Polyhedrization of Discrete Convex Volumes
In recent years the problem of obtaining a reversible discrete surface polyhedrization (DSP) is attracting an increasing interest within the discrete geometry community. In this paper we propose the first algorithm for obtaining a reversible polyhedrization with a guaranteed performance, i.e., together with a bound on the ratio of the number of facets of the obtained polyhedron and one with a minimal number of facets. The algorithm applies to the case of a convex DSP when a discrete surface M is determined by a convex body in ℝ3. The performance estimation is based on a new lower bound (in terms of the diameter of M) on the number of 2-facets of an optimal polyhedrization. That bound easily extends to an arbitrary dimension n. We also discuss on approaches for solving the general 3D DSP.
Keywordsdiscrete geometry reversible polyhedrization polyhedron decomposition
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