Abstract
For a subdivision Δ of a region in d-dimensional Euclidean space, we consider computation of dimension and of basis function in spline space Skr(Δ) consisting of all C piecewise polynomial functions over Δ of degree at most k. A computational scheme is presented for computing the dimension and bases of spline space Skr(Δ). This scheme based on the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For bivariate splines, explicit basis functions of Skr(Δ) are obtained for any integer k and r when Δ is a cross-cut partition.
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