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Semispaces of Configurations
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0(nlogn affine hull arrangement A(H arrangements of hyperplanes assume belongs bisects boundary called cell complex Chapter circular sequence collinear combinatorial compute configuration contains convex hull convex polytope convP corresponding data structure defined Delaunay triangulation deletion denote described determine DT(S dual Edelsbrunner endfor endpoint Exercise extremal query facet fc-face Figure finite set following result half-plane half-space ham-sandwich cut hyper hyperplane h implies incidence graph integer numbers intersection Lemma Let H line segments linear program lower bound minimum spanning tree multiset n-sequence node non-empty non-vertical hyperplanes number of faces Observation pairs permutation Pl and P2 plane point sets pointer points in E2 polygon Procedure Proof Prove real number recursive search problem Section set of points set of sites sites in E2 skeleton solution solve stabbing region Step storage subface subset superface Theorem tion transversal triangulation unbounded upper bound vector vertex vertical hyperplane vertical line vertical projection Voronoi diagrams zonotope
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