Interval implicitization of rational curves Original Research Article

In this paper, we propose a new concept called interval implicitization of rational curves, that is, finding an interval algebraic curve with lower degree which bounds a given parametric rational curve such that some objective function involving the width and the tension of the interval algebraic curve is minimized. An algorithm is presented to compute the interval implicit representation of a rational curve by solving two optimal problems, each with a quadratic (or linear) objective function and linear constraints. Some examples are also provided to demonstrate the algorithm.