Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
On Translational Motion Planning of a Convex Polyhedron in 3-Space
SIAM Journal on Computing
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
Guarding scenes against invasive hypercubes
Computational Geometry: Theory and Applications
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Computational Geometry: Theory and Applications
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
Vertical Ray Shooting and Computing Depth Orders for Fat Objects
SIAM Journal on Computing
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Computing the visibility map of fat objects
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We show that any locally-fat (or 茂戮驴, β-covered) polyhedron with convex fat faces can be decomposed into O(n) tetrahedra, where nis the number of vertices of the polyhedron. We also show that the restriction that the faces are fat is necessary: there are locally-fat polyhedra with non-fat faces that require 茂戮驴(n2) pieces in any convex decomposition. Furthermore, we show that if we want the polyhedra in the decomposition to be fat themselves, then the worst-case number of tetrahedra cannot be bounded as a function of n. Finally, we obtain several results on the problem where we want to only cover the boundary of the polyhedron, and not its entire interior.