中文摘要：

限制在光滑曲面上的插值曲线是计算机辅助几何设计中一个较新研究方向，实现在曲面上曲线插值的主要思想是利用曲面与其参数之间的对应关系，将其转化为一般的曲线插值问题．提出了一种新的、实用的算法，将曲面上插值点列和单位切向量投影到平面上，在平面上构造样条插值曲线，该样条插值曲线的插值柱面与曲面的交线即为过曲面上给定点列的G^1插值曲线．

英文摘要：

In computer aided geometric design,an interpolation curve restricted on a given smooth surface is a new research aspect. The main solution is to transfer to the common curve interpolation based on the relation between the surface and its parameter domain. A new and practical method is introduced in this paper. The basic idea is as follows, at first the given data points and tangent vectors on the surface are projected to a plane,then construct a spline curve interpolating the projected data points on the plane. The intersect curve of the surface and the projecting cylinder of the spline curve is the G^1 continous interpolation curve.