CAREER: Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering Design

职业：基于物理的计算机动画和交互式工程设计的多分辨率基础

• 批准号: 0643268
• 负责人: Eitan Grinspun
• 金额: $ 32.3万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-03-15 至 2013-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0643268&HistoricalAwards=false
• 关键词: CAREER; Multiresolution; Foundations; Physics; Based

Multiresolution Foundations for Physics-Based Computer Animation and Interactive Engineering DesignPI: Eitan Grinspun, Columbia UniversityPhysical simulations enable scientists and engineers to study complex systems for which direct, controlled experimentation is costly, dangerous, or intractable. Exploratory studies enable engineers to gather qualitative intuition, or feel for the subject system, which in turn leads to the posing of new hypotheses and directions for experimentation. While exploratory processes are inherently interactive, today's computational barriers limit the exploration of important systems to non-interactive modalities. This research seeks to overcome these obstacles with novel methods that quickly but coarsely resolve the physics, skipping over irrelevant data to capture only the coarse variables that drive design decisions. The investigators develop simulation techniques that address the vision of a rapid, interactive design cycle, with a specific focus on the physical simulation of thin shells flexible surfaces such as air bags, biological membranes, and textiles, with pervasive applications in automotive design, biomedical device optimization, and feature film production. In a synergistic pedagogical thrust, this project trains young scientists with a deep understanding of computation, mathematics, and application domain areas despite being in high demand, this combination of skills remains rare.The investigators are developing a principled, methodical approach to coarsening an existing discrete geometric model of a mechanical system, using adaptive, multi-resolution decompositions. Whereas adaptivity is commonly studied in the context of error estimators for mesh refinement, interactivity suggests a focus on how best to give up precision in a simulation. Therefore, this research (i) builds on early work in the field of discrete differential geometry to formulate coarse geometric representations of physical systems that preserve key geometric and physical invariants, (ii) investigates the convergence, resolution- and meshing-dependence of discrete differential operators, and (iii) contributes toward a software platform for interactive design space exploration with concrete applications in automotive, biomedical, and feature-film engineering.

基于计算机动画和交互工程设计的多分辨率物理基础：Eitan grspun，哥伦比亚大学物理模拟使科学家和工程师能够研究复杂的系统，这些系统的直接、受控实验是昂贵的、危险的或难以处理的。探索性研究使工程师能够获得定性的直觉，或对主题系统的感觉，这反过来又导致提出新的假设和实验方向。虽然探索过程本质上是交互式的，但今天的计算障碍将重要系统的探索限制在非交互式模式上。这项研究试图用新颖的方法来克服这些障碍，这种方法可以快速但粗略地解决物理问题，跳过不相关的数据，只捕获驱动设计决策的粗略变量。研究人员开发了模拟技术，以解决快速、交互式设计周期的愿景，特别关注薄壳柔性表面（如安全气囊、生物膜和纺织品）的物理模拟，并在汽车设计、生物医学设备优化和电影制作中广泛应用。在协同教学的推动下，该项目培养了对计算、数学和应用领域有深刻理解的年轻科学家，尽管需求量很大，但这种技能的结合仍然很少见。研究人员正在开发一种原则性的、有条理的方法，使用自适应的、多分辨率的分解来粗化现有的机械系统离散几何模型。虽然自适应通常是在网格细化的误差估计器的背景下研究的，但交互性建议关注如何在模拟中最好地放弃精度。因此，本研究(i)建立在离散微分几何领域的早期工作的基础上，以制定保留关键几何和物理不变量的物理系统的粗略几何表示，（ii）研究离散微分算子的收敛性，分辨率和网格依赖性，以及（iii）为交互式设计空间探索的软件平台做出贡献，并在汽车，生物医学和电影工程中有具体应用。