HCC: CGV: Small: Semi-Regular Volumetric Parameterizations , Meshes, and Datafitting

PI: Elaine Cohen，犹他大学体积模型在计算机图形学、计算机辅助几何设计、可视化和医疗数据分析中越来越普遍。制定高质量的参数化和光滑表示是一个难题。虽然可以创建基于C0基的非结构化四面体，但对于许多问题，基于半结构化光滑六面体的表示可以提供更高保真度的仿真、模型表示和分析。然而，这种表示的自动创建仍然是一个具有挑战性的问题。至少部分原因是它们需要大量的人工交互和努力，目前用于创建平滑表示的技术尚未被广泛采用。我们在使用数学理论为特殊类型的体积创建表示方面的成功初步结果为扩展理论创建处理更复杂体积形状的算法打开了一扇门。半规则参数化简化了许多几何处理和分析算法，允许它们扩展到体积处理，并且支持使用光滑的高阶基进行模拟。本研究通过以下方式为异构体积创建自动参数化和数据拟合技术：(1)为使用半正则张量积参数化表示体积模型的技术提供理论基础；(2)在参数化上拟合体积的高阶光滑表示，然后使用相关的光滑基进行模拟。我们正在为这样的算法解决域匹配、形状失真和计算几何中的问题。正在研究的形状包括从扫描数据导出的多边界多边形模型和以光滑NURBS表面表示的设计边界模型。缺乏将曲面模型转换为张量积体积参数化和体积光滑表示的算法和软件工具，这是本研究正在克服的一个问题。这些结果正在图形模拟问题的一个有意义的子集上进行测试，特别是在物体弹性变形的情况下。

Project Title: Semi-Regular Volumetric Parameterizations, Meshes, and Datafitting Project PI: Elaine Cohen, University of UtahVolumetric 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.