In this paper, we propose a new concept called interval parametrization of algebraic curves, that is, we find an interval B&ier curve which bounds a given algebraic curve such that the bound is as tight as possible. An algorithm is presented to compute the interval parametrization of algebraic curves. The algorithm starts by finding the algebraic conditions that the interval Bfizier curve bounds the alge-braic curve, and then converts the problem into solving a non-linear programming problem with four variables. The non-linear programming is then approximately simplified to solving two non-linear programming problems with two variables. Some examples are provided to demonstrate the algorithm.
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