Dual bases for spline spaces on cells

The purpose of this paper is twofold. First, we extend the basic dimension result for spline spaces on simple cells to a class of spline spaces which satisfy additional smoothness conditions at the interior vertex. This extension is useful for the study of super spline spaces. Secondly, and more importantly, we show how to choose minimal determining sets of Bezier coordinates for these spaces. These in turn are useful for constructing explicit locally supported bases for spline spaces on general triangulations.