Title: Finding soap films in non-Euclidean geometry
Abstract: In many computer graphics applications we approximate a smooth surface with one made up of tiny triangles. A common problem is to determine which way to move the vertices (the corners of the triangles), so that the total surface area decreases. If the boundary of the surface remains fixed, this allows us to find the soap film surface spanned by that boundary curve. In Euclidean geometry this leads to the famous “cotan-Laplace formula.” After reviewing this formula we will introduce spherical and hyperbolic space, and discuss a solution to the same problem in those geometries.
Dr. Bachman is Professor of Mathematics at Pitzer College and Director of the Claremont Center for the Mathematical Sciences.