Towards and open curved kernel
Towards and open curved kernel
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DOI：
10.1145/997817.997882
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发表时间：
2004-06
期刊：
影响因子：
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通讯作者：
I. Emiris;Athanasios Kakargias;Sylvain Pion;M. Teillaud;Elias P. Tsigaridas
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文献类型：
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作者：
I. Emiris;Athanasios Kakargias;Sylvain Pion;M. Teillaud;Elias P. Tsigaridas
我们的工作是为了满足在许多应用中对曲线对象的健壮和高效操作的日益增长的需求。CGAL库的内核提供了几个功能，然而，这些功能大多局限于线性对象。这里我们主要讨论平面中圆锥弧的排列。我们的第一个贡献是设计、实现和测试了一个用于计算圆弧排列的内核。对于任意二次曲线也存在一个初步的C++实现。我们讨论了几何对象的表示和谓词。我们的实现旨在包含在CGAL库中。我们的第二个贡献是关于二次曲线情形的精确和有效的代数算法。它们处理包括退化在内的所有输入，并且它们作为SYNAPS 2.1库的一部分实现。我们的工具包括Sturm序列、结果式、笛卡尔法则和变化点。第三，我们在圆弧上的实验表明，我们的方法比现有的使用核心1.6x和LEDA 4.5的替代方法更好。
Our work goes towards answering the growing need for the robust and efficient manipulation of curved objects in numerous applications. The kernel of the CGAL library provides several functionalities which are, however, mostly restricted to linear objects. We focus here on the arrangement of conic arcs in the plane. Our first contribution is the design, implementation and testing of a kernel for computing arrangements of circular arcs.A preliminary C++ implementation exists also for arbitrary conic curves. We discuss the representation and predicates of the geometric objects. Our implementation is targeted for inclusion in the CGAL library. Our second contribution concerns exact and efficient algebraic algorithms for the case of conics. They treat all inputs, including degeneracies, and they are implemented as part of the library SYNAPS 2.1.Our tools include Sturm sequences, resultants, Descartes' rule, andisolating points. Thirdly, our experiments on circular arcs show that our methods compare favorably to existing alternatives using CORE 1.6x and LEDA 4.5.