Cases of clip a line segment-pq

Case 1: As we determine a new value of t_E that is value of parameter t for any potentially entering (PE) point we select t_max as:  t_max = max {t_max, t_E}. The initial value of t_max = 0 is considered.

Case 2: As we find a new value of t_L that is value of parameter t for any potentially leaving (PL) point then t_max value is updated by t_min = min {t_min, t_L}. The initial value of t_min = 1 is considered.

At last when value of t for all edges are determined and if t_max < t_min then line is visible else not. As well as line is visible from

P + t_max (Q - P)        to   P + t_min (Q - P) that is

P + t (Q - P) hence t_max   ≤ t ≤ t_min

t_max < t_min       (draw line)

t_max < t_min       (reject line)