Abstract
We show that the boundary of a three-dimensional polyhedron withr reflex angles and arbitrary genus can be subdivided intoO(r) connected pieces, each of which lies on the boundary of its convex hull. A remarkable feature of this result is that the number of these convex-like pieces is independent of the number of vertices. Furthermore, it is linear inr, which contrasts with a quadratic worst-case lower bound in the number of convex pieces needed to decompose the polyhedron itself. The number of new vertices introduced in the process isO(n). The decomposition can be computed inO(n+rlogr) time.
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Communicated by L. J. Guibas.
This work was mostly done while the author was a graduate student at Princeton University.
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Chazelle, B., Palios, L. Decomposing the boundary of a nonconvex polyhedron. Algorithmica 17, 245–265 (1997). https://doi.org/10.1007/BF02523191
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DOI: https://doi.org/10.1007/BF02523191