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, Mathieu，南加州大学 该项目的主要研究目标是为计算机图形学中的不规则采样开发新的数学和计算工具。数字几何正在迅速成为一种新的无处不在的媒介，补充了以前的声音、图像和电影的电子数据类型。然而，几何学需要处理弯曲流形上的不规则、不均匀采样，这是一个完全不同的问题，需要新颖的基本工具。因此，这项工作的目标是更好地理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，用于快速预测建模和/或模拟。我们将为离散/微分几何建立统一的基础，定义连续情况的模拟离散。该项目将为计算微分几何这一新兴领域提供理论基础，并为计算机图形学领域的发展提供强大、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，无论是在软件产品中（从游戏到 MRI 数据的计算机辅助分割），在网络上下载，甚至在小型 PDA 上3D扫描能力。大量的直接应用证明了这项研究的重要性：- 3D 对象压缩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举措。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，例如生物学、医学和地质学。