CG_HW4_S10 - b) it belongs to two triangles, abc and abd ,...

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UML CS Advanced Algorithms (Computational Geometry) 91.504 Spring, 2010 Homework #4 Assigned : Thursday, 3/4 Due : Thursday, 3/11 . 1. Review and study for the midterm exam! 2. (50 points) Delaunay Triangulations : In his book “ Geometry and Topology for Mesh Generation ,” Herbert Edelsbrunner sets up the following locally Delaunay definition for an edge ab of a planar triangulation K : An edge K ab is locally Delaunay if: a) it belongs to only one triangle and therefore bounds the convex hull, or
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Unformatted text preview: b) it belongs to two triangles, abc and abd , and d lies outside the circumcircle of abc . Example : (recreation of Edelsbrunners Figure 1.8) To the left edge ab is locally Delaunay and to the right it is not. Edelsbrunner claims that a locally Delaunay edge is not necessarily an edge of the Delaunay triangulation. Your task is to construct such an example. a b c d a b c d...
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