POLYHEDRONMEANBREADTH Mean breadth of a convex polyhedron.

   BREADTH = polyhedronMeanBreadth(V, E, F)
   Return the mean breadth (average of polyhedron caliper diameter over
   all direction) of a convex polyhedron.

   The mean breadth is computed using the sum, over the edges of the
   polyhedron, of the edge dihedral angles multiplied by the edge length, 
   the final sum being divided by (4*PI).

   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 plane, with the outer normal oriented outwards
   of the polyhedron.

   Typical values for classical polyhedra are:
     cube side a               breadth = (3/2)*a
     cuboid sides a, b, c      breadth = (a+b+c)/2
     tetrahedron side a        breadth = 0.9123*a
     octaedron side a          beradth = 1.175*a
     dodecahedron, side a      breadth = 15*arctan(2)*a/(2*pi)
     icosaehdron, side a       breadth = 15*arcsin(2/3)*a/(2*pi)

   Example
   [v e f] = createCube;
   polyhedronMeanBreadth(v, e, f)
   ans = 
       1.5

   See also
   meshes3d, meshEdgeFaces, meshDihedralAngles, checkMeshAdjacentFaces
   trimeshMeanBreadth

   References
   Stoyan D., Kendall W.S., Mecke J. (1995) "Stochastic Geometry and its
       Applications", John Wiley and Sons, p. 26
   Ohser, J., Muescklich, F. (2000) "Statistical Analysis of
       Microstructures in Materials Sciences", John Wiley and Sons, p.352

Package: matgeom