We present the construction of a suitable normalized B-spline representation for reduced cubic Clough-Tocher splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. Geometrically, the problem can be interpreted as the determination of a set of triangles that must contain a specific set of points. This leads to a natural definition of tangent control triangles. We also consider a stable computation of the Bezier control net of the spline surface.

Speleers, H. (2010). A normalized basis for reduced Clough-Tocher splines. COMPUTER AIDED GEOMETRIC DESIGN, 27(9), 700-712 [10.1016/j.cagd.2010.09.003].

A normalized basis for reduced Clough-Tocher splines

Speleers H.
2010-12-01

Abstract

We present the construction of a suitable normalized B-spline representation for reduced cubic Clough-Tocher splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. Geometrically, the problem can be interpreted as the determination of a set of triangles that must contain a specific set of points. This leads to a natural definition of tangent control triangles. We also consider a stable computation of the Bezier control net of the spline surface.
dic-2010
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Clough-Tocher splines; Normalized B-splines; Control points; Control triangles; Bezier control net
Speleers, H. (2010). A normalized basis for reduced Clough-Tocher splines. COMPUTER AIDED GEOMETRIC DESIGN, 27(9), 700-712 [10.1016/j.cagd.2010.09.003].
Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215120
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