Curvature continuous bi-4 constructions for scaffold- and sphere-like surfaces

•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≠4n≠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.

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 nn 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,…,10n=5,…,10. Additionally, for sphere-like meshes, we exhibit bi-quartic curvature continuous surfaces with polar parameterization.