矩形域上一种非张量积型样条曲面插值

Interpolation of Non Tensor-product Spline on Rectangular Domain

为降低造型所用样条曲面的次数,提出了一种非张量积形式的组合箱样条曲面。其基本思想为利用由4片三角箱样条曲面片组合构成的矩形片作为模块构造曲面。相较于双三次B样条曲面,其总次数为4次且支撑域更小,而在边界处具有和双三次B样条类似的导矢性质。进一步利用其显式表达式求出角点和控制顶点的关系,得到构造插值曲面的方法。最后,文末给出了计算实例,表明了方法的可行性。

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 hi-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 comer 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.