基于双参数四点细分法的曲面造型

将双参数四点细分曲线方法进行推广，提出了基于双参数四点细分法的曲面造型方法，并对其收敛性进行了分析。该方法通过对两个参数的适当调节能够较容易地控制极限曲面的形状，极限曲面能够达到C4连续，可以应用到对曲面的连续性要求较高的曲面造型中去。在给定初始数据的条件下，可通过对形状参数的适当选择来实现对极限曲面的形状调整和控制，试验表明该算法生成光滑曲面是有效的。

Surface modeling based on 4-point subdivision scheme with two parameters

This paper expanded 4-point subdivision scheme with two parameters for curve design,presented the 4-point subdivision surface scheme with two parameters and analyzed the convergence of the scheme.The scheme can control limit surface shape through properly adjusting the two parameters.The limit surface may attain to C~4 continuity.The scheme can be applied to the surface modeling which demands much higher continuity.On the condition of the given initial data,we can adjust and control the limit surface shape through selecting appropriate parameters.The method is effective in generating smooth surfaces.