Approximate Merging of a Pair of Rational Bézier Curves by Interval Bézier Curve

To compress the data of geometric information,based on the center curve and error curve of the interval Bézier curve,the approximate merging of a pair of rational Bézier curves by interval Bézier curve was obtained.The basic idea is to get the polynomial Bézier curve as the center curve which approximately merges the neighbouring rational Bézier curves by using the perturbation theory first.Then,we compute the error curve with constant or non-constant interval by solving linear equations or solving a quadratic programming problem.Both of the two error curves can be improved by the application of the well-known subdivision approach to this method.Several numerical examples are presented to illustrate the correctness and validity of the algorithm.