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In this paper, we give an efficient algorithm of degree reduction of B\'eziercurves with box constraints. The idea is to combine the previous iterativeapproach, that has been presented recently in (P. Gospodarczyk, Comput. AidedDes. 62 (2015), 143--151), with a fast method of construction of dual basesfrom (P. Wo\'zny, J. Comput. Appl. Math. 260 (2014), 301--311) and a newefficient method of modification of dual bases.

Efficient degree reduction of B\'ezier curves with box constraints using dual bases