Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space. (March 2016)

• Record Type: Journal Article
• Authors: Jia, Xiaohong; Wang, Wenping; Choi, Yi-King; Mourrain, Bernard; Tu, Changhe
• Is Part Of: Journal of symbolic computation. Volume 73(2016)
• Page Start: 221
• Page End: 243
• Publication Date: 2016-03
• Subjects: Intersection curve -- Moving quadrics -- Signature sequence -- Index sequence -- Jordan form; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.05.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We propose a symbolic algorithm for detecting the variations in the topological and algebraic properties of the intersection curve of two quadratic surfaces (QSIC) that are moving or deforming in PR 3 (real projective 3-space). The core of our algorithm computes all the critical instants when the QSIC changes type using resultants and Jordan forms. These critical instants partition the time axis into intervals within which the QSIC is invariant. The QSIC at the computed critical instants and within the time intervals can both be exactly determined using symbolic technique. Examples are provided to illustrate our algorithm.