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.

三角剖分是代表有限点样本给出的几何对象的首选方法。突出的示例包括有限元方法产生的图片，优化的多型或计算机图形中的表面。 关于对象的三角剖分及其之间如何相互联系的知识对于这些应用至关重要。看似规范和直截了当的方法表现良好，或者根本不正确，具体取决于复杂且高度涉及的数学特性。 在这个项目中，我们结合了几何和拓扑观点，以解决有关三角剖分的备受瞩目的问题。这将释放应用程序中组合方法和实际算法的全部潜力。