Design of Rational Bézier Developable Surface Pencil Through A Common

This paper studies the problem of designing a rational Bézier developable surface pencil with a common isogeodesic, and provides an algorithm for the representation of complicated geometric models in industrial applications which need to satisfy that the shape surface can be developed and a given curve is geodesic. By employing the local Frenet orthonormal frame, the explicit expression of the rational Bézier developable surface pencil is derived. Furthermore, the order of the rational Bézier developable surface pencil interpolating a planar or non-planar curve as its geodesic is discussed. The formulae of the control net vertices for the derived surface are presented. Finally, the effectiveness and correctness of the algorithm are verified by examples of the rational Bézier developable surface pencil through a degree 2 or 3 Bézier curve as a common geodesic