Computation and modeling in piecewise Chebyshevian spline spaces

Carolina Vittoria Beccari, Giulio Casciola, Lucia Romani

Published 2016-11-07Version 1

A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. For such spaces, we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. To illustrate the proposed computational approach, we provide several examples of interest in various applications, ranging from Geometric Modeling to Isogeometric Analysis.