Globally Optimal Direction Fields

Thursday, June 20, 2019 - 9:00am - 10:00am
Keller 3-180
Peter Schroeder (California Institute of Technology)
Given a discrete surface (an oriented 2-manifold simplicial complex in R^3) one may ask for the smoothest direction field on such a surface. Unless the surface is a torus such fields must have singularities. Where should these be? What does optimal mean? What about line fields, or cross fields? What are they good for anyway? In this tutorial lecture I will use this application to talk about discrete notions of parallel transport, connections, and the connection Laplacian on a surface, all of which turn out to be fundamental tools in geometry processing far beyond this particular application.