In CAD and curve-fitting fields, we want to generate such rational cubic Bezier curve which is a unique curve passed given points and convenient to connect other curve segments with C1 connection. However, the method proposed in paper [1] can not meet above objective. in this paper, we propose a new method for generating a unique rational cubic Bezier curve which passed given points. The generated curve is with given tangent vectors at its two end points, and it is convenient to connect other curve segments with C1 connection. Also, some examples of curve generated by this method are given.

The research for rational quadratic Bézier curve and its applications for generating conics and curve-fitting have been reported in some papers. But rational cubic Bézier curves, for the complexity of computation of the weight parameters and the difficulty of the shape control, have very rarely been applied up to the present. In this letter, we proposed a new method to generate a rational cubic Bézier curve. For a given point S (assuming the curve pass it) and a given value of the intermediate variable t in the point, we can compute the weight parameters of the rational cubic Bézier curve according to the relation of the control polygon and the given point, and can generate the curve. Then we explained the relation among shape of curve, given point S and intermediate varisble t. As the samples of using the method, we showed the generation of the gear-shape curve, symmetrical curve and spindle-shape curve, etc.. Finally, we discuss the application of this method for curve-fitting.