Curvature continuous bi-4 constructions for scaffold- and sphere-like surfaces. (September 2016) - Karčiauskas, Kȩstutis; Peters, Jörg
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.