Project Title: Semi-Regular Volumetric Parameterizations, Meshes, and Datafitting
Project PI: Elaine Cohen, University of Utah
Volumetric models are increasingly pervasive in computer graphics, computer-aided geometric design, visualization, and medical data analysis. Formulating high quality parameterizations and smooth representations is a difficult problem. Although it is possible to create unstructured tetrahedral based C0 bases, there are many problems for which semi-structured smooth hexahedral based representations give higher fidelity simulations, model representations, and analyses. However, automatic creation of such representations is still a challenge problem. At least partially because they require much manual interaction and effort, current techniques to create smooth representations have not been widely adopted. Our successful initial results in using mathematical theory to create representations for special classes of volumes has opened a door for extending the theory to create algorithms that deal with more complex volumetric shapes. A semi-regular parameterization facilitates many geometric processing and analysis algorithms, allowing their extension to volumetric processing, and it supports the use of smooth higher-order bases for simulation.
This research is creating automatic parameterization and data fitting techniques for heterogeneous volumes through i) developing a theoretical basis for techniques to represent volumetric models using semi-regular tensor product parameterizations, and ii) fitting higher order smooth representations of the volumes over the parameterizations and then using associated smooth bases for simulation. We are addressing domain matching, shape distortion, and issues in computational geometry for such algorithms. Shapes that are being investigated include multi-boundary polygonal models derived from scanned data and designed boundary models represented as smooth NURBS surfaces. Algorithms and software tools to help transform surface models to tensor product volume parameterizations and smooth representations of volumes were lacking, one issue that this research is overcoming. The results are being tested on a meaningful subset of graphics simulation problems, particularly in the case of elastic deformations of objects.