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4.5 Smoothing

The LS method also provides a simple way to smooth a given geometry. Setting the surface velocity in the LS equation equal to the mean curvature leads to a smoothed surface [110]. The definition of the mean curvature and its approximation were given in Section 3.3.2. The introduction of a lower limit $ {\kappa}_{\text{min}}<0$ and an upper limit $ {\kappa}_{\text{max}}>0$ for regions with negative and positive curvature, respectively, controls the amount of smoothing. The smoothing algorithm is realized by setting the surface velocity field as follows

$\displaystyle {V}({\vec{p}})= \begin{cases}0&\text{if}\ {\kappa}_{\text{min}}\l...
...{p}})\leq{\kappa}_{\text{max}},\\ -{\kappa}({\vec{p}})&\text{else,} \end{cases}$ (4.17)

and solving the LS equation over time until all surface velocities are equal to 0. Figure 4.7 demonstrates smoothing for the test structure given in Figure 4.5 with $ {\kappa }_{\text {min}}=-0.1$ and $ {\kappa }_{\text {max}}=0.05$ .

Figure 4.7: The final surface after a smoothing operation is applied to the geometry given in Figure 4.5a. The curvature is limited by $ {\kappa }_{\text {min}}=-0.1$ and $ {\kappa }_{\text {max}}=0.05$ .
Image fig_4_7


next up previous contents
Next: 4.6 Multiple Material Regions Up: 4. A Fast Level Previous: 4.4.3 Pattern Transfer

Otmar Ertl: Numerical Methods for Topography Simulation