Cubic subdivision schemes with double knots

摘要

We investigate univariate and bivariate binary subdivision schemes based on cubic B-splines with double knots. It turns out that double knots change the behaviour of a uniform cubic scheme from primal to dual. We focus on the analysis of new bivariate cubic schemes with double knots at extraordinary points. These cubic schemes produce C~1 surfaces with the original Doo-Sabin weights.