Polynomial spline surfaces with rational linear transitions

•We explore a class of polynomial tensor-product spline surfaces on 3-6 polyhedra.•A 3-6 polyhedron has quadrilateral facets with vertices of valence either 3 or 6.•This restriction allows exclusively rational linear transition maps between splines.•Bi-cubic tensor-product splines are joined either C1 or G1.•The simple transition supports a hierarchy of splines.

We explore a class of polynomial tensor-product spline surfaces on 3-6 polyhedra, whose vertices have valence n=3 or n=6. This restriction makes it possible to exclusively use rational linear transition maps between the pieces: transitions between the bi-cubic tensor-product spline pieces are either C1 or they are G1 (tangent continuous) based on one single rational linear reparameterization. The simplicity of the transition functions yields simple formulas for a hierarchy of splines on subdivided 3-6 polyhedra.

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