Approximate Merging of a Pair of Bézier Curves

This paper deals with the problem of approximate merging of two adjacent Bézier curves into one Bézier curve. We propose a method by using the matrix representation of subdivided Bézier curve and by minimizing the distance function defined between the original Bézier curves and the merged Bézier curve. Continuity at the endpoints of curves has been considered in the merging process, and approximate merging with points constraints are also discussed. It is shown that the degree elevation of the original Bézier curves could reduce the merging error. We provide examples to demonstrate the algorithm.