Shape Analysis of Generalized Cubic Curves. (August 2020)

• Record Type: Journal Article
• Authors: Gabrielides, Nikolaos C.; Sapidis, Nickolas S.
• Is Part Of: Computer aided design. Volume 125(2020)
• Publication Date: 2020-08
• Subjects: Generalized cubic curve -- Shape analysis -- Monotonicity -- Convexity -- Torsion -- Inflection; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2020.102849
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: "Generalized cubic curves" were introduced in Costantini and Manni (2006) as a special case of the more general results in Goodman and Mazure (2001) and Costantini, Lyche and Manni (2005). In this work, the shape of these curves is analyzed in R n, n = 1, 2, 3, proving that well-known theorems, which hold for cubic polynomials, hold also for this class of curves. Graphical abstract: Highlights: Generalized cubic curves representation with totally positive bases. Construction and properties of generalized cubic curves. Shape analysis of spatial and planar generalized cubic curves and generalized cubic functions. Generalized cubic curves via Pruess spline representation.