IGS'16 Summer School: Laplace-Beltrami: The Swiss Army Knife of Geometry Processing

Course 6
Laplace-Beltrami: The Swiss Army Knife of Geometry Processing
Etienne Vouga (UT Austin)
Abstract:
A remarkable variety of basic geometry processing tools can be expressed in terms of the Laplace-Beltrami operator on a surface-understanding these tasks in terms of fundamental 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.).
Brief Biography:
Etienne Vouga is an assistant professor of computer science at the University of Texas at Austin. He received his PhD from Columbia University in 2013, where he worked with Eitan Grinspun, and worked at Harvard University in 2014 as a postdoc, applying ideas of discrete differential geometry and geometry processing to problems involving crumpling and growth of thin shells. Etienne's research interests are applying geometric principles to physical simulation and inverse designs problems involving surfaces and shells.
Etienne Vouga, Keenan Crane, and Justin Solomon developed the tutorial on the Laplace-Beltrami operator together for the SGP Summer School. Etienne will be presenting the tutorial in place of Keenan Crane, who for reasons outside his control cannot attend the summer school.