C2 and C3 continuous Bezier spline curve with given tangent polygon

This paper proposes an approach of constructing planar piecewise Bezier curve of 4th or 5th degree with all edges tangent to a given control polygon and the curve segments are joined together with C2 and C3 continuity. The segmented Bezier curves are all shape-preserving to their tangent polygon. Finally, a few numerical examples illustrate that the method given in this paper is effective for CAGD.