We construct a suitable B-spline representation for a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r-1. They are defined on a triangulation with Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction involves the determination of triangles that must contain a specific set of points. We further consider a number of CAGD applications. We show how to define control points and control polynomials (of degree 2r-1), and we provide an efficient and stable computation of the Bernstein-Bézier form of such splines.

Speleers, H. (2013). Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations. CONSTRUCTIVE APPROXIMATION, 37(1), 41-72 [10.1007/s00365-011-9151-x].

Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations

Speleers H.
2013-01-01

Abstract

We construct a suitable B-spline representation for a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r-1. They are defined on a triangulation with Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction involves the determination of triangles that must contain a specific set of points. We further consider a number of CAGD applications. We show how to define control points and control polynomials (of degree 2r-1), and we provide an efficient and stable computation of the Bernstein-Bézier form of such splines.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - Analisi Numerica
English
Con Impact Factor ISI
Bernstein-Bézier form; Control points; Control polynomials; Macro-elements; Normalized B-splines; Smooth Powell-Sabin splines
Speleers, H. (2013). Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations. CONSTRUCTIVE APPROXIMATION, 37(1), 41-72 [10.1007/s00365-011-9151-x].
Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/122295
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