带参数的一类均匀B-L样条曲线曲面及应用

Application of a class of uniform B-L spline curves and surfaces with parameters

文章在三角函数空间Φ=span{1,sint,cost,sin2t,cos2t,…,sinnt,cosnt}中,构造n=6时的三角多项式样条;给出了带2个参数的B-L样条;根据需要调整这2个参数中的任何一个或同时调整2个,实现对曲线形状的控制,获得所需要的形状;该方法构造的曲线具有对称性,可以精确表示直线段、三次多项式曲线,并推广到曲面的情形。

In this paper, a class of B-L （Bézier-like） spline curves with two parameters defined on the space φ = span{1, sint, cost, sin2t, cos2t sinnt, cosnt } is constructed in the case of n=6. By changing either of these two parameters or both of them, the shape of the curves can be changed as it is wanted. These B-L spline curves are of symmetric and can express precisely lines and cubic polynomial curves. These B-L spline curves are generalized to the cases of B-L spline surfaces.