Smooth multi-sided blending of biquadratic splines

Biquadratic (bi-2) splines are the simplest choice for converting a regular quad meshes into smooth tensor-product spline surfaces. Existing methods for blending three, five or more such bi-2 spline surfaces using surface caps consisting of pieces of low polynomial degree suffer from artifacts ranging from flatness to oscillations. The new construction, based on reparameterization of the bi-2 spline data, yields well-distributed highlight lines for a range of challenging test data. The construction uses n pieces of degree bi-4 (bi-3 when n ∈ {3, 5}) and applies both to primal (Catmull-Clark-like) and dual (Doo-Sabin-like) input layouts. (a) input (b) surface pieces (c) capped bi-2 surface (d) highlight lines1 Figure 1: Pairwise joining and capping a collection of bi-2 spline surfaces. (a) Input: one planar and four cylindric pieces. (b) The input is pairwise blended by bi-2 splines and the remaining gap is filled by a G1 cap consisting of five patches of degree bi-3. (c) output and (d) surface interrogation.