Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations. (English) Zbl 1264.41014
Piecewise polynomial splines in two dimensions are considered with given smoothness and polynomial degree, being \(r\) and \(3r-1\), respectively. The piecewise structure is defined on a triangulation and the refinement takes place using the Powell-Sabin split. Among other results, efficient and stable methods for computing Bernstein-Bézier forms are derived, normalised Powell-Sabin B-splines are considered and practical issues are discussed.
Reviewer: Martin D. Buhmann (Gießen)
MSC:
| 41A15 | Spline approximation |
| 65D07 | Numerical computation using splines |
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
Keywords:
smooth Powell-Sabin splines; normalized B-splines; macro-elements; control points; control polynomials; Bernstein-Bézier formReferences:
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