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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
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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