Starting from a general B-spline representation for C1 cubic Powell-Sabin splines on arbitrary triangulations, we focus on the construction of a B-spline representation for a particular subspace defined on three-directional triangulations with C2 super-smoothness over each of the macro-triangles. We analyze the properties of the basis and point out the relation with simplex splines. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the spline space, and derive subdivision rules under dyadic refinement. Finally, we show simple conditions ensuring global C2 smoothness on the domain.
Groselj, J., Speleers, H. (2021). Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 386 [10.1016/j.cam.2020.113245].
Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision
Speleers H.
2021-04-01
Abstract
Starting from a general B-spline representation for C1 cubic Powell-Sabin splines on arbitrary triangulations, we focus on the construction of a B-spline representation for a particular subspace defined on three-directional triangulations with C2 super-smoothness over each of the macro-triangles. We analyze the properties of the basis and point out the relation with simplex splines. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the spline space, and derive subdivision rules under dyadic refinement. Finally, we show simple conditions ensuring global C2 smoothness on the domain.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
