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

Sylvain Petitjean (1)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility

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.

Domaines: Géométrie algorithmique [cs.CG]

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. ⟨inria-00431724⟩