Curve Of The (generalized) Arc Spline Approximation

Arcs are widely applied in CAGD and industrial manufacture. In CNC machinery, NC tool paths are always made of circular and straight-line segments. In this paper, we discuss the error analysis of arc approximation of the curve, and the interpolation of curve data by blended generalized circles.The organization of the paper is as follows.In chapter one, we summarize modeling technology of free curve and surface in CAGD. Then, we review the existing work about the arc spline.In chapter two, we introduce several methods to construct arcs and arc splines. Especially, we introduce the arc spline which is based on the vector valued continued fraction form.In chapter three, we discuss the approximation of planar curves by arc spline which is based on the vector valued continued fraction form, and give its error formula and approximation algorithm.In chapter four, we give several error analysis when approximating quadratic Bézier curves by single arc spline. Furthermore, we present an algorithm which can reduce the approximation segments of arc.In chapter five, we discuss the interpolation of 2D or 3D discrete data by G~2 blended generalized circular spline, which is compatible with NURBS system.At last, we summarize the main ideas of this paper, and discuss the future work.