Triangulations in the Plane and in Space

空间分解在几乎所有与几何空间有关的计算领域都起着重要作用。例如，有限元近似方法基于“网格”，网格是将域分解成更小更简单的部分的细胞复合体。根据不同的应用程序，不同的质量标准控制着创建分解的方式。本研究将研究分解，重点是三角剖分（简单细胞复合体），以及满足质量标准的可能性和不可能性，如简单数量的约束、角度的上下界限和其他形状描述符。

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.