Abstract
In this paper we give a new deflnition of minimally and quasi-minimally supported C 2 quartic bivariate B-splines associated with the four-directional mesh of the plane, introduced in (7,19), which is convenient to show that theses B-splines satisfy the reflnement equation and we determine the associated matrix mask, we prove that the family of these B-splines is stable and the associated subdivision scheme converges. These results can be extended to various cases in the spline space of class C 3k+2 and degree 4k + 4, but in these cases the supports of the masks are larger.
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