CS 6301: Computational Geometry

Instructor Information:

Course Description

This course will cover basic computational geometry topics, such as computing convex hulls, computing Voronoi diagrams and Delaunay triangulations, motion planning, and the main methods for developing geometric algorithms. We will also discuss various geometric data structures for point location and range searching, some geometric approximation algorithms, and topics related to high dimensional data analysis.

Textbooks and Materials

• David Mount's lecture notes: Free Online
• Computational Geometry: Algorithms and Applications, third edition. Mark de Berg, Otfried Cheong, Marc Van Kreveld, Mark Overmars

Schedule

• 01/15: Introduction to Computational Geometry, Convex Hulls [Mount 1,3 / Mark 1]
• 01/17: Convex Hulls continued [Mount 3,4 / Mark 1]
• 01/22: Line segment intersection [Mount 5 / Mark 2]
• 01/24: Polygon triangulation [Mount 6 / Mark 3]
• 01/29: Polygon triangulation continued [Mount 6 / Mark 3]
• 01/31: Halfplane intersection and point-line duality [Mount 7 / Mark 4.2,8.2,11.4]
• 02/05: Linear Programming [Mount 8 / Mark 4]
• 02/07: Class canceled
• 02/12: Linear Programming continued [Mount 8 / Mark 4]
• 02/14: Trapezoidal Maps [Mount 9 / Mark 6]
• 02/19: Trapezoidal Maps and Point Location [Mount 10 / Mark 6]
• 02/21: Voronoi Diagrams [Mount 11 / Mark 7]
• 02/26: Delaunay Triangulation Properties [Mount 12 / Mark 9]
• 02/28: Delaunay Triangulation Computation [Mount 13 / Mark 9]
• 03/05: Line Arrangements [Mount 14 / Mark 8]
• 03/07: Line Arrangement Applications [Mount 15 / Mark 8]
• 03/12: Motion planning [Mount 20 / Mark 13]
• 03/26: Orthogonal Range Searching [Mount 31,32 / Mark 5]
• 03/28: k-center clustering [Erickson J.10]
• 04/02: Well Separated Pair Decomposition [Mount 17,18]