After smoothing a node its position $ \boldsymbol{P}_i$ has changed into $ \boldsymbol{P}^*_i$ satisfying:

$\displaystyle \boldsymbol{P}^*_i = \omega \frac{\sum_{j}\frac{1}{\overline{h}_j...
...l{P}_j }{\sum_{j} \frac{1}{\overline{h}_j^2 } } + (1-\omega ) \boldsymbol{P}_i,$ (716)

where $ j$ are the neighbors of $ i$, $ \overline{h}_j:=(h_i+h_j)/2$ ($ h_i$ is the desired edge length in node $ i$) and $ \omega$ is a relaxation factor taking the value of $ 0.5$. Defining the quality of the ball to be the quality of its worst element (i.e. highest value), a node $ i$ is only smoothed if the quality of its ball after smoothing has a smaller value (i.e. is better) than before smoothing.