Exact Geometric Computation

9402464 YAP几何算法出现在许多应用领域。这类算法的非稳健性是一个主要问题。由于几何算法的特点是同时存在数值和组合元素，这里的非稳健性问题似乎比纯粹的数值计算更难处理。有证据表明，目前基于机器浮点运算的实现方法在处理非健壮性方面存在根本不足。该项目建议使用精确计算来实现此类算法。这是一种全新的计算模式，包括一套丰富的计算策略。初步分析表明，对于一类重要的问题(有理有界深度问题)，精确计算是非常有效的。这项研究的两个目标是确定这种方法的实际可行性。探讨精确计算的理论基础。实际目标包括设计关键的软件包，并将其应用于重要的应用领域。这里的一个新话题是对精度敏感的算法领域，它有望刺激对使用传统复杂性参数似乎难以解决的问题进行新的算法研究。***

9402464 Yap Geometric algorithms arise in many application areas. The non- robustness of such algorithms is of major concern. As geometric algorithms are characterized by the presence of both numerical and combinatorial elements, non-robustness problems here appear more intractable than in purely numerical computation. Evidence suggests that current implementation approaches, based on machine floating-point arithmetic, are fundamentally inadequate in dealing with non-robustness. This project proposes to use exact computation for implementing such algorithms. This is a fundamentally new computing paradigm that includes a rich set of computational tactics. Initial analysis indicates that exact computation can be quite effective for an important class of problems (the rational bounded-depth problems). The two goals of the research are To establish the practical viability of this approach. To investigate the theoretical bases for exact computation. The practical goal involves the design of key software packages, and to apply this to a significant application area. A new topic here is the area of precision-sensitive algorithms, which promises to stimulate new algorithmic research on problems which seems intractable using traditional complexity parameters. ***