Algorithm 1.

Original ODT for Smoothing Inner Vertices

for every inner vertex x0 do

For every adjacent tetrahedron τ do Compute Sτ, nτ and ||xτ,i − x0||2 Sum up all the values of $\frac{1}{3}{S}_{\tau }{\mathbf{n}}_{\tau }{\displaystyle \sum _{k=1}^3}{\left|\right|x_{\tau ,k}-x_0\left|\right|}^2$ Compute the volume of Ω0, i.e. |Ω0| Compute x* using (3)