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Example

Without going into details of the solution (its similar to curves), one example is given. It is constructed in such a way, that multiple knots are inserted in the given surface from figure 10 and the surface is disturbed with help of random numbers.

Figure: The isophotes of the disturbed Bézier-spline surface and after fairing with the extended functional (max_error=$0.6247\%$, $305$ sec.).
\begin{figure} \centerline{\hfill \epsfxsize 75mm \epsfbox{hood_dist_mult.ps} \hfill \epsfxsize 75mm \epsfbox{hood_mult_smooth.ps} \hfill}\end{figure}

Figure: The isophotes of the faired Bézier-spline surface with previous knot removal (max_error=$0.66\%$, $8.34$ sec.).
\begin{figure}\centerline{\epsfxsize 75mm \epsfbox{hood_mult_smooth_rem.ps}}\end{figure}