CANCELLED - EU Regional School - Crane Seminar
Prof. Dr. Crane - Laplace-Beltrami: The Swiss Army Knife of Geometry Processing
Carnegie Mellon University
A remarkable variety of fundamental 3D geometry processing tools can be expressed in terms of the Laplace-Beltrami operator on a surface—understanding these tasks in terms of basic PDEs such as heat flow, Poisson equations, and eigenvalue problems leads to an efficient, unified treatment at the computational level. The central goal of this tutorial is to show students 1. how to build the Laplacian on a triangle mesh, and 2. how to use this operator to implement a diverse array of geometry processing tasks. We will also discuss alternative discretizations of the Laplacian (e.g., on point clouds and polygon meshes), recent developments in discretization (e.g., via power diagrams), and important properties of the Laplacian in the smooth setting that become essential in geometry processing (e.g., existence of solutions, boundary conditions, etc.).