Smooth Bi-3 spline surfaces with fewest knots
Converting a quadrilateral input mesh into a C1 C 1 surface with one bi-3 tensor-product splinepatch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G1 G 1 construction.
spline surfaces construction bicubic geometry continuity catmullrom splines