### Abstract

We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06 |

Pages | 217-226 |

Number of pages | 10 |

Volume | 2006 |

State | Published - 2006 |

Event | 22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States Duration: Jun 5 2006 → Jun 7 2006 |

### Other

Other | 22nd Annual Symposium on Computational Geometry 2006, SCG'06 |
---|---|

Country | United States |

City | Sedona, AZ |

Period | 6/5/06 → 6/7/06 |

### Fingerprint

### Keywords

- Bezier curves
- Computational geometry
- Curve intersection
- Exact geometric computation
- Robust numerical algorithms
- Subdivision method

### ASJC Scopus subject areas

- Software
- Geometry and Topology
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06*(Vol. 2006, pp. 217-226)

**Complete subdivision algorithms, I : Intersection of Bezier curves.** / Yap, Chee K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06.*vol. 2006, pp. 217-226, 22nd Annual Symposium on Computational Geometry 2006, SCG'06, Sedona, AZ, United States, 6/5/06.

}

TY - GEN

T1 - Complete subdivision algorithms, I

T2 - Intersection of Bezier curves

AU - Yap, Chee K.

PY - 2006

Y1 - 2006

N2 - We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

AB - We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

KW - Bezier curves

KW - Computational geometry

KW - Curve intersection

KW - Exact geometric computation

KW - Robust numerical algorithms

KW - Subdivision method

UR - http://www.scopus.com/inward/record.url?scp=33748060965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748060965&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33748060965

SN - 1595933409

SN - 9781595933409

VL - 2006

SP - 217

EP - 226

BT - Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06

ER -