A sharp degree bound on G2-refinable multi-sided surfaces. (August 2020)

• Record Type: Journal Article
• Authors: Karčiauskas, Kȩstutis; Peters, Jörg
• Is Part Of: Computer aided design. Volume 125(2020)
• Publication Date: 2020-08
• Subjects: flexibility-increasing refinement -- Generalized spline -- Multi-sided -- Lower bound -- Free-form surface -- Good shape; 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.2020.102867
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Refinement of a space of splines should yield additional degrees of freedom for modeling and engineering analysis, both along boundaries and in the interior. Yet such additional flexibility fails to materialize for multi-sided G 2 surface constructions when the polynomial degree is too low. This paper establishes a tight lower bound on the polynomial degree of flexibility-increasing refinable multi-sided G 2 surface constructions within a C 2 spline complex — by ruling out bi-5 constructions and by exhibiting a multi-sided bi-6 construction that yields good highlight line and curvature distributions. The bi-6 construction consists of one 2 × 2 macro-patch for each of the n sectors that join to form the multi-sided surface. Graphical abstract: Highlights: Refinement should yield additional freedom for modeling and engineering analysis. Not so for bi-5 multi-sided G2 constructions compatible with C2 cubic splines: for bi-5 with C 2 sectors some G -edges remain a single polynomial under refinement. A bi-6 construction yields good shape and refinement increases flexibility everywhere. This characterizes flexibility-increasing refinable multi-sided G 2 constructions.