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

$${V}({\vec{p}})= \begin{cases}0&\text{if}\ {\kappa}_{\text{min}}\l... ...{p}})\leq{\kappa}_{\text{max}},\\ -{\kappa}({\vec{p}})&\text{else,} \end{cases}$$ (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 ${\kappa }_{\text {max}}=0.05$ .