矩形拓扑曲线网格上G~1有理插值曲面的构造

 就矩形拓扑曲线网格上的Ｇ￣１有理曲面插值问题作了研究,提出了一种在空间矩形拓扑曲线网格上构造有理插值曲面的方法。进而给出了一种曲面内部形状可调而边界连接条件不受影响的有理曲线网格插值方法。此法无需考虑内网点处的扭矢协调问题及求解连续性方程,其最终产生的曲面自然达到Ｇ￣１连续。

THE CONSTRUCTION OF G￣1 RATIONAL INTERPOLATION SURFACE THROUGH RECTANGULAR CURVE NETWORKS

he G￣1 rational surface interpolation through topologically rectangular curve net-works is discussed.A method is presented to produce the G￣1 rational surface interpolating the given curve networks.Futhermore,another approach is developed to allow modifying the inner shape of interpolation surface patches without changing the G￣1 continuity between adjacent in-terpolation patches.Compared with the usual methods, according to the methods glven in this article, designer need not consider the compatibility of the twists on grid points;the G￣1 conti-nuity of the resulting surface is natural.