Computing the Riemannian center of mass on meshes

Speaker: Claudio Mancinelli, University of Genova

Abstract: The Riemannian center of mass provides the equivalent to the Euclidean affine average on manifolds. In spite of its many potential applications in computer graphics and geometric modeling, there exist surprisingly few algorithms to compute it. In this talk, a direct method for computing the Riemannian center of mass on a triangle mesh is described. Such a method works in the polyhedral metric and uses a piecewise-linear interpolation of gradients of the distance fields from a set of control points. Applications for tracing splines on a surface and comparison to other methods at the state of the art will be presented as well.

Biography: Claudio Mancinelli is a research fellow at the University of Genova. He got both his BSc and his MSc in Applied Mathematics at the University of Genova, respectively in 2015 and 2017. He obtained his PhD in 2022, supervised by Professor E. Puppo. His research interests are focused in Geometry Processing and Discrete Differential Geometry.

Host: Prof. Kai Hormann