Triangulations: linking geometry and topology with combinatorics

三角测量：用组合学将几何和拓扑联系起来

• 批准号: DP220102588
• 负责人: Dr Jonathan Spreer
• 金额: $ 30.94万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220102588
• 关键词: Triangulations; linking; geometry; topology; combinatorics

Triangulations are the method of choice to represent geometric objects given by a finite sample of points. Prominent examples include the pictures produced by the finite element method, polytopes in optimisation, or surfaces in computer graphics. Knowledge about the triangulations of an object and how they relate to each other is essential for these applications. Seemingly canonical and straightforward methods perform well - or not at all, depending on intricate and highly involved mathematical properties. In this project we combine geometric and topological viewpoints to tackle high-profile questions about triangulations. This will unlock the full potential of combinatorial methods and practical algorithms in applications.

三角剖分是表示由有限样本点给出的几何对象的一种选择方法。突出的例子包括有限元方法产生的图片，优化中的多面体，或计算机图形学中的曲面。 关于物体的三角剖分以及它们如何相互关联的知识对于这些应用来说是必不可少的。看似规范和直截了当的方法表现良好--或者根本没有，这取决于复杂和高度复杂的数学性质。 在这个项目中，我们结合几何和拓扑观点来处理有关三角剖分的引人注目的问题。这将充分释放组合方法和实用算法在应用中的潜力。