论文标题
简单曲线的同位素排列：基于细分的精确数值方法
Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision
论文作者
论文摘要
本文介绍了第一个纯数值（即非代数）细分算法，用于简单曲线的简单排列的同位素近似。从某种意义上说，任何三个曲线都没有共同的相交，任何两条曲线在横向上相交，并且每条曲线都是非单一的，则该布置很“简单”。将曲线作为零集的分析函数$ f：\ mathbb {r}^2 \ rightArrow \ Mathbb {r}^2 $，以及$ f的有效间隔形式，\ frac {\ frac {\ partial {f}}} {\ partial {\ partial {x}}， \ frac {\ partial {f}} {\ partial {y}} $可用。我们的解决方案概括了Plantinga-Vegter（2004）和Lin-YAP（2009）的同位素曲线近似算法。 我们根据间隔方法使用经过认证的数值原始图。这种算法具有许多有利的属性：它们是实用的，易于实施的，没有实现差距，将拓扑与几何计算整合在一起，并且具有自适应和局部复杂性。 Lien等人出现了本文的一个版本。 （2014）。
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "simple" in the sense that any three curves have no common intersection, any two curves intersect transversally, and each curve is non-singular. A curve is given as the zero set of an analytic function $f:\mathbb{R}^2\rightarrow \mathbb{R}^2$, and effective interval forms of $f, \frac{\partial{f}}{\partial{x}}, \frac{\partial{f}}{\partial{y}}$ are available. Our solution generalizes the isotopic curve approximation algorithms of Plantinga-Vegter (2004) and Lin-Yap (2009). We use certified numerical primitives based on interval methods. Such algorithms have many favorable properties: they are practical, easy to implement, suffer no implementation gaps, integrate topological with geometric computation, and have adaptive as well as local complexity. A version of this paper without the appendices appeared in Lien et al. (2014).
