Tuesday, February 7, 2012
IST Lunch Bunch
Smooth Direction Fields on Surfaces
Peter Schröder, Professor, Computing & Mathematical Sciences, Caltech
Consider a smooth surface with fur on it. Mathematically we can think of this as a surface with a ("comb") direction specified at each point. Such orientation fields are an integral part of many algorithms in computer graphics ranging from (fur) shading to the construction of quadrilateral meshes for finite element simulations. These direction fields should vary smoothly over the surface and optionally take given guidance data into account. We also know that such fields will have singularities which must be placed somewhere. <br><br> Traditional approaches to this problem have resulted in rather difficult optimization problems. In this talk I will describe a new approach which allows us to find the globally optimal smooth field over all possible choices of singularities (type and placement) through minimization of a simple quadratic energy. <br><br> Joint work with Felix Knöppel, Keenan Crane, and Ulrich Pinkall.