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Polyhedra :: cellDecompose

cellDecompose -- computes the regular cell decomposition

Synopsis

Description

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)

Ways to use cellDecompose :