We consider a new B-spline representation for the space of cubic splines defined on a triangulation with a Powell-Sabin refinement. The construction is based on lifting particular triangles and line segments from the domain. We prove that the B-splines form a locally supported stable basis and a convex partition of unity. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the cubic spline space and show how to compute the Bernstein-Bezier form of such a spline in a stable way. The B-spline representation induces a natural control structure that is useful for geometric modelling. Finally, we explore how classical quadratic Powell-Sabin splines and cubic Clough-Tocher splines can be expressed in the new B-spline representation.
Groselj, J., Speleers, H. (2017). Construction and analysis of cubic Powell–Sabin B-splines. COMPUTER AIDED GEOMETRIC DESIGN, 57, 1-22 [10.1016/j.cagd.2017.05.003].
Construction and analysis of cubic Powell–Sabin B-splines
Speleers H.
2017-10-01
Abstract
We consider a new B-spline representation for the space of cubic splines defined on a triangulation with a Powell-Sabin refinement. The construction is based on lifting particular triangles and line segments from the domain. We prove that the B-splines form a locally supported stable basis and a convex partition of unity. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the cubic spline space and show how to compute the Bernstein-Bezier form of such a spline in a stable way. The B-spline representation induces a natural control structure that is useful for geometric modelling. Finally, we explore how classical quadratic Powell-Sabin splines and cubic Clough-Tocher splines can be expressed in the new B-spline representation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
