createTetrakaidecahedron

CREATETETRAKAIDECAHEDRON Create a 3D mesh representing a tetrakaidecahedron.

   [V, E, F] = createTetrakaidecahedron;
   Create a mesh structure representing a tetrakaidecahedron, composed of
   both square and hexagonal faces. Tetrakaidecahedron can be used to tile
   the 3D Euclidean space.

   V is a 24-by-3 array with vertex coordinates,
   E is a 36-by-2 array containing indices of neighbour vertices,
   F is a 14-by-1 cell array containing vertex indices array of each face.

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

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

   Example
   [n, e, f] = createTetrakaidecahedron;
   drawMesh(n, f);
   
   See also
   meshes3d, drawMesh

0001 function varargout = createTetrakaidecahedron()
0002 %CREATETETRAKAIDECAHEDRON Create a 3D mesh representing a tetrakaidecahedron.
0003 %
0004 %   [V, E, F] = createTetrakaidecahedron;
0005 %   Create a mesh structure representing a tetrakaidecahedron, composed of
0006 %   both square and hexagonal faces. Tetrakaidecahedron can be used to tile
0007 %   the 3D Euclidean space.
0008 %
0009 %   V is a 24-by-3 array with vertex coordinates,
0010 %   E is a 36-by-2 array containing indices of neighbour vertices,
0011 %   F is a 14-by-1 cell array containing vertex indices array of each face.
0012 %
0013 %   [V, F] = createTetrakaidecahedron;
0014 %   Returns only the vertices and the face vertex indices.
0015 %
0016 %   MESH = createTetrakaidecahedron;
0017 %   Returns the data as a mesh structure, with fields 'vertices', 'edges'
0018 %   and 'faces'.
0019 %
0020 %   Example
0021 %   [n, e, f] = createTetrakaidecahedron;
0022 %   drawMesh(n, f);
0023 %
0024 %   See also
0025 %   meshes3d, drawMesh
0026 
0027 %   ---------
0028 %   author : David Legland
0029 %   e-mail: david.legland@inra.fr
0030 %   INRA - TPV URPOI - BIA IMASTE
0031 %   created the 10/02/2005.
0032 %
0033 
0034 %   HISTORY
0035 %   04/01/2007: remove unused variables
0036 
0037 nodes = [...
0038     1 0 2;0 1 2;-1 0 2;0 -1 2;...
0039     2 0 1;0 2 1;-2 0 1;0 -2 1;...
0040     2 1 0;1 2 0;-1 2 0;-2 1 0;-2 -1 0;-1 -2 0;1 -2 0;2 -1 0;...
0041     2 0 -1;0 2 -1;-2 0 -1;0 -2 -1;...
0042     1 0 -2;0 1 -2;-1 0 -2;0 -1 -2];
0043 
0044 edges = [...
0045     1 2;1 4;1 5;2 3;2 6;3 4;3 7;4 8;...
0046     5 9;5 16;6 10;6 11;7 12;7 13;8 14;8 15;...
0047     9 10;9 17;10 18;11 12;11 18;12 19;13 14;13 19;14 20;15 16;15 20;16 17;....
0048     17 21;18 22;19 23;20 24;21 22;21 24;22 23;23 24];
0049     
0050     
0051 faces = {...
0052     [1 2 3 4], ...
0053     [1 4 8 15 16 5], [1 5 9 10 6 2], [2 6 11 12 7 3], [3 7 13 14 8 4],...
0054     [5 16 17 9], [6 10 18 11], [7 12 19 13], [8 14 20 15],...
0055     [9 17 21 22 18 10], [11 18 22 23 19 12], [13 19 23 24 20 14], [15 20 24 21 17 16], ...
0056     [21 24 23 22]};
0057 faces = faces';
0058     
0059 % format output
0060 varargout = formatMeshOutput(nargout, nodes, edges, faces);
0061