### 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.

Original language | English (US) |
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Title of host publication | ISSAC'08 |

Subtitle of host publication | Proceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008 |

Number of pages | 1 |

DOIs | |

State | Published - 2008 |

Event | 21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 - Linz, Hagenberg, Austria Duration: Jul 20 2008 → Jul 23 2008 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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### Other

Other | 21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 |
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Country | Austria |

City | Linz, Hagenberg |

Period | 7/20/08 → 7/23/08 |

### Keywords

- Evaluation bound
- Im
- Meshing
- Root bound
- Singularity

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*ISSAC'08: Proceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008*(Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1390768.1390783