The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Finding all systems of weight functions associated with a given extended Chebyshev space
Journal of Approximation Theory
How to build all Chebyshevian spline spaces good for geometric design?
Numerische Mathematik
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We consider geometrically continuous polynomial splines defined on a given knot-vector by lower triangular connection matrices with positive diagonals. In order to find out which connection matrices make them suitable for design, we regard them as examples of geometrically continuous piecewise Chebyshevian splines. Indeed, in this larger context we recently achieved a simple characterisation of all suitable splines for design. Applying it to our initial polynomial splines will require us to treat polynomial spaces on given closed bounded intervals as instances of Extended Chebyshev spaces, so as to determine all possible systems of generalised derivatives which can be associated with them.