Algorithm 2: Area Division: Calculate $S_{D_i}$

Require:  $T\ne Ø$

Ensure: $min\left(n\right)$

1: $f(x,y,z)=0\Leftarrow fit\left(SFV\right)$

2: $n\Leftarrow 0$

3: while $T\ne Ø$ do

4:  $n\Leftarrow n+1$

5:  $find$ $the$ $bottom$ $left$ $corner$ $(x0,y0)$ $of$T

6:  $len\Leftarrow l;$ $wd\Leftarrow w$

7:  repeat

8:   $flag\Leftarrow false$

9:   $S_{D_n}\Leftarrow Ø$

10:   for  $\forall (x_i,y_j)\in T$ do

11:    if  $(x0\le x_i\le x0+len)$ and  $(y0\le y_j\le y0+wd)$ then

12:    $S_{D_n}\Leftarrow S_{D_n}\cup (x_i,y_j)$

13:    end if

14:   end for

15:  for  $\forall (x_i,y_j)\in S_{D_n}$do

16:    for  $z_k=h_{i,j}(x_i,y_j)$to  $z_{max }$do

17:    $L_{D_n}\Leftarrow (x_i,y_j,z_k)$

18:   $A_{D_n}\Leftarrow Ø$

19:   for  $\forall (x,y,z)\in SFV$do

20:     if $(x,y,z)$ $covered$ $by$ $D_n$ then

21:    $A_{D_n}\Leftarrow A_{D_n}\cup (x,y,z)$

22:     end if

23:   end for

24:    $find$ $max\left(x\right),$ $min\left(x\right),$ $max\left(y\right),$ $min\left(y\right)$ $of A_{D_n}$

25:    if $S_{D_n}\subseteq A_{D_n}$ and  $\left(max\right(x)-min(x\left)\right)\le l$ and  $\left(max\right(y)-min(y\left)\right)\le w$ then

26:     $flag\Leftarrow true;$ $break$

27:     end if

28:   end for

29:    if  $flag==true$then

30:    $break$

31:     end if

32:   end for

33:   $len\Leftarrow len-{\delta }_l;$ $wd\Leftarrow wd-{\delta }_w$

34:   until  $flag==true$

35:   $T\Leftarrow T\backslash S_{D_n}$

36:  end while