createDodecahedron

CREATEDODECAHEDRON Create a 3D mesh representing a dodecahedron.

   [V, E, F] = createDodecahedron;
   Create a 3D mesh representing a dodecahedron
   V is the 20-by-3 array of vertex coordinates
   E is the 30-by-2 array of edge vertex indices
   F is the 12-by-5 array of face vertex indices

   [V, F] = createDodecahedron;
   Returns only the vertices and the face vertex indices.

   MESH = createDodecahedron;
   Returns the data as a mesh structure, with fields 'vertices', 'edges'
   and 'faces'.

   Example
   [v, e, f] = createDodecahedron;
   drawMesh(v, f);

   Use values given by P. Bourke, see:
   http://local.wasp.uwa.edu.au/~pbourke/geometry/platonic/
   faces are re-oriented to have normals pointing outwards.

   See also
   meshes3d, drawMesh
   createCube, createOctahedron, createIcosahedron, createTetrahedron

0001 function varargout = createDodecahedron()
0002 %CREATEDODECAHEDRON Create a 3D mesh representing a dodecahedron.
0003 %
0004 %   [V, E, F] = createDodecahedron;
0005 %   Create a 3D mesh representing a dodecahedron
0006 %   V is the 20-by-3 array of vertex coordinates
0007 %   E is the 30-by-2 array of edge vertex indices
0008 %   F is the 12-by-5 array of face vertex indices
0009 %
0010 %   [V, F] = createDodecahedron;
0011 %   Returns only the vertices and the face vertex indices.
0012 %
0013 %   MESH = createDodecahedron;
0014 %   Returns the data as a mesh structure, with fields 'vertices', 'edges'
0015 %   and 'faces'.
0016 %
0017 %   Example
0018 %   [v, e, f] = createDodecahedron;
0019 %   drawMesh(v, f);
0020 %
0021 %   Use values given by P. Bourke, see:
0022 %   http://local.wasp.uwa.edu.au/~pbourke/geometry/platonic/
0023 %   faces are re-oriented to have normals pointing outwards.
0024 %
0025 %   See also
0026 %   meshes3d, drawMesh
0027 %   createCube, createOctahedron, createIcosahedron, createTetrahedron
0028 %
0029 
0030 %   ---------
0031 %   author : David Legland
0032 %   e-mail: david.legland@inra.fr
0033 %   INRA - TPV URPOI - BIA IMASTE
0034 %   created the 29/07/2010.
0035 %
0036 
0037 %   HISTORY
0038 
0039 % golden ratio
0040 phi = (1+sqrt(5))/2;
0041 
0042 % coordinates pre-computations
0043 b = 1 / phi ; 
0044 c = 2 - phi ;
0045 
0046 % use values given by P. Bourke, see:
0047 % http://local.wasp.uwa.edu.au/~pbourke/geometry/platonic/
0048 tmp = [ ...
0049  c  0  1 ;   b  b  b ;   0  1  c  ; -b  b  b  ; -c  0  1 ;  ...
0050 -c  0  1 ;  -b -b  b ;   0 -1  c  ;  b -b  b  ;  c  0  1 ;   ...
0051  c  0 -1 ;   b -b -b ;   0 -1 -c  ; -b -b -b  ; -c  0 -1 ;  ...
0052 -c  0 -1 ;  -b  b -b ;   0  1 -c  ;  b  b -b  ;  c  0 -1 ; ...
0053  0  1 -c ;   0  1  c ;   b  b  b  ;  1  c  0  ;  b  b -b ; ...
0054  0  1  c ;   0  1 -c ;  -b  b -b  ; -1  c  0  ; -b  b  b ; ...
0055  0 -1 -c ;   0 -1  c ;  -b -b  b  ; -1 -c  0  ; -b -b -b ; ...
0056  0 -1  c ;   0 -1 -c ;   b -b -b  ;  1 -c  0  ;  b -b  b ; ...
0057  1  c  0 ;   b  b  b ;   c  0  1  ;  b -b  b  ;  1 -c  0 ;  ...
0058  1 -c  0 ;   b -b -b ;   c  0 -1  ;  b  b -b  ;  1  c  0 ; ...
0059 -1  c  0 ;  -b  b -b ;  -c  0 -1  ; -b -b -b  ; -1 -c  0 ; ...
0060 -1 -c  0 ;  -b -b  b ;  -c  0  1  ; -b  b  b  ; -1  c  0 ;  ...
0061 ];
0062 
0063 % extract coordinates of unique vertices
0064 [verts, M, N] = unique(tmp, 'rows', 'first'); %#ok<ASGLU>
0065 
0066 % compute indices of face vertices, put result in a 12-by-5 index array
0067 ind0 = reshape((1:60), [5 12])';
0068 faces = N(ind0);
0069 
0070 % extract edges from faces
0071 edges = [reshape(faces(:, 1:5), [60 1]) reshape(faces(:, [2:5 1]), [60 1])];
0072 edges = unique(sort(edges, 2), 'rows');
0073 
0074 
0075 % format output
0076 varargout = formatMeshOutput(nargout, verts, edges, faces);