Minimizing the maximal ratio of weights of a rational Bézier curve

This paper presents a solution to the problem of reparameterizing a rational curve by a Möbius transformation such that the maximal ratio of weights in the reparameterized representation is minimized. The problem is reduced to solving a linear programming problem, which can be solved directly and simply. The result can be used to reparameterize rational curves so as to yield tight bounds on derivatives.