Geometric Skeletons for Topologically Evolving Domains

拓扑演化域的几何骨架

• 批准号: 0927105
• 负责人: Horea Ilies
• 金额: $ 31.99万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0927105&HistoricalAwards=false
• 关键词: Geometric; Skeletons; Topologically; Evolving; Domains

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The objective of this award is to develop a fundamentally new approach to construct families of geometric skeletons for 2- and 3-dimensional geometric shapes that can be either rigid or undergoing drastic topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations, can generate novel, more stable skeletons, and intrinsically supports localized and parallel skeleton computations for domains with rigid or evolving boundaries. The goals of the research program are to develop new theoretical foundations for geometric skeletons as geometric and topological descriptors of shape, as well as a computational framework capable of efficiently computing local changes to the skeleton induced by local changes to the boundary of the domain.If successful, this research will lead to powerful generic algorithms for computing families of geometric skeletons for complex spatial environments. This, in turn, could transform all geometrically intensive areas of science, including almost all engineering disciplines, by providing access to new and potent descriptors of shape. Applications that would benefit from the new approach include geometric modeling of engineering artifacts, fully automated mesh generation for engineering analysis, feature recognition and defeaturing of engineering models, and real-time trajectory planning of autonomous vehicles and machine tools with adaptive geometric constraints. Furthermore, this new framework will stimulate critical new avenues of interdisciplinary research involving engineering, biology, computer science, and human-computer interaction. This program will perform targeted outreach to K-12 students, teachers and local school district serving groups that have traditionally been underrepresented in the engineering disciplines via several University of Connecticut outreach programs. The integration of geometric reasoning and algorithmic design into the engineering curriculum will help develop a new generation of engineers that will be able to exploit the capabilities of modern geometric algorithms in conjunction with traditional mechanical engineering knowledge.

该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。该奖项的目的是开发一种从根本上进行新的方法，用于建造2和3维几何形状的几何骨骼家庭，可以是刚性或经历急剧拓扑变形的。我们的方法依赖于用R功能来计算形状的建设性表示，这些函数以实现的半空间为逻辑操作，可以生成新颖，更稳定的骨架，并且本质上支持具有刚性或界限的域的局部和并行骨骼计算。研究计划的目标是为形状的几何和拓扑描述制定新的理论基础，以及一个计算框架，能够有效地计算出局部变化对域的局部变化引起的骨架的局部变化。反过来，这可以通过提供新的和有效的形状描述符来改变所有几何密集的科学领域，包括几乎所有工程学科。将从新方法中受益的应用包括工程工具的几何建模，用于工程分析的全自动网格生成，特征识别和工程模型的失败以及具有自动驾驶汽车的实时轨迹计划以及具有自适应几何学约束的机床。此外，这个新框架将刺激涉及工程，生物学，计算机科学和人类计算机互动的跨学科研究的关键新途径。该计划将对K-12学生，老师和当地学区服务团体进行有针对性的宣传，这些小组传统上通过康涅狄格大学的几个外展计划在工程学科中的人数不足。将几何推理和算法设计集成到工程课程中将有助于开发新一代的工程师，这些工程师将能够与传统的机械工程知识结合使用现代几何算法的能力。