G¹ Continuous Interpolation Curve on Smooth Surface

In computer graphics and computer aided geometric design,the techniques of generating an interpolation curve that is restricted on a given smooth surface and holds geometric continuity have shown more and more wide applications.We propose an approach of constructing Bézier spline curve of degree 3 to interpolate the given points on the smooth surface and then project the curve onto this surface with ruled surface.The projected curve keeps G¹ continuity.Theoretical deduction and experimentation show that such an approach is effective and produces good results.