ITR: A Unified Representation for Non-homogeneous Models Manifesting Surface, Volume, and Vector Attributes

ITR：表现表面、体积和矢量属性的非齐次模型的统一表示

• 批准号: 0218809
• 负责人: Elaine Cohen
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-15 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0218809&HistoricalAwards=false
• 关键词: ITR; Unified; Representation; Non; homogeneous

This research project will develop improved mathematical representations of three-dimensional objects, for use across a variety of applications. Underlying model representations in computer graphics, computer-aided geometric design, engineering analysis, and medical visualization have historically been driven by different requirements. Thus, different algorithmic and computational foundations have evolved yielding two largely disparate formulations. Differences in model representations impede cross-pollination of valuable techniques, hinder model sharing, and limit cross-area applications. To attack this historically intractable problem, a unified mathematical representation that can work across a broad spectrum of applications will be developed, based on an extended, multidimensional, parametric tensor product B-spline hyper-volume. High dimensional NURBs (Non-Uniform Rational B-Splines) are used as a basis because of their ubiquity in practice, universality in modeling, good overall computational and interactive behavior, and extensive understanding. Distinguishing itself from the straightforward generalization, the extended representation will support a non-hyperrectangular domain (non-hexahedral for the trivariate) appropriate to the model, and include supplementary attributes, defined over a common multidimensional parametric domain. The attributes will model both functional characteristics and data represented as scalars or vectors.Recent advances in several key technologies are creating demand for higher dimensional representations and corresponding visualization algorithms to design and analyze truly solid geometry, i.e., working in a design space of non-homogeneous materials manifesting multidimensional attributes. This calls for fundamental advances in our computing and visualization environments. One of the practical applications is designing optical lenses that achieve refracting power by smoothly varying the index of refraction and keeping a simple geometric shape. The combination of simple shape with no discontinuities in the index of refraction offers substantial optical and mechanical advantages over traditional multifarious lens systems. The project will also have educational benefits, training students in the laboratory to help them become leaders in this increasingly important field.

该研究项目将开发改进的三维对象的数学表示形式，以在各种应用中使用。 在历史上，计算机图形，计算机辅助几何设计，工程分析和医学可视化中的基础模型表示是由不同的要求驱动的。因此，不同的算法和计算基础已经演变出来，产生了两种不同的不同配方。模型表示的差异阻碍了宝贵技术的交叉授粉，阻碍模型共享和限制跨区域应用。 为了攻击这个历史上棘手的问题，将基于扩展的，多维的，参数张量产品B-Spline Hyper-dolume的统一数学表示，可以在广泛的应用程序中起作用。高维NURB（非均匀的理性B-Splines）被用作基础，因为它们在实践中无处不在，建模方面的普遍性，良好的整体计算和互动行为以及广泛的理解。 将自身与直接的概括区分开，扩展表示将支持适合模型的非hy型角域（非远视面体），并包括在常见的多维参数域上定义的补充属性。该属性将建模功能特征和表示为标量或向量的数据。几种关键技术的进展是对更高维表示的需求和相应的可视化算法创造需求，以设计和分析真正的固体几何形状，即，在非同质材料的设计空间中起作用，表现出多维属性属性。这需要在我们的计算和可视化环境中取得基本进步。实际应用之一是设计光透镜，通过平稳地改变折射率并保持简单的几何形状来实现折射功率。与传统多种透镜系统相比，简单形状没有不连续性的简单形状没有不连续性。 该项目还将具有教育福利，培训实验室的学生，以帮助他们成为这个日益重要的领域的领导者。