实用的可展曲面上的C^1曲线插值方法

Practical algorithm for constructing C^1 continuous interpolation curve on developable surface

曲面上的曲线插值是计算机辅助几何设计的重要课题之一。利用可展曲面可与平面贴合的性质,构造一个等距对应将可展曲面展成平面,从而将可展曲面上的曲线插值归结为通常的R2上插值曲线的构造,并证明所得的插值曲线为C1连续。最后以柱面、锥面以及切线曲面为例构造插值曲线,图例显示该算法具有满意的效果。

The interpolation curve on a given surface is one of the important tasks of CAGD. The character that the developable surface can be jointed with plane, may be used to construct one isometric correspondence, then, the developable surface will be developed into plane. Therefore, the interpolation curve on the developable surface is ended into the construction of interpolation curve in R^2 generally, and it proved that the interpolation curve is C^1 continuous. In the end, the cylndrical surface, conical surface and tangent surface are used as examples to construct the interpolation curve. And it shows that this algorithm is effective.