@inproceedings{63dc25b8dfb04b888623947a57ce4cd9,

title = "Isotopic arrangement of simple curves: An exact numerical approach based on subdivision",

abstract = "We present a purely numerical (i.e., non-algebraic) subdivision algorithm for computing an 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 on the plane, along with effective interval forms of the function and its partial derivatives. 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 preliminary implementation is available in Core Library.",

keywords = "Isotopy, arrangement of curves, interval arithmetic, marching-cube, subdivision algorithms",

author = "Lien, {Jyh Ming} and Vikram Sharma and Gert Vegter and Chee Yap",

year = "2014",

doi = "10.1007/978-3-662-44199-2_43",

language = "English (US)",

isbn = "9783662441985",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "277--282",

booktitle = "Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings",

note = "4th International Congress on Mathematical Software, ICMS 2014 ; Conference date: 05-08-2014 Through 09-08-2014",

}