Approximation by interval Bezier curves

The interval Bezier curve, which, unlike other curve and surface approximation schemes, can transfer a complete description of approximation errors between diverse CAD/CAM systems that impose fundamentally incompatible constraints on their canonical representation schemes, is described. Interval arithmetic, which offers an essentially infallible way to monitor error propagation in numerical algorithms that use floating-point arithmetic is reviewed. Affine maps, the computations of which are key operations in the de Casteljau subdivision and degree-elevation algorithms for Bezier curves, the floating-point error propagation in such computations, approximation by interval polynomials, and approximation by interval Bezier curves are discussed.<>