Point-augmented biquadratic C1 subdivision surfaces

Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented and the polar bi-2 subdivision are complemented by a new primal bi-2 subdivision scheme. All surfaces are C and can be combined.