Interpolation of Non Tensor-product Spline on Rectangular Domain

To decrease the degree of spline surfaces used in modeling, a combined non tensor-product box spline surface is proposed. The basic idea is that four pieces of triangular box spline patches are combined to form a rectangular piece as the module structure of a surface. Compared with the bi-cubic B spline surface, the box spline possesses a similar derivative property on the boundary but with a smaller support and lower degree(B-spline surface of degree is four). Furthermore, in terms of the explicit expression of the spline, the relationship between the corner point and control vertices is revealed, and an approach of constructing the interpolating surface is obtained. At last, at the end of the paper an example is given to show the validity of the method.