4. Bivariate Spline Spaces

In the previous chapter we gave a brief description of bivariate spline spaces on the three- and four-directional meshes. We are now going to discuss the more general setting and study some of the interesting subspaces. In particular, we will give the dimension of a bivariate spline space and its super spline subspace on a quasi-crosscut partition. Lower and upper bounds of the dimension of spline and super spline spaces on an arbitrary triangulation are also established, and approximation order is discussed.