According to a recent result by Farouki (1997), the optimal bilinear p
arameter transformation of an integral Bezier curve (which produces a
rational parameterization whose parametric speed is as uniform as poss
ible) can be computed by solving a quadratic equation. This note prese
nts a simplified derivation of this result. In addition we outline its
generalization to rational curves. (C) 1997 Elsevier Science B.V.