Digital Geometry Processing

Peter Schroder

Department of Computer Science and Applied & Computational Mathematics

California Institute of Technology

Abstract:

Discrete (or sampled) geometry representations pop up in all areas of engineering practice and scientific inquiry. Examples range from 3D scanning for reverse engineering to remote sensing, physical simulation, and data analysis among many others. In my talk I will discuss some of the mathematical and algorithmic tools recently developed to enable efficient and robust processing of such digital geometry. I will use surface compression and adaptive solvers for PDEs as example applications to argue that multiresolution tools can be of great benefit in this area.

These first steps in the area of Digital Geometry Processing point to the importance of careful discretization of geometry, functions, and operators acting on them. In the second part of my talk I will discuss some early results in structure preserving discretizations and the benefits these have for robust computations. These first glimpses are quite exciting and I will argue that such discretizations should form the foundation for a fresh approach to computation in general.

Brief Biography:

Peter Schroder is a Professor of Computer Science and Applied & Computational Mathematics at Caltech where he leads the Multi-Res Modeling Group. His expertise is in the area of numerical algorithms for geometric modeling, computer graphics, and physical simulation with a particular emphasis on wavelet and more general multiresolution approaches. His work was most recently honored when he was named a Discover Award Finalist (2001). He is a Packard Fellow and has led a number of cross-disciplinary projects at Caltech bringing together engineering design, computer science, control & dynamical systems, and numerical analysis teams.