Decompositions and Boundary Coverings of Non-convex Fat Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Decompositions and boundary coverings of non-convex fat polyhedra
Computational Geometry: Theory and Applications
Computing the visibility map of fat objects
Computational Geometry: Theory and Applications
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We present new results for three problems dealing with a set $\mathcal{P}$ of $n$ convex constant-complexity fat polyhedra in 3-space. (i) We describe a data structure for vertical ray shooting in $\mathcal{P}$ that has $O(\log^2 n)$ query time and uses $O(n\log^2 n)$ storage. (ii) We give an algorithm to compute in $O(n\log^3 n)$ time a depth order on $\mathcal{P}$ if it exists. (iii) We give an algorithm to verify in $O(n\log^3 n)$ time whether a given order on $\mathcal{P}$ is a valid depth order. All three results improve on previous results.