Dimension elevation for Chebyshevian splines
The author deals with the dimension elevation problem for Chebyshevian splines which consists in increasing the knot multiplicity -- a Chebyshevian version of the classical degree elevation process for a polynomial spline. The increasing of the degree for a polynomial spline is motivated by gaining more flexibility possibilities for parametric curves by adding \(q+1\) degrees of freedom, \(q\) being the number of joints. The problem of how to obtain the new poles from the initial ones has been solved. In case of Chebyshevian splines, the author describes the original spline space based on a given extended Chebyshevian space as embedded in a larger one (dimension of the new extended Chebyshevian space is increased by one). Starting from this point, the author proposes some methods to compute new poles of any spline in the original spline space in terms of its initial poles.
scientific article; zbMATH DE number 5842759