Classes start January 05, 2012 at 4:30 pm.
F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, New York, NY, Springer-Verlag, 1985.
Herbert Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag
Subir Kumar Ghosh, Visibility algorithms in the plane, Cambridge University Press, 2007.
Data Structures and Algorithms: Volumes I and III by Kurt Mehlhorn, Springer-Verlag.
Ketan Mulmuley, Computational Geometry: An Introduction
through Randomized Algorithms.
Motwani and Raghavan, Randomized Algorithms.
K. Mehlhorn and S. Naher, LEDA: A Platform for
Combinatorial and Geometric Computing, Cambridge, UK, Cambridge University
Press, 1999.
Mark de Berg, Otfried Schwarzkopf, Marc van Kreveld and Mark Overmars, Computational Geometry: Algorithms and Applications, Springer.
Joseph O' Rourke, Computational Geometry in C, Cambridge University Press.
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CS60064 COMPUTATIONAL GEOMETRY L-T-P: 3-0-0, Credits: 3
Convex hulls: construction in 2d and 3d, lower bounds; Triangulations: polygon triangulations, representations, point-set triangulations, planar graphs; Voronoi diagrams: construction and applications, variants; Delaunay triangulations: divide-and-conquer, flip and incremental algorithms, duality of Voronoi diagrams, min-max angle properties; Geometric searching: point location, fractional cascading, linear programming with prune and search, finger trees, concatenable queues, segment trees, interval trees; Visibility: algorithms for weak and strong visibility, visibility with reflections, art-gallery problems; Arrangements of lines: arrangements of hyperplanes, zone theorems, many-faces complexity and algorithms; Combinatorial geometry: Ham-sandwich cuts, Helly's theorems, k-sets, polytopes and hierarchies, polytopes and linear programming in d-dimensions, complexity of the union of convex sets, simply connected sets and visible regions; Sweep techniques: plane sweep for segment intersections, Fortune's sweep for Voronoi diagrams, topological sweep for line arrangements; Randomization in computational geometry: algorithms, techniques for counting; Robust geometric computing; Applications of computational geometry.
References
1. Mark de Berg, Otfried Schwarzkopf, Marc van Kreveld and Mark Overmars, Computational Geometry: Algorithms and Applications, Springer.
2. F. P. Preparata and Michael I. Shamos, Computational Geometry: An Introduction, Springer.
3. Joseph O' Rourke, Computational Geometry in C, Cambridge University Press.
4. Lecture Notes by David Mount.