Technical Section: Generating fair, C2 continuous splines by blending conics

We present a flexible, stable and locally adjustable conic blending method for the sparse points interpolation, which can avoid the potential pitfalls and unacceptable cases appeared in the circular blending method. Two interpolatory schemes are proposed to generate fair, C^2 continuous splines. One of both schemes is compatible with the NURBS curves. The blended spline curve is consistent with the interpolation control polygon and can be locally adjusted by free parameters. Experimental examples and analysis are presented to show the efficiency of the proposed method.