Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Optimality of the Delaunay triangulation in Rd
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Mathematical Programming: Series A and B
Computers and Operations Research
Primal-dual methods for vertex and facet enumeration (preliminary version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
An Algorithm for Approximate Multiparametric Convex Programming
Computational Optimization and Applications
Automatica (Journal of IFAC)
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Using a pair of theorems linking Delaunay partitions and linear programming, we develop a method to generate all simplices in a Delaunay partition of a set of points, and suggest an application to a piecewise linear non-convex optimization problem. The same method is shown to enumerate all facets of a polytope given as the convex hull of a finite set of points. The dual problem of enumerating all vertices of a polytope P defined as the intersection of a finite number of half-spaces is also addressed and solved by sequentially enumerating vertices of expanding polytopes defined within P. None of our algorithms are affected by degeneracy. Examples and computational results are given.