2018/05/11 by Allaoui, Mohamed, Goudjo, Aurélien
#Computational Geometry (cs.CG) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1805.04433
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines (α\mathbf Bik )i=0k 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\longrightarrow ∞. 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.