Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
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
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
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
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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We show that any locally-fat (or (@a,@b)-covered) polyhedron with convex fat faces can be decomposed into O(n) tetrahedra, where n is 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 @W(n^2) pieces in any convex decomposition. Furthermore, we show that if we want the tetrahedra in the decomposition to be fat themselves, then their number cannot be bounded as a function of n in the worst case. Finally, we obtain several results on the problem where we want to only cover the boundary of the polyhedron, and not its entire interior.