Syzygies for translational surfaces. (November 2018)

• Record Type: Journal Article
• Authors: Wang, Haohao; Goldman, Ron
• Is Part Of: Journal of symbolic computation. Volume 89(2018)
• Page Start: 73
• Page End: 93
• Publication Date: 2018-11
• Subjects: Translational surface -- Syzygy -- μ-basis -- Implicit equation; 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.2017.11.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A translational surface is a rational tensor product surface generated from two rational space curves by translating one curve along the other curve. Translational surfaces are invariant under rigid motions: translating and rotating the two generating curves translates and rotates the translational surface by the same amount. We construct three special syzygies for a translational surface from a μ -basis of one of the generating space curves, and we show how to compute the implicit equation of a translational surface from these three special syzygies. Examples are provided to illustrate our theorems and flesh out our algorithms.