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的核心组件，对于工程和产品原型、手术模拟、假体设计、牙科、建筑、计算机动画和游戏来说是不可或缺的。对高级建模工具的需求相当大，用户表示？的意图直接，同时能够处理复杂的模型鲁棒。表面优化技术统一了传统的高质量的表面和现有的几何数据在一个单一的自然框架，通过指定合适的优化函数管理的表面行为的从头建模。这个框架在概念上是独立于表示的：曲面可以近似为样条曲面、细分曲面、网格或隐式形式。虽然这个框架是非常有吸引力的实际应用，表面优化很少找到它的方式进入工业应用，现有的交互式技术不够强大，而更精确和可靠的方法是太慢，以交互式used.This研究项目开发的基本数学和算法技术，使表面优化方法的主流几何造型应用程序必不可少。该研究正在解决以下问题：形状表示及其准确性，使建模的表面只依赖于用户输入，而不是特定的选择采样或近似的基础;强大而有效的建模算法，以确保可预测的和响应的行为在交互式应用程序;多样的控制，允许足够的自由任意形状的操作。研究的方法有两个关键组成部分：多场几何描述，建立在离散几何，高阶几何建模，有限元和新的多尺度数值求解器，联合收割机强大的全局算法在粗尺度快速，准确的算法在细尺度，以实现应用所需的性能和鲁棒性的想法。新方法的背景下，高层次的建模任务，包括从二维投影或图纸建模，基于特征和外观的编辑和模板拟合牙科CAD的探索。