Multiresolution surface parametrization and applications

This thesis presents an algorithm for computing the surface parameterization of irregular connectivity triangle meshes of arbitrary genus 2-manifold and applications of the parameterization in progressive transmission, editing, morphing, animation, geometry compression, and rendering.; The triangle mesh is one of the most common representations of 3D models. It can represent surfaces of arbitrary topology with irregular connectivity. Unfortunately, due to the complex structure and tremendous size, they are often difficult to handle in common tasks such as storage, display, manipulation, and transmission.; In the first part of this thesis, we propose an algorithm: MAPS (Multiresolution Adaptive Parameterization of Surfaces), for parameterizing arbitrary irregular triangle meshes by defining a mapping between the original model and a simple base domain. We also demonstrate its usefulness in converting irregular meshes to meshes with subdivision connectivity with guaranteed error bounds. The subdivision connectivity property generalizes classical wavelet representations and is thus of immediate use in multiresolution editing and compression.; In the second part of the thesis, we present a new method for user-controlled morphing of two homeomorphic triangle meshes of arbitrary topology. Our method employs the MAPS algorithm and allows the user to modify the mapping interactively by specifying any number of feature pairs.; In the third part of the thesis, we introduce a new surface representation:DSS (Displaced Subdivision Surface). It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement field using a unified subdivision framework, which allows for simple and efficient evaluation of analytic surface properties. The resulting surface is C1 everywhere except at the extraordinary vertices. We present a simple, automatic scheme based on the MAPS approach for converting complex geometric models into such a representation. We demonstrate that DSS offers a number of benefits, including better geometry compression, easy editing, interactive animation, scalable and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. The displacement map can also be used to generate a bump map for the rendering of coarser tessellations. This improves rendering performance on graphics systems where geometry processing is a bottleneck.