Algorithm 2 Concave surface converting algorithm.

1:Initialize line set $L=\varnothing$, and put all strips into set ${\Omega }_1$ and $R=1$. 2:for each ${\Omega }_r$ do 3: if $|{\Omega }_r|>3$ then 4:  The strips in ${\Omega }_r$ are fitted into a line according to their horizontal locations with the fitted error ${\epsilon }^l$. 5:  if ${\epsilon }^l<={\epsilon }^{th}$ then 6:   Put this line into L, and remove the corresponding strips in ${\Omega }_r$. 7:  else 8:   Split the strips at the maximum fitting error into ${\Omega }_{R+1}$ and ${\Omega }_{R+2}$; $R=R+2$. 9:  end if 10: else if$\overrightarrow{{\mathbf{S}}_{i-1}{\mathbf{S}}_i}·\overrightarrow{{\mathbf{S}}_{i+1}{\mathbf{S}}_i}>0$ and $\sqrt{{(X_{i-1}-X_{i+1})}^2+{(Z_{i-1}-Z_{i+1})}^2}<W^s$ then 11:  Delete ${\mathbf{S}}_i$; put the line composed of ${\mathbf{S}}_{i+1}$ and ${\mathbf{S}}_{i-1}$ into L. 12:end if 13: end for 14:Merge collinear line segments in L.