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

项目名称：半规则体积参数化、网格和数据拟合项目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、可视化和医学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困难的问题。虽然可以创建基于非结构化四面体的C0基，但是存在许多问题，其中基于半结构化光滑六面体的表示给出更高保真度的模拟、模型表示和分析。然而，自动创建这样的表示仍然是一个具有挑战性的问题。至少部分是因为它们需要大量的手动交互和努力，当前创建平滑表示的技术尚未被广泛采用。我们成功地使用数学理论来创建特殊类别的体积表示的初步结果打开了一扇门，扩展的理论，以创建算法，处理更复杂的体积形状。半正则参数化简化了许多几何处理和分析算法，使它们可以扩展到体积处理，并支持使用光滑高阶基进行模拟。本研究通过i）为使用半正则张量积参数化表示体积模型的技术开发理论基础，以及ii）在参数化上拟合体积的高阶平滑表示，然后使用相关联的平滑基进行模拟。我们正在解决域匹配，形状失真，并在计算几何等算法的问题。正在研究的曲面包括从扫描数据导出的多边界多边形模型和表示为光滑NURBS曲面的设计边界模型。算法和软件工具，以帮助转换表面模型张量积体积参数化和光滑的体积表示缺乏，本研究正在克服的一个问题。结果正在测试的图形模拟问题的一个有意义的子集，特别是在物体的弹性变形的情况下。

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.