Reparametrization of Interval Bézier Curve on Rectangular and Circular Domain

Interval Bezier curve are new representation forms of parametric curves that can embody a complete description of coefficient errors. Using this new representation, the problem of lack of robustness in all state-of-the art CAD systems can be largely overcome. In this paper we discuss this concept to form a new curve over rectangular and circular domain such that its parameter varies in an arbitrary range [a, b] instead of standard parameter [0, 1]. Where a and b are real and, we also want that curve gets generated within the given error tolerance limit.