Abstract: An algorithm is presented to determine whether the degree of Bézier curve can be reduced
by polynomial reparameterization. In the algorithm, for any Bézier curve, the relation between the
basis functions before and after reparameterization is expressed as a system of equations. Instead of
solving the equations, the polynomial for reparameterization and the control points of the lower
degree Bézier curve can be calculated directly by a pyramid algorithm of coefficient
reparameterization. In addition, the polynomial for reparameterization is unique to within a scale
factor and a constant. Compared with the previous algorithm by examples, this algorithm possesses
shorter computational time.

Key words: Bézier curve, polynomial, reparameterization, basis function, pyramid algorithm