  This paper deals with the merging problem of segments of a composite B\'ezier
curve, with the endpoints continuity constraints. We present a novel method
which is based on the idea of using constrained dual Bernstein polynomial basis
(P. Wo\'zny, S. Lewanowicz, Comput. Aided Geom. Design 26 (2009), 566--579) to
compute the control points of the merged curve. Thanks to using fast schemes of
evaluation of certain connections involving Bernstein and dual Bernstein
polynomials, the complexity of our algorithm is significantly less than
complexity of other merging methods.
