Recognizing implicitly given rational canal surfaces. (May 2016)

• Record Type: Journal Article
• Authors: Vršek, Jan; Lávička, Miroslav
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 367
• Page End: 377
• Publication Date: 2016-05
• Subjects: Canal surfaces -- Algebraic surfaces -- Surface recognition -- Rational surfaces -- Medial axis transform; 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.2015.08.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in geometric modelling, Computer-Aided Design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). It is known that if the squared medial axis transform is a rational curve then so is also the corresponding surface. However, starting from a polynomial it is not known how to decide if the corresponding algebraic surface is a rational canal surface or not. Our goal is to formulate a simple and efficient algorithm whose input is a polynomial with the coefficients from some subfield of R and the output is the answer whether the surface is a rational canal surface. In the affirmative case we also compute a rational parameterization of the squared medial axis transform which can be then used for finding a rational parameterization of the corresponding implicitly given canal surface.