Chris Bishop : Conformal maps and optimal meshes

I will describe a linear time algorithm for computing the Riemann map from the unit disk onto an n-gon. The method depends on results from computational geometry (fast computation of the medial axis) and hyperbolic geometry (a theorem of Dennis Sullivan about convex sets in hyperbolic 3-space), as well as classical conformal and quasiconformal theory. Conversely, the fast mapping algorithm implies new results in computational geometry, e.g., (1) quadrilateral meshing for polygons and PSLGs (planar straight line graphs) with optimal time and optimal angle bounds, (2) the first polynomial time algorithm for refining general planar triangulations into non-obtuse triangulations (no angles > 90 degrees; this is desirable for various applications and 90 is the best bound that can be achieved in polynomial time). The talk is intended to be a colloquium-style overview, but I would be happy to discuss more technical details, as requested.

• Category: Applied Math and Analysis
• Duration: 01:34:51
• Date:  February 24, 2014 at 4:25 PM
• Views: 105
• Tags:   seminar, Applied Math And Analysis Seminar