Algorithm 3.

Advanced B-ODT Smoothing for Boundary Vertices with Feature Preserving

for every boundary vertex x0 do

Compute the feature line of x0, suppose the unit vector of this line is d. Compute the following coefficients: $A=\frac{1}{4}\mid {\mathrm{\Omega }}_0\mid -\frac{1}{60}{\displaystyle \sum _{i=1}^m}<\mathbf{d},Y_i+Y_{i+1}><\mathbf{d},Y_i\times Y_{i+1}>$ $B=\frac{1}{12}<\mathbf{d},{\displaystyle \sum _{\tau \in {\mathrm{\Omega }}_{\ast }}}{S}_{\tau }{\mathbf{n}}_{\tau }{L}_{\tau }>-\frac{1}{60}{\displaystyle \sum _{i=1}^m}(Y_i^2+Y_{i+1}^2+Y_i{Y}_{i+1})<\mathbf{d},Y_i\times Y_{i+1}>$ Compute x* as x* = x0 + f d with $f=-\frac{B}{2A}$.