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

Abstract

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