Abstract
The skeleton of a polyhedral set is the union of its edges and vertices. Let P be a set of fat, convex polytopes in three dimensions with n vertices in total, and let f max be the maximum complexity of any face of a polytope in P. We prove that the total length of the skeleton of the union of the polytopes in P is at most O(α(n)· log * n · log f max) times the sum of the skeleton lengths of the individual polytopes.
Original language | English (US) |
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Pages (from-to) | 53-64 |
Number of pages | 12 |
Journal | Discrete and Computational Geometry |
Volume | 48 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2012 |
Keywords
- Combinatorial complexity
- Convex polytopes
- Fat polytopes
- Skeleton of union
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics