Characterizing the intersection pattern of two conics: a {B}ezoutian-based approach

Sylvain Petitjean 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We show how to efficiently detect the type of the intersection of two arbitrary plane conics. The characterization uses geometric predicates of bidegree $(6,6)$ in the two input conics. While we already proved similar results recently, the approach spelled out here attaches geometric meaning to the predicates and brings substantial geometric insight to the characterization problem, which was previously treated purely algebraically. A key tool in the new method is the Bezoutian.
Document type :
Conference papers
Joint international conferences : 9th Asian Symposium on Computer Mathematics (ASCM 2009) and 3rd International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2009), Dec 2009, Fukuoka, Japan. 2009
Liste complète des métadonnées

https://hal.inria.fr/inria-00431724
Contributor : Sylvain Petitjean <>
Submitted on : Friday, November 13, 2009 - 9:28:48 AM
Last modification on : Tuesday, October 25, 2016 - 5:02:48 PM

Identifiers

  • HAL Id : inria-00431724, version 1

Collections

Citation

Sylvain Petitjean. Characterizing the intersection pattern of two conics: a {B}ezoutian-based approach. Joint international conferences : 9th Asian Symposium on Computer Mathematics (ASCM 2009) and 3rd International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2009), Dec 2009, Fukuoka, Japan. 2009. 〈inria-00431724〉

Share

Metrics

Record views

312