Abstract
We show that the boundary of a three-dimensional polyhedron with r reflex angles and arbitrary genus can be subdivided into O(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 in r, which contrasts with a quadratic worst-case lower bound on the number of convex pieces needed to decompose the polyhedron itself. The number of new vertices introduced in the process is O(n). The decomposition can be computed in O(n+r log r) time.
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© 1992 Springer-Verlag Berlin Heidelberg
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Chazelle, B., Palios, L. (1992). Decomposing the boundary of a nonconvex polyhedron. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_33
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DOI: https://doi.org/10.1007/3-540-55706-7_33
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