Smooth multi-sided blending of biquadratic splines

• A quad mesh is converted into a smooth tensor-product spline surface.
• Multi-sided holes between bi-quadratic spline surfaces are filled by pieces of low polynomial degree.
• The resulting surfaces have well-distributed highlight lines for a range of challenging test data.
• The input spline data are reparameterized.
• The construction applies both to primal (Catmull–Clark-like) and dual (Doo–Sabin-like) input layouts.

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}n∈{3,5}) and applies both to primal (Catmull–Clark-like) and dual (Doo–Sabin-like) input layouts.

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