**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.