  We introduce here a direct method to construct multivariate explicit B-spline
bases. B-splines are piecewise polynomials, which are defined on adjacent
tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity
is enforced by making sure that all directional derivatives of order $r$, and
lower, on the boundaries of adjacent tetrahedra give the same values for both
tetrahedra. The method presented here is explicit, in that we will provide an
algorithm with which one can analytically construct the B-spline base that
enforces $C^{r}$ continuity for a given geometry.
