Abstract
The spaces of bivariate splines on a particular triangulation are considered. The dimension of the space of splines with degree 2 and with smoothness order 1 on this triangulation has long been known to depend on the geometry of the triangulation. This result is extended to the space of splines of degree $2r$ and smoothness order r. The dimension of the spline space is shown to have a similar dependence on geometry for all values of $r \geqq 1$.
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