An explicit method for G3G3 merging of two Bézier curves

This paper presents an explicit method for the G3G3 merging problem of two Bézier curves. The main idea is to express the L2L2 distance as a quadratic function of some parameters provided by G3G3 continuity conditions. An efficient non-iterative algorithm is proposed to obtain the optimal merged curve when the L2L2 distance is minimized. The uniqueness of the global minimum is also proven. This method can be applied to two adjacent curves with different degrees and has the ability to obtain satisfactory merging results by using curves of lower degree. The efficiency and accuracy of the proposed explicit method are illustrated through several comparative examples.