Computation and modeling in piecewise Chebyshevian spline spaces

摘要: A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property preserved under arbitrary knot insertion. The interest in spaces that are justified by the fact that, similarly as polynomial splines, related parametric curves exhibit desired properties of convex hull inclusion, variation diminution intuitive relation between curve shape location control points. For all good-for-design spaces, paper we construct set functions, called transition which allow efficient computation basis, even case nonuniform multiple knots. Moreover, show how coefficients representations associated with refined partition raised order can conveniently be expressed means functions. This result allows us to provide effective procedures generalize classical insertion degree raising algorithms splines. To illustrate benefits proposed computational approaches, several examples dealing different types design.