Approximate merging of quartic λ-Bézier curves

A method which can deal with approximating two adjacent quartic λ-Bézier curves by one quartic λ-Bézier curve, was presented for the approximate merging of existing curve design. After the fitting method of the curves was combined with the theory of the general inverse matrix, the explicit formula of control points of the merged quartic λ-Bézier curve was given directly. In the merging process, two cases were considered respectively. One is the case without constraints of endpoints interpolations; the other is the case with constraints of endpoints interpolations. Eventually, some merging examples were discussed and the errors of approximate merging were given. Experimental results illustrate that the proposed method has a good merging effect and is easy to implement and simple to error estimation, which can be widely applied to the approximate merging of curve in CAD/CAM systems.