Name
Title | ||
|---|---|---|
Isotopic Arrangement of Simple Curves: An Exact Numerical Approach Based on Subdivision. |
Abstract | ||
|---|---|---|
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). |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/978-3-662-44199-2_43 | ICMS |
Field | DocType | Citations |
Discrete mathematics,Family of curves,Algebraic number,Analytic function,Partial derivative,Subdivision,Zero set,Interval arithmetic,Mathematics,Computation | Conference | 0 |
PageRank | References | Authors |
0.34 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jyh-ming Lien | 1 | 651 | 50.28 |
| Vikram Sharma | 2 | 229 | 20.35 |
| Gert Vegter | 3 | 456 | 36.31 |
| Chee Yap | 4 | 0 | 1.01 |