This function computes the regular cell decomposition of
P given by the weight vector
w. This is computed by placing the i-th lattice point of
P on height
w_i in n+1 space, taking the convexHull of these with the ray (0,...,0,1), and projecting the compact faces into n space. Note that the polyhedron must be compact, i.e. a polytope and the length of the weight vector must be the number of lattice points.
P = crossPolytope 3 |
w = matrix {{1,2,2,2,2,2,1}} |
L = cellDecompose(P,w) |
apply(L,vertices) |