Projective and affine symmetries and equivalences of rational curves in arbitrary dimension. (July 2018)

• Record Type: Journal Article
• Authors: Hauer, Michael; Jüttler, Bert
• Is Part Of: Journal of symbolic computation. Volume 87(2018)
• Page Start: 68
• Page End: 86
• Publication Date: 2018-07
• Subjects: Projective equivalences -- Affine equivalence -- Symmetry detection -- Rational curve -- Homogeneous polynomials; 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.2017.05.009
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a new algorithm to decide whether two rational parametric curves are related by a projective transformation and detect all such projective equivalences. Given two rational curves, we derive a system of polynomial equations whose solutions define linear rational transformations of the parameter domain, such that each transformation corresponds to a projective equivalence between the two curves. The corresponding projective mapping is then found by solving a small linear system of equations. Furthermore we investigate the special cases of detecting affine equivalences and symmetries as well as polynomial input curves. The performance of the method is demonstrated by several numerical examples.