Six-Point Subdivision Schemes with Cubic Precision

This paper presents 6-point subdivision schemes with cubic precision. We first derive a relation between the 4-point interpolatory subdivision and the quintic B-spline refinement. By using the relation, we further propose the counterparts of cubic and quintic B-spline refinements based on 6-point interpolatory subdivision schemes. It is proved that the new family of 6-point combined subdivision schemes has higher smoothness and better polynomial reproduction property than the B-spline counterparts. It is also showed that, both having cubic precision, the well-known Hormann-Sabin’s family increase the degree of polynomial generation and smoothness in exchange of the increase of the support width, while the new family can keep the support width unchanged and maintain higher degree of polynomial generation and smoothness.