Approximate Merging of a Pair of CE-Bézier Curves

Cubic extension Bezier (CE-Bezier) curve with multiple shape parameters is one of the most important extensions of the cubic Bezier curve.It not only inherits the outstanding properties of the cubic Bezier curve,but with a good performance on adjusting their local shapes by changing the shape control parameters.In order to develop the basic theory of CE-Bezier curve,a new method to deal with approximating two adjacent CE-Bezier curves by one CE-Bezier curve is presented for the approximate merging of existing curve design.By combining the fitting method of curves and the theory of the general inverse matrix,the explicit formula of control points of the merged CE-Bezier curve can be given directly.Eventually,some merging examples are discussed and the errors of approximate merging are given as well.Experiments illustrate that the proposed method not only has a good merging effect,but is easy to implement and simple to error estimation.