, edges, faces)
0002 %MESHDIHEDRALANGLES Dihedral at edges of a polyhedal mesh.
0003 %
0004 %   ALPHA = meshDihedralAngles(V, E, F)
0005 %   where V, E and F represent vertices, edges and faces of a mesh,
0006 %   computes the dihedral angle between the two adjacent faces of each edge
0007 %   in the mesh. ALPHA is a column array with as many rows as the number of
0008 %   edges. The i-th element of ALPHA corresponds to the i-th edge.
0009 %
0010 %   Note: the function assumes that the faces are correctly oriented. The
0011 %   face vertices should be indexed counter-clockwise when considering the
0012 %   supporting plane of the face, with the outer normal oriented outwards
0013 %   of the mesh.
0014 %
0015 %   Example
0016 %   [v, e, f] = createCube;
0017 %   rad2deg(meshDihedralAngles(v, e, f))
0018 %   ans =
0019 %       90
0020 %       90
0021 %       90
0022 %       90
0023 %       90
0024 %       90
0025 %       90
0026 %       90
0027 %       90
0028 %       90
0029 %       90
0030 %       90
0031 %
0032 %   See also
0033 %   meshes3d, polyhedronMeanBreadth, trimeshMeanBreadth, dihedralAngle, meshEdgeFaces
0034 %
0035 
0036 % ------
0037 % Author: David Legland
0038 % e-mail: david.legland@inra.fr
0039 % Created: 2010-10-04,    using Matlab 7.9.0.529 (R2009b)
0040 % Copyright 2010 INRA - Cepia Software Platform.
0041 
0042 % compute normal of each face
0043 normals = meshFaceNormals(vertices, faces);
0044 
0045 % indices of faces adjacent to each edge
0046 edgeFaces = meshEdgeFaces(vertices, edges, faces);
0047 
0048 % allocate memory for resulting angles
0049 Ne = size(edges, 1);
0050 alpha = zeros(Ne, 1);
0051 
0052 % iterate over edges
0053 for i = 1:Ne
0054     % indices of adjacent faces
0055     indFace1 = edgeFaces(i, 1);
0056     indFace2 = edgeFaces(i, 2);
0057     
0058     % normal vector of adjacent faces
0059     normal1 = normals(indFace1, :);
0060     normal2 = normals(indFace2, :);
0061     
0062     % compute dihedral angle of two vectors
0063     alpha(i) = vectorAngle3d(normal1, normal2);
0064 end
0065