HCC: Medium: Robust and Accurate Modeling with Multifield Geometry

HCC：中：使用多场几何进行稳健且准确的建模

• 批准号: 0905502
• 负责人: Denis Zorin
• 金额: $ 73.91万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-15 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905502&HistoricalAwards=false
• 关键词: HCC; Medium; Robust; Accurate; Modeling

Computer tools for creating, analyzing and modifying geometry are the core component in computer-aided design systems, indispensable for engineering and product prototyping, surgical simulation, prosthesis design, dentistry, architecture, computer animation and games. There is a considerable demand for high-level modeling tools, expressing the user?s intent directly while being capable of handling complex models robustly. Surface optimization techniques unify traditional ab initio modeling of high-quality surfaces and manipulation of existing geometric data in a single natural framework by specifying suitable optimization functionals governing the surface behavior. This framework is conceptually representation-independent: the surface can be approximated by spline patches, subdivision surfaces, meshes or in implicit form. While this framework is highly appealing for practical applications, surface optimization rarely finds its way into industrial applications, as existing interactive techniques are not sufficiently robust, while the more precise and reliable methods are too slow to be used interactively.This research project develops fundamental mathematical and algorithmic techniques essential for bringing surface optimization methods to mainstream geometric modeling applications. The research is addressing the following problems: shape representation and its accuracy, such that the modeled surfaces depend solely on the user input and not the particular choice of sampling or approximation basis; robust and efficient modeling algorithms to ensure predictable and responsive behavior in interactive applications; diverse control to allow sufficient freedom for arbitrary shape manipulation. The investigated approach has two key components: multifield geometry descriptions, building on ideas from discrete geometry, high-order geometric modeling, and finite elements and novel multiscale numerical solvers that combine robust global algorithms at coarse scales with fast and accurate algorithms at fine scales to achieve the performance and robustness needed in applications. The new methods are explored in the context of high-level modeling tasks, including modeling from two-dimensional projections or drawings, feature-based and appearance-based editing and template fitting for dental CAD.

用于创建，分析和修改几何形状的计算机工具是计算机辅助设计系统中的核心组件，对于工程和产品原型制作，手术模拟，假体设计，牙科，建筑，计算机动画和游戏都是必不可少的。对高级建模工具有很大的需求，直接表达用户的意图，同时能够坚固地处理复杂模型。表面优化技术通过指定控制表面行为的合适的优化功能来统一对单个自然框架中现有几何数据的传统AB始于对现有几何数据的操纵。该框架在概念上是无关的：可以通过样条斑块，细分表面，网格或隐式形式近似表面。尽管该框架对实际应用具有很高的吸引力，但表面优化很少能进入工业应用，因为现有的交互式技术不够健全，而更精确，更可靠的方法太慢而无法交互式使用。该研究项目开发了基本的数学和算法技术来实现表面优化的基本化方法。该研究正在解决以下问题：形状表示及其准确性，因此建模的表面仅取决于用户的输入，而不是采样或近似基础的特定选择；强大而有效的建模算法，以确保交互式应用中的可预测和响应性行为；多样化的控制，以允许足够的自由进行任意形状操纵。研究的方法具有两个关键组成部分：多场几何描述，基于离散几何形状，高阶几何建模以及有限元素以及新颖的多尺度数值求解器的想法，它们结合了强大的全球算法，以稳健的全球算法与尺度上的稳定性算法与快速准确的算法相结合，以实现应用程序和稳健性，以实现应用程序的性能和稳健性。在高级建模任务的上下文中探索了新方法，包括从二维投影或图纸的建模，基于功能的基于功能的和基于外观的编辑以及用于牙科CAD的模板拟合。