Curvature continuous bi-4 constructions for scaffold- and sphere-like surfaces. (September 2016)

• Record Type: Journal Article
• Authors: Karčiauskas, Kȩstutis; Peters, Jörg
• Is Part Of: Computer aided design. Volume 78(2016)
• Page Start: 48
• Page End: 59
• Publication Date: 2016-09
• Subjects: Curvature continuity -- Scaffold surface -- Multi-sided -- Bi-4 spline -- Free-form surface; 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.2016.05.005
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Scaffold surfaces bound geometric structures that have a dual characterization as a curve network and a solid. A subset of scaffold surfaces can be modeled with minimal single-valence (MSV) meshes, i.e. meshes consisting of vertices of a single irregular valence n two of which are separated by exactly one regular, 4-valent vertex. We present an algorithm for constructing piecewise bi-quartic surfaces that join with curvature continuity to form scaffold surfaces for MSV meshes, for n = 5, …, 10 . Additionally, for sphere-like meshes, we exhibit bi-quartic curvature continuous surfaces with polar parameterization. Highlights: Scaffold surfaces have a dual characterization as a curve network and a solid. A subset of scaffold surfaces is minimal single-valent (MSV). MSV vertices have a single valence n ≠ 4 and are separated by one 4-valent vertex. Curvature continuous MSV scaffold surfaces are constructed as bi-quartic surfaces. Curvature continuous sphere-like surfaces are constructed as bi-quartic polar surfaces.