We consider a cubic spline space defined over a triangulation with Powell-Sabin refinement. The space has some local super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline space. The basis functions have a local support, they are nonnegative, and they form a partition of unity. We also show how to compute the Bezier control net of such a spline in a stable way.
Speleers, H. (2015). A new B-spline representation for cubic splines over Powell-Sabin triangulations. COMPUTER AIDED GEOMETRIC DESIGN, 37, 42-56 [10.1016/j.cagd.2015.05.002].
A new B-spline representation for cubic splines over Powell-Sabin triangulations
Speleers H.
2015-08-01
Abstract
We consider a cubic spline space defined over a triangulation with Powell-Sabin refinement. The space has some local super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline space. The basis functions have a local support, they are nonnegative, and they form a partition of unity. We also show how to compute the Bezier control net of such a spline in a stable way.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
