  We introduce here Cartesian splines or, for short, C-splines. C- splines are
piecewise polynomials which are defined on adjacent Cartesian coordinate
systems and are Cr continuous throughout. The Cr continuity is enforced by
constraining the coefficients of the polynomial to lie in the null-space of
some smoothness matrix H. The matrix-product of the null-space of the
smoothness matrix H and the original polynomial base results in a new base, the
so-called C-spline base, which automatically enforces Cr continuity throughout.
In this article we give a derivation of this C-spline base as well as an
algorithm to construct C-spline models.
