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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1007/bf00277143

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1572-9265

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Design with Lsplines

Authors: Martine Brilleaud MarieLaurence Mazure
Publish Date: 2013/03/17
Volume: 65, Issue: 1, Pages: 91-124
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Abstract

We recently obtained a criterion to decide whether a given space of parametrically continuous piecewise Chebyshevian splines ie splines with pieces taken from different Extended Chebyshev spaces could be used for geometric design One important field of application is the class of Lsplines that is splines with pieces taken from the null space of some fixed real linear differential operator generally investigated under the strong requirement that the null space should be an Extended Chebyshev space on the support of each possible Bspline In the present work we want to show the practical interest of the criterion in question for designing with Lsplines With this in view we apply it to a specific class of linear differential operators with real constant coefficients and odd/even characteristic polynomials We will thus establish necessary and sufficient conditions for the associated splines to be suitable for design Because our criterion was achieved via a blossoming approach shape preservation will be inherent in the obtained conditions One specific advantage of the class of operators we consider is that hyperbolic and trigonometric functions can be mixed within the null space on which the splines are based We show that this produces interesting shape effects

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