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\(C^2\) quadratic trigonometric polynomial curves with local bias. (English) Zbl 1075.65024

In seiner Arbeit “Piecewise quadratic trigonometric polynomial curves” [Math. Comput. 72, No. 243, 1369–1377 (2003; Zbl 1072.65019)] entwickelte der Autor \(C^2\)-stetige quadratische trigonometrische polynomiale Kurven. Die vorliegende Arbeit bringt durch Einführung lokaler Formparameter in den Basisfunktionen eine Erweiterung dieses Kurventyps. Damit ergeben sich zusätzliche Möglichkeiten bei der Kurvenmodellierung. Die Basisfunktionen selbst sind quadratische trigonometrische Polynome. In einem Knoten der Multiplizität \(k\) \((k= 1,2,3)\) erweisen sich die Basisfunktionen sowie die trigonometrischen polynomialen Kurven als \(C^2\)-stetig für \(k= 1\), stetig für \(k= 2\) und unstetig für \(k= 3\). Weitere Kurveneigenschaften werden hergeleitet und durch Figuren illustriert. Als besonders wertvolle Eigenschaft zeigt sich, dass die lokalen Formparameter lediglich zwei benachbarte Kurvensegmente beeinflussen. Abschließend werden die quadratischen trigonometrischen Bézierkurven als spezielle quadratische trigonometrische polynomiale Kurven dargestellt.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D07 Numerical computation using splines

Citations:

Zbl 1072.65019
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References:

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