A new class of curves of rational B-spline type
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A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines (^α B_i^k)_i=0^k which depends on an index α∈ (-∞,0)∪ (1,+∞). 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 α⟶∞. The associated B-splines curves verify the traditional properties particularly that of a convex hull and we see a certain "conjugated symmetry" related to α. The case of open knot vectors without an inner node leads to a new family of rational Bezier curves that will be separately, object of in-depth analysis.
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