Research On The Dimension Of Multivariate Weak Spline Space

Usually,multivariate spline function is smooth on every point of net lines. But in some domains,such as CAGD, finite-element and Hermit interpolation, the smooth conditions of the piecewise polynomial are special. Multivariate weak spline is such a case,which don't need the piecewise polynomial is smooth on all points but some points on net lines.In this paper,we gave a new construction method of the minimal determining set for the multivariate weak spline space on the star domain by using B-net method.we summarized the case of W_k~μ(St(V))(k≥ 2μ + 1), discussed the the case of W_k~μ(St(V))(k ≤2μ+1) and gave some examples.