This is the problem of finding a conformally equivalent metric to a given one with isolated (and few) cone singularities. In my talk I will describe a recent algorithm which finds conformally equivalent discrete metrics on triangle meshes as the minimum of a convex energy. This problem brings together pretty ideas from discrete differential geometry, computational geometry, convex optimization, and even sparse approximation.

Joint work with Ulrich Pinkall and Boris Springborn (both of TU Berlin).