  A piecewise Chebyshevian spline space is good for design when it possesses a
B-spline basis and this property is preserved under knot insertion. The
interest in such kind of spaces is justified by the fact that, similarly as for
polynomial splines, the related parametric curves exhibit the desired
properties of convex hull inclusion, variation diminution and intuitive
relation between the curve shape and the location of the control points. For a
good-for-design space, in this paper 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. This result allows us to provide effective procedures
that generalize the classical knot insertion and degree raising algorithms for
polynomial splines. We further discuss how the approach can straightforwardly
be generalized to deal with geometrically continuous piecewise Chebyshevian
splines as well as with splines having section spaces of different dimensions.
From a numerical point of view, we show that the proposed evaluation method is
easier to implement and has higher accuracy than other existing algorithms.
