Explicit algorithms for multiwise merging of Bézier curves

This paper presents a novel scheme, called Cr,sCr,smultiwise merging  , for merging multiple segments of Bézier curves using a single Bézier curve. It is considered as an extension of the existing pairwise merging, to avoid the limitations caused by recursively applying pairwise merging to the multiple case. An explicit algorithm is developed to obtain the merged curve, which preserves CrCr and CsCs continuity at the endpoints and is optimal in the sense that the L2L2 or l2l2 distance is minimized. As an application we develop explicit algorithms for G1G1 multiwise merging, always producing better results than C1C1 multiwise merging.