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A package for exact kinetic data structures and sweepline algorithms

机译:精确动力学数据结构和扫掠线算法的软件包

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摘要

In this paper we present a package for implementing exact kinetic data structures built on objects which move along polynomial trajectories. We discuss how the package design was influenced by various considerations, including extensibility, support for multiple kinetic data structures, access to existing data structures and algorithms in CGAL, as well as debugging. Due to the similarity between the operations involved, the software can also be used to compute arrangements of polynomial objects using a sweepline approach. The package consists of three main parts, the kinetic data structure framework support code, an algebraic kernel which implements the set of algebraic operations required for kinetic data structure processing, and kinetic data structures for Delaunay triangulations in one and two dimensions, and Delaunay and regular triangulations in three dimensions. The models provided for the algebraic kernel support both exact operations and inexact approximations with heuristics to improve numerical stability.
机译:在本文中,我们提供了一个程序包,用于实现基于沿多项式轨迹移动的对象的精确动力学数据结构。我们讨论了包装设计如何受到各种考虑因素的影响,包括可扩展性,对多种动力学数据结构的支持,对CGAL中现有数据结构和算法的访问以及调试。由于所涉及操作之间的相似性,该软件还可以用于使用扫掠线方法来计算多项式对象的排列。该软件包包括三个主要部分:动力学数据结构框架支持代码,实现动力学数据结构处理所需的一组代数运算的代数内核,以及一维和二维Delaunay三角剖分以及Delaunay和常规的动力学数据结构。三个维度的三角剖分。为代数核提供的模型支持精确运算和启发式算法的不精确近似,以提高数值稳定性。

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