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)