Tangent direction controlled subdivision scheme for curve

This paper discusses a new non-linear tangent direction controlled subdivision scheme for curve interpolation. Given a sequence of points with their tangent directions, every adjacent pair of points and their tangent directions make a new point and its tangent direction, this operation generates a new sequence of points and their tangent directions, this is one step of subdivision. Repeat this process continuously, this paper proves that the limit of the subdivision operation is a G1 continuous curve, interpolating the given conditions (positions series and their tangent directions). Examples are presented, and some reconstruct circular arcs.