An Hermite-Interpolatory Subdivision Scheme with Tension Control

For representing elements of the linear spaces spanned respectively by the functions｛1,x,x²,x³｝,｛1,x,e^sx,e^-sx｝ and ｛1,x,e^isx,e^-isx｝,the paper presents a C¹ non-stationary Hermiteinterpolatory subdivision scheme which provides users with a tension parameter that,through proper adjustment within its range of definition can reproduce cubic polynomials,trigonometric functions and hyperbolic functions．Moreover,for certain given parameters,all conic sections can be reproduced exactly by this scheme．The convergence analysis of the subdivision method is given as well．Finally, we illustrate the effects of using the tension parameter and tangent vectors to generate subdivision curves．