Geometric Tools and Applications

本研究的目标是设计、分析和实现一个 几何计算工具的集合。 选择这些工具， 解决应用领域中现有的计算问题，包括数据 压缩，分子生物学，地理信息系统， 计算流体动力学 特别考虑了以下领域。 (1)最近邻算法的实用算法和数据结构 在高维度中的邻居搜索，以及 应用程序 数据压缩的问题。 （二） 算法和数据结构 检测交点并模拟一组 在二维和三维空间中移动物体。 (3)建设和 维持三角测量， 规定的形状要求和 地理信息系统和网格生成的应用 在计算流体力学中。 强调的是实用性、可实施性 这些问题，无论是理论上还是经验上， 分析他们的表现。

The goal of this research is the design, analysis, and implementation of algorithms and data structures for a collection of geometric computational tools. These tools are chosen to directly address existing computational problems in application areas including data compression, molecular biology, geographic information systems, and computational fluid dynamics. In particular the following areas are considered. (1) Practical algorithms and data structures for nearest neighbor searching in high dimensions, and applications to problems in data compression. (2) Algorithms and data structures for detecting intersections and simulating the motion of a set of moving objects in two and three dimensional space. (3) Construction and maintenance of triangulations with specified shape requirements and applications to geographic information systems and mesh generation in computational fluid dynamics. Emphasis is on practical, implementable to these problems, and both theoretical and empirical analyses of their performance.