JJ-splines

Both the 4-point and the uniform cubic BB-spline subdivisions double the number of vertices of a closed-loop polygon kPkP and produce sequences of vertices fjfj and bjbj respectively. We study the JJ-spline subdivision scheme JsJs, introduced by Maillot and Stam, which blends these two methods to produce vertices of the form vj=(1−s)fj+sbjvj=(1−s)fj+sbj. Iterative applications of JsJs yield a family of limit curves, the shape of which is parameterized by s. They include four-point subdivision curves (J0J0), uniform cubic BB-spline curves (J1J1), and uniform quintic BB-spline curves (J1.5J1.5). We show that the limit curve is at least C1C1 when −1.7≤s≤5.8−1.7≤s≤5.8, C2C2 when 0