Algorithm 3 No parallel straight edges

1:if $n==1$ and $A==small$ then 2:    Use $(x_{E_1},y_{E_1})$ and ${\theta }_{E_1}$ 3:else if $n==0$ then 4:    Draw lines $L_n$ about $(x_c,y_c)$ at rotating intervals 5:    Find points $A^{\prime }$ and $B^{\prime }$ intersecting P 6:    if $m\ne 0$ then 7:        for i = 1 to m do 8:           Discard any $L_n$ if intersects $C_i$ 9:    Find $L_n$ with shortest length $A^{\prime }{B}^{\prime }$ 10:    Use points $A^{\prime }$, $B^{\prime }$ and ${\theta }_{A^{\prime }{B}^{\prime }}$