createOctahedron

CREATEOCTAHEDRON Create a 3D mesh representing an octahedron.

   [V, E, F] = createOctahedron;
   Create a 3D mesh representing an octahedron
   V is a 6-by-3 array with vertices coordinate, E is a 12-by-2 array
   containing indices of neighbour vertices, and F is a 8-by-3 array
   containing array of vertex index for each face.

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

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

   Vertices are located on grid vertices:
    ( ±1,  0,  0 )
    (  0, ±1,  0 )
    (  0,  0, ±1 )

   Edge length of returned octahedron is sqrt(2).
   Surface area of octahedron is 2*sqrt(3)*a^2, approximately 6.9282 in
   this case.
   Volume of octahedron is sqrt(2)/3*a^3, approximately 1.3333 in this
   case.

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

   See also
   meshes3d, drawMesh
   createCube, createIcosahedron, createDodecahedron, createTetrahedron
   createCubeOctahedron

0001 function varargout = createOctahedron()
0002 %CREATEOCTAHEDRON Create a 3D mesh representing an octahedron.
0003 %
0004 %   [V, E, F] = createOctahedron;
0005 %   Create a 3D mesh representing an octahedron
0006 %   V is a 6-by-3 array with vertices coordinate, E is a 12-by-2 array
0007 %   containing indices of neighbour vertices, and F is a 8-by-3 array
0008 %   containing array of vertex index for each face.
0009 %
0010 %   [V, F] = createOctahedron;
0011 %   Returns only the vertices and the face vertex indices.
0012 %
0013 %   MESH = createOctahedron;
0014 %   Returns the data as a mesh structure, with fields 'vertices', 'edges'
0015 %   and 'faces'.
0016 %
0017 %   Vertices are located on grid vertices:
0018 %    ( ±1,  0,  0 )
0019 %    (  0, ±1,  0 )
0020 %    (  0,  0, ±1 )
0021 %
0022 %   Edge length of returned octahedron is sqrt(2).
0023 %   Surface area of octahedron is 2*sqrt(3)*a^2, approximately 6.9282 in
0024 %   this case.
0025 %   Volume of octahedron is sqrt(2)/3*a^3, approximately 1.3333 in this
0026 %   case.
0027 %
0028 %   Example
0029 %     [v, e, f] = createOctahedron;
0030 %     drawMesh(v, f);
0031 %
0032 %   See also
0033 %   meshes3d, drawMesh
0034 %   createCube, createIcosahedron, createDodecahedron, createTetrahedron
0035 %   createCubeOctahedron
0036 %
0037 
0038 %   ---------
0039 %   author : David Legland
0040 %   e-mail: david.legland@inra.fr
0041 %   INRA - TPV URPOI - BIA IMASTE
0042 %   created the 10/02/2005.
0043 %
0044 
0045 %   HISTORY
0046 %   04/01/2007: remove unused variables
0047 
0048 nodes = [1 0 0;0 1 0;-1 0 0;0 -1 0;0 0 1;0 0 -1];
0049 
0050 edges = [1 2;1 4;1 5; 1 6;2 3;2 5;2 6;3 4;3 5;3 6;4 5;4 6];
0051 
0052 faces = [1 2 5;2 3 5;3 4 5;4 1 5;1 6 2;2 6 3;3 6 4;1 4 6];
0053 
0054 % format output
0055 varargout = formatMeshOutput(nargout, nodes, edges, faces);