AASERT: Software Tools for Experimentation in Computational Geometry

Abstract : This research has considered problems in computer graphics and visualization. The work has aimed to bring theoretical tools to practical problems as well as to develop tools with which to aid in the building of geometric software. The problem of creating a parameterization of the surface of a mesh that can be applied at multiple resolutions has been studied. Such a parameterization has a number of applications. We were originally motivated by the desire to be able to progressively transmit meshes by having a hierarchical representation. To solve this problem the MAPS (Multiresolution Adaptive Parameterization of Surfaces) system for finding a full surface parameterization has been developed. The parameterization is computed in hierarchical fashion. While previous methods removed a small number of vertices per iteration, we are able to remove a fraction of the vertices. As the name suggests, the parameterization is also adaptive. Thus, we can use it as a basis of resampling the surface to smooth the mesh, make it more regular or to supersample areas of high curvature.