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.

0133983 Desbrun，MathieuU南加州在这个项目的主要研究目标是开发新的数学和计算工具，在计算机图形学的不规则采样。数字几何正迅速成为一种新的无处不在的媒体，补充了以前的电子数据库的声音，图像和电影。然而，几何学需要处理不规则的，非均匀的采样生活在弯曲的流形，一个根本不同的问题，需要新颖的，基本的工具。因此，这项工作的目标是更好地了解和处理不规则抽样。基于我们的理论结果，我们将开发新的实用算法，用于快速和预测建模和/或仿真。我们将为离散/微分几何建立统一的基础，定义连续情况下的模拟离散化。该项目将提供计算微分几何新兴领域的理论基础，以及将推进计算机图形学领域的强大，可靠的工具。这些基础和计算工具将促进和加速3D模型在我们日常生活中的扩展，无论是软件产品（从游戏到计算机辅助MRI数据分割），还是网络下载，甚至是具有3D扫描功能的小型PDA。大量的即时应用证明了这项研究的重要性：-压缩3D对象以实现最佳存储和传输;-3D对象建模，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规划。该项目的教育方面包括旨在将项目进展纳入研究生和本科生课程的倡议。这项工作的长期影响可能会出现在具有重要几何和计算成分的领域，如生物学，医学和地质学。