Fairing geometric modeling based on 4-point interpolatory subdivision scheme. (Q1427236)

A 4-point interpolatory subdivision scheme for curve design was proposed by \textit{N.Dyn, D. Levin} and \textit{J. A. Gregory} [Comput. Aided Geom. Design 4, 257--268 (1987; Zbl 0638.65009)], see also \textit{Z. Cai} [Comput. Aided Geom. Design, 12, 459--468 (1995; Zbl 0875.68846)]. The authors analyze here the local support properties of 4-point interpolatory subdivision scheme and \(G^1\)-continuity conditions between surfaces and between curves. An efficient method to generate natural boundary points and a surface modeling method with the entire fairing property by combining energy optimization with subdivision scheme are also given.