Abstract: This paper proposes an approach to constructing planar piecewise quadratic and cubic Bézier curve with all edges tangent to a given polygon and the curve segments are joined together with C1-continuity. The segmented Bézier curves are all shape preserving to their tangent polygon. All control points of the Bézier curve segments can be calculated simply by the vertices of the given polygon. The curve can locally or globally approximate the tangent polygon by the adjustment of the control parameters. Experiments show that the method given in this paper is simple, intuitive, effective and easy to control.

Key words: computer aided geometric design, tangent polygon, Bézier curve, C1-continuity, shape preserving