Offsets of polynomial Be´zier curves: Hermite approximation with error bounds

A method is presented for determining the error bound in approximating the offset of a polynomial Bezier curve using Hermite interpolation. The method is based on interval arithmetic and polynomials in Bernstein form. In particular, we show how an offset of a Bezier curve can itself be represented as a Bezier curve in which one of the control points is a rectangular interval. The size of this interval control point bounds the approximation error.