Vertex-rounding a three-dimensional polyhedral subdivision
Steven Fortune · 1998
Let P be a polyhedral subdivision in lR3 with a t,otal of n faces.We show ghat t,here is an embedding u of the vertices, edges, and facets of P into a subdivision &, where every vertes coordinate of Q is an integral multiple of 2-p"fian+'l.For each face f of P, the Hausdorff distance in the 1;, metric between f and o(f) is at most, 3/2.The embedding u preserves or collapses vertical order on faces of P. The subdivision Q has O(n4) vertices in the worst, case, and can be computed in the same time.