Department of Computer Science Colloquium
Thursday March 28th, 2002 at 4:15pm 
Upson Hall B17

Local Surface Parameterizations

Emil Praun
Princeton University

3D computer graphics has become a part of everyday life, partly due to its heavy use in the movie industry, computer gaming, virtual reality and online applications. These media deal primarily with rendering 3D models, which are commonly represented as triangle meshes. For efficiency, however, fine detail is not modeled using triangles, but stored separately in texture maps or similar regularly sampled structures. This separation between the representations of overall shape and fine detail spurs the need for good surface parameterizations - mappings to the plane that have few discontinuities, low distortion, and roughly uniform sampling. The fundamental challenge is that continuous, global parameterizations do not exist in general for arbitrary surfaces, not even for very simple objects: the celebrated "hairy ball theorem" states that one cannot comb a hairy ball without having a part or a cowlick. Fortunately, by relaxing the continuity constraint in favor of lower distortion and automatic generation, one can supplant global parameterizations with local parameterizations on a set of (possibly overlapping) patches. My thesis develops technology for several forms of local parameterization in the context of the applications driving this research. The applications I will present include 3D mesh watermarking, generating surface texture from example, rendering surfaces with fur or in a non-photorealistic "hatching" style, and consistent parameterizations of multiple surfaces.