  A piecewise Chebyshevian spline space is a space of spline functions having
pieces in different Extended Chebyshev spaces and where the continuity
conditions between adjacent spline segments are expressed by means of
connection matrices. Any such space is suitable for design purposes when it
possesses an optimal basis (i.e. a totally positive basis of minimally
supported splines) and when this feature is preserved under knot insertion.
Therefore, when any piecewise Chebyshevian spline space where all knots have
zero multiplicity enjoys the aforementioned properties, then so does any spline
space with knots of arbitrary multiplicity obtained from it. In this paper, we
provide a practical criterion and an effective numerical procedure to determine
whether or not a given piecewise Chebyshevian spline space with knots of zero
multiplicity is suitable for design. Moreover, whenever it exists, we also show
how to construct the optimal basis of the space.
