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01-12-2016

A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form

Authors: Çetin Dişibüyük, Ron Goldman

Published in: Calcolo | Issue 4/2016

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Abstract

We develop a general, unified theory of splines for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special Müntz spaces of splines by invoking a novel variant of the homogeneous polar form where we alter the diagonal property. Using this polar form, we derive de Boor type recursive algorithms for evaluation and differentiation. We also show that standard knot insertion procedures such as Boehm’s algorithm and the Oslo algorithm readily extend to these general spline spaces. In addition, for these spaces we construct compactly supported B-spline basis functions with simple two term recurrences for evaluation and differentiation, and we show that these B-spline basis functions form a partition of unity, have curvilinear precision, and satisfy a dual functional property and a Marsden identity.

previous article A Jacobi–Davidson type method for computing real eigenvalues of the quadratic eigenvalue problem

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Title: A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form
Authors: Çetin Dişibüyük
Ron Goldman
Publication date: 01-12-2016
Publisher: Springer Milan
Published in: Calcolo / Issue 4/2016
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-015-0172-x

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