Output sensitive construction of levels and Voronoi diagrams in Rd of order 1 to k
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Randomized multidimensional search trees (extended abstract): dynamic sampling
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
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108 Efficient, randomized algorithms are given for the following problems: (1) construction of levels of order 1 to k in an arrangement of hyperplanes in any dimension; (2) construction of higher order Voronoi diagrams of order 1 to k in any dimension; (3) hidden surface removal for completely general scenes (intersecting and curved faces are allowed). A combinatorial tool in the form of a mathematical series called a theta series is associated with a configuration of polytopes in R/sup d/. It is used to study the combinatorial, as well as algorithmic, complexity of the geometric problems under consideration.