Cubic subdivision schemes with double knots

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 C1C1 surfaces with the original Doo–Sabin weights.

► We investigate univariate and bivariate cubic subdivision schemes.
► Double knots change the behaviour of a uniform cubic scheme from primal to dual.
► We analyse new bivariate cubic schemes with double knots at extraordinary points.
► These cubic schemes produce C1C1 surfaces with the original Doo–Sabin weights.