B-splines with arbitrary connection matrices

We consider a space of Chebyshev splines whose left and right derivatives satisfy linear constraints that are given by arbitrary non-singular connection matrices. We show that for almost all knot sequences such spline spaces have basis functions whose support is equal to the support of the ordinary B-splines with the same knots. Consequently, there are knot insertion and evaluation algorithms analogous to de Boor’s algorithm for ordinary splines.