Interval Implicitization of Rational Surfaces

In this paper,we put forward a new method called interval implicitization of rational surfaces, that is,finding an interval algebraic surface with lower degree to bound a given rational surface and minimize some objective function involving the width and the tension of the interval algebraic surface.The center implicitization surface can approximate the given rational surface within some tolerance.By solving three optimal problems,an algorithm is proposed to compute the interval implicit representation of a rational surface, and some examples are provided to demonstrate the algorithm.