Abstract: 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.