Degeneracy in Geometric Computation

今天，几何数据和几何结构几乎被用于所有 科学的分支，如果只是在结果和数据的显示。 在 在大多数应用程序中，几何数据本质上是 在这个意义上说，它是非常不同的数据获得的， 一种随意的方式。 不幸的是，简并配置通常会带来 关于计算机程序的严重鲁棒性和正确性问题 来操纵数据。 造成这种弱点的两个主要原因是， 目前的软件是奇异结构的空间退化 以及如果我们试图检测和 对简并构型进行分类。 本研究是一个系统的研究 在几何数据的退化，跨越其调查， 组合结构，确定的计算复杂性 退化，以及-最重要的-系统的方法来科普 退化数据

Today, geometric data and geometric structures are used in almost all branches of science, if only in the display of results and data. In the majority of the applications, the geometric data is inherently degenerate in the sense that it is very different from data obtained in a random fashion. Unfortunately, degenerate configurations often bring about serious robustness and correctness problems for computer programs that manipulate the data. The two main reasons for this weakness of current software are the bizarre structure of the space of degeneracies and the accuracy problems that arise if we attempt to detect and classify degenrate configurations. This research is a systematic study of degeneracy in geometric data that spans the investigation of its combinatorial structure, the computational complexity of determining degeneracy, and - most importantly - systematic ways to cope with degenerate data.