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Published in:
2014 | OriginalPaper | Chapter
Isotopic Arrangement of Simple Curves: An Exact Numerical Approach Based on Subdivision
Authors : Jyh-Ming Lien, Vikram Sharma, Gert Vegter, Chee Yap
Published in: Mathematical Software – ICMS 2014
Publisher: Springer Berlin Heidelberg
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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.