EAGER: Foundations of robust surface parametrization and resampling

EAGER：稳健表面参数化和重采样的基础

• 批准号: 1247240
• 负责人: Denis Zorin
• 金额: $ 10万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1247240&HistoricalAwards=false
• 关键词: EAGER; Foundations; robust; surface; parametrization

Processing 3D shape information (geometry) efficiently is crucial for many domains: for example, computer-aided design, scientific computing, urban planning and cultural heritage preservation. The amount of geometric data generated and stored is rapidly increasing. The most common way to represent geometric data is with unstructured meshes. Unstructured meshes enjoy many attractive features, but inherently limit the efficiency and accuracy of many algorithms for geometry processing and physical simulation, as well as compactness of representations, compared to image processing algorithms. Mesh parametrization is the fundamental geometric processing technique used both in the context of converting surfaces to image-like representations, and for mapping data to surfaces. While significant progress has been made in the development of high-quality global parametrization algorithms a number of important questions are unresolved, limiting the potentially broad applicability of these techniques.This exploratory project is developing mathematical and algorithmic bases for controlling global parametrization quality as well as limiting the possible amount of local distortion. The techniques being developed, based on the theory of quasiconformal maps and efficient greedy optimization algorithms, will serve as a foundation for future work on robust, high-quality and scalable global parametrization.

处理3D形状信息（几何）对许多领域至关重要：例如，计算机辅助设计，科学计算，城市规划和文化遗产保存。生成和存储的几何数据量正在迅速增加。表示几何数据的最常见方法是使用非结构化网格。非结构化的网格具有许多吸引人的功能，但与图像处理算法相比，许多算法对几何处理和物理模拟以及表示的紧凑性的效率和准确性。网格参数化是在将表面转换为图像状表示的背景下以及将数据映射到表面的基本几何处理技术。尽管在高质量的全球参数化算法的发展方面取得了重大进展，但许多重要问题尚未解决，这限制了这些技术的潜在广泛适用性。该探索性项目正在开发数学和算法基础，以控制全球参数化质量，并限制了局部失真的量。基于准文化图和有效的贪婪优化算法的理论开发的技术将成为未来在鲁棒，高质量和可扩展全局参数化的工作的基础。