Similarity detection of rational space curves. (March 2018)

• Record Type: Journal Article
• Authors: Alcázar, Juan Gerardo; Hermoso, Carlos; Muntingh, Georg
• Is Part Of: Journal of symbolic computation. Volume 85(2018)
• Page Start: 4
• Page End: 24
• Publication Date: 2018-03
• Subjects: Similarity detection -- Space algebraic curves -- Rational curves -- Recognition; 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.2017.07.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra setting. Helical curves, where curvature and torsion are proportional, need to be distinguished as a special case. The algorithm is easy to implement, as it involves only standard computer algebra techniques, such as greatest common divisors and resultants, and Gröbner basis for the special case of helical curves. Details on the implementation and experimentation carried out using the computer algebra system Maple 18 are provided.