Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Weighted skeletons and fixed-share decomposition
Computational Geometry: Theory and Applications
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A simple cell complex C in Euclidean d-space E^d is a covering of E^d by finitely many convex j-dimensional polyhedra (the j-faces of C), each of which is in the closure of exactly d-j+1 d-faces of C. An algorithm that recognises when C is the projection of the set of faces bounding some convex polyhedron P(C) in E^d^+^1, and that constructs P(C) provided its existence is outlined. The method is optimal at least for d=2. No complexity results were previously known for both problems. The results have applications in statics, to the recognition of Voronoi diagrams, and to planar point-location,