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Unformatted text preview: COT5405: GEOMETRIC ALGORITHMS ✦ Objects: Po ints in Rn, Segments, Lines, Circles, Triangles Polygons, Polyhe dra ✦ Applications ✦ Vision, Graphics, Visualizations, ✦ Databases, Data mining, Networks, GIS ✦ Scientific Computing, Engineering, CAD ✦ Comp Biology, Physics simulations, ✦ Operations research, Prof. Alper Ungor - An Shor t Introduction to Computational Geometr y or the unique convex p olygon that contains P and whose vertices are al P might have interior p oints that are not vertices of the convex hull. Introduction Triangulations Delaunay Triangulations SAMPLE PROBLEMS / CONCEPTS otivation: Terrains ✦ Convex Hulls a terrain is the graph of a function f : A ⊂ R2 → R we know only height values for a set of measurement points Motivation Voronoi diagrams ? ✦ Triangulations how can we interpolate the height at other points? Voronoi diagrams Spatial interp olation Voronoi diagram A set of p oints and its convex hull. Convex hull vertices are black; interior p oints are white. using a triangulation ✦ Just to make things concrete, we will represent the p oints in P by th n two arr...
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