CAREER: Fast, Predictive Modeling and Simulation in Computer Graphics: Theoretical and Computational Foundations

职业：计算机图形学中的快速预测建模和仿真：理论和计算基础

• 批准号: 0133983
• 负责人: Mathieu Desbrun
• 金额: $ 32.5万
• 依托单位: University of Southern California
• 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: 2002-01-15 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0133983&HistoricalAwards=false
• 关键词: CAREER; Fast; Predictive; Modeling; Simulation

0133983Desbrun, MathieuU of Southern CaliforniaThe primary research objective in this project is to develop new mathematical and computational tools for irregular sampling in Computer Graphics. Digital geometry is rapidly emerging as a new ubiquitous medium, complementing the previous electronic datatypes for sound, images and movies. However, geometry requires to deal with irregular, non-uniform sampling living on curved manifolds, a radically different problematic that calls for novel, fundamental tools. Thus, this work is targeted towards a better understanding and handling of irregular sampling. Building on our theoretical results, we will develop new practical algorithms for fast and predictive modeling and/or simulation. We will establish a unified foundation for discrete/differential geometry, defining mimetic discretizations of the continuous case.This project will provide both theoretical foundations in the nascent field of Computational Differential Geometry, and robust, reliable tools that will advance the field of Computer Graphics. These foundations and computational tools will facilitate and accelerate the expansion of 3D models in our everyday life, be it in software products (ranging from games to computer-aided segmentation of MRI data), on the web for downloads, or even on small PDAs with 3D scanning abilities. The large number of immediate applications demonstrates the significance of this research:- Compression of 3D objects for optimal storage and transmission;- Modeling of 3D objects, including texturing, editing, smoothing;- Haptic rendering and sculpting of virtual objects;- Realtime virtual surgery training and planning.The educational aspect of the project includes initiatives designed to incorporate the project advancements in the graduate and undergraduate curriculum. The long-term impact of this work will likely be seen in fields that have significant geometric and computational components, such as biology, medicine, and geology.

0133983desbrun，南加州的Mathieuu，该项目的主要研究目标是开发用于计算机图形中不规则采样的新数学和计算工具。数字几何形状正在迅速成为一种新型无处不在的介质，并补充了先前的电子数据类型，以获得声音，图像和电影。但是，几何形状需要处理生活在弯曲的歧管上的不规则，不均匀的采样，这是一个完全不同的问题，需要新颖的基本工具。因此，这项工作旨在更好地理解和处理不规则采样。在理论结果的基础上，我们将开发用于快速和预测性建模和/或模拟的新实用算法。我们将建立一个统一的离散/差分几何形状基础，定义连续案例的模拟离散。本项目将在计算差异几何形状的新生领域提供理论基础，以及可靠的可靠工具，这些工具将推进计算机图形领域。这些基础和计算工具将在我们的日常生活中促进和加速3D模型的扩展，无论是在软件产品中（从游戏到计算机辅助的MRI数据范围），在网上下载，甚至在具有3D扫描能力的小型PDA上。大量的直接应用显示了这项研究的重要性： - 3D对象的最佳存储和传输压缩； - 3D对象的建模，包括纹理，编辑，平滑； - 虚拟对象的触觉渲染和雕刻； - 实时虚拟手术培训和计划。这项工作的长期影响可能会在具有重要的几何和计算成分（例如生物学，医学和地质学）的领域中看到。