A new class of curves of rational B-spline type
Mohamed Allaoui, Aur\'elien Goudjo

TL;DR
This paper introduces a novel class of rational B-spline functions based on a new rational parametrization, offering unique properties and potential for new curve designs, with a focus on their mathematical characteristics and asymptotic behavior.
Contribution
It presents a new family of rational B-splines dependent on a parameter, expanding the theoretical framework and properties of B-spline curves and functions.
Findings
The new rational B-splines satisfy positivity and partition of unity.
They form a true basis for approximating continuous functions.
Asymptotic behavior recovers classical regularity.
Abstract
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines which depends on an index . This family of functions verifies, among other things, the properties of positivity, of partition of the unit and, for a given degree k, constitutes a true basis approximation of continuous functions. We loose, however, the regularity classical optimal linked to the multiplicity of nodes, which we recover in the asymptotic case, when . The associated \mbox{B-splines} curves verify the traditional properties particularly that of a convex hull and we see a certain "conjugated symmetry" related to . The case of open knot vectors without an inner node leads to a new family of…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques
