@inproceedings{9385990674bb4ae89fe4be57953cd015,

title = "Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves",

abstract = "Given a real function f(X, Y), a box regionB and ε 0, we want to compute an ε-isotopic polygonal approximation to the curve C: f(X, Y) = 0 within B. We focus on subdivision algorithms because of their adaptive complexity. Plantinga & Vegter (2004) gave a numerical subdivision algorithm that is exact when the curve C is non-singular. They used a computational model that relies only on function evaluation and interval arithmetic. We generalize their algorithm to any (possibly non-simply connected) region B that does not contain singularities of C. With this generalization as subroutine, we provide a method to detect isolated algebraic singularities and their branching degree. This appears to be the first complete numerical method to treat implicit algebraic curves with isolated singularities.",

keywords = "Evaluation bound, Im, Meshing, Root bound, Singularity",

author = "Michael Burr and Choi, {Sung Woo} and Benjamin Galehouse and Yap, {Chee K.}",

year = "2008",

doi = "10.1145/1390768.1390783",

language = "English (US)",

isbn = "9781595939043",

series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",

pages = "87",

booktitle = "ISSAC'08",

note = "21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 ; Conference date: 20-07-2008 Through 23-07-2008",

}