DR. JAN HADENFELD
		The Ranking-List The best location has now be found by changing a control point. Solving the next problem is to determine the faired control point. That means we have to find the index $r$ of the control point. We want to change the control point where the largest improvement of the fairness functional is given. We call this improvement $$z_r = E_l(\bar{\bf d}_r) - E_l(\widetilde{\bf d}_r) \ge 0$$ (17) ranking-number. Following up some calculations we obtain by inserting the control point $\widetilde{\bf d}_r$ (14) $$z_r = \left(\bar{\bf d}_r - \widetilde{\bf d}_r \right)^2 \cdot \int_a^b \left( N_{r,k}^{(l)}(t) \right)^2 \; dt\;\;\;.$$ (18) This ranking-number is a weighted function of the squared change of control point $\bar{\bf d}_r$. The ranking-numbers have to be calculated for all involved control in order to find the largest improvement. This ranking-list then has to be sorted. The whole ranking-list has to be calculated only in the first step for all control points because the control point $\widetilde{\bf d}_r$ influences only the ranking-numbers $z_i$ with the index $r - k + 1\le i \le r + k - 1$ and these ranking-numbers only have to be recalculated in the following step.