This course covers fundamental algorithms for efficiently solving geometric problems, especially ones involving 2D polygons and 3D polyhedrons. Topics include elementary geometric operations; polygon visibility, triangulation, and partitioning; computing convex hulls; proximity searching, Voronoi diagrams, and Delaunay triangulations with applications; special polygon and polyhedron algorithms such as point containment and extreme point determination; point location in a planar graph subdivision; dimension reduction in data; and robot motion planning around polygon obstacles. Applications to such areas as computer graphics, big data analytics and pattern recognition, geometric databases, numerical taxonomy, and robotics will be addressed. The course covers theory to the extent that it aids in understanding how the algorithms work. Emphasis is placed on algorithm design and implementation. Programming projects are an important part of the coursework. Prerequisite(s): Foundations of algorithms. Some familiarity with linear algebra.
605.621 Foundations of Algorithms. Some familiarity with linear algebra.