Multivariate splines and hyperplane arrangements

In this paper, we use the so-called conformality method of smoothing cofactor (abbr. CSC) and hyperplane arrangements to study truncated powers and box splines in R2R2. By the relation between hyperplane arrangements and truncated powers, we give the expressions of the truncated powers. Moreover, by means of the CSC method, the least smoothness degrees of the truncated powers and the box splines on each direction of partition edges are studied.