Bounding interval rational Bezier curves with interval polynomial Bezier curves

In this paper we put forward and study the problem of bounding an interval rational Bezier curve with an interval polynomial Bezier curve. We propose three different methods-hybrid method, perturbation method and linear programming method to solve this problem. Examples are illustrated to compare the three different methods. The empirical results show that the perturbation method and the linear programming method produce much tighter bounds than the hybrid method, though they are computationally several times more expensive.