Implicitizing rational surfaces using moving quadrics constructed from moving planes. (November 2016)

• Record Type: Journal Article
• Authors: Lai, Yisheng; Chen, Falai
• Is Part Of: Journal of symbolic computation. Volume 77(2016)
• Page Start: 127
• Page End: 161
• Publication Date: 2016-11
• Subjects: Rational surface -- Implicitization -- Moving plane -- Moving quadric; 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.2016.02.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: This paper presents a new algorithm for implicitizing tensor product surfaces of bi-degree ( m, n ) with no base points, assuming that there are no moving planes of bi-degree ( m − 1, n − 1 ) following the surface. The algorithm is based on some structural results: (1) There are exactly 2 n linearly independent moving planes of bi-degree ( m, n − 1 ) following the surface; (2) mn linearly independent moving quadrics of bi-degree ( m − 1, n − 1 ) following the surface can be constructed from the 2 n linearly independent moving planes; (3) The mn linearly independent moving quadrics form a compact determinant of order mn which exactly gives the implicit equation of the rational surface. Complexity analysis and experimental results show that the new algorithm is significantly more efficient than the previous methods.