Explicit algorithms for multiwise merging of Bézier curves

This paper presents a novel scheme, called C r , s multiwise merging, for merging multiple segments of Bezier curves using a single Bezier 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 C r and C s continuity at the endpoints and is optimal in the sense that the L 2 or l 2 distance is minimized. As an application we develop explicit algorithms for G 1 multiwise merging, always producing better results than C 1 multiwise merging.

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