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

摘要

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. Crown Copyright (C) 2016 Published by Elsevier Ltd. All rights reserved.