Triangulations in the Plane and in Space

平面和空间中的三角测量

• 批准号: 8921421
• 负责人: Herbert Edelsbrunner
• 金额: $ 15.7万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8921421&HistoricalAwards=false
• 关键词: Triangulations; Plane; Space

Abstract Decompostitions of space play a major role in almost all areas of computing that have to do with geometric spaces. For example, finite element approximation methods are based on "meshes" that are cell complexes decomposing domains into smaller and simpler parts. Depending on the application different quality criteria govern the way the decompostition is created. This research will study decompositions with emphasis of triangulations (simplicial cell complexes) and the possibilities and impossibilities to meet quality criteria such as constrained numbers of simplices and lower and upper bounds on angles and other shape descriptors.

空间分解在几乎所有与几何空间有关的计算领域中都扮演着重要的角色。例如，有限元近似方法是基于“网格”的，即将区域分解成更小和更简单的部分的单元复合体。根据应用程序的不同，不同的质量标准控制分解的创建方式。这项研究将重点研究三角剖分(单纯细胞复合体)的分解，以及满足质量标准的可能性和不可能性，例如受限的简单数目和角度和其他形状描述符的上下界。