Liang-Barsky Line Clipping Algorithm

• For given window with (XWmin, YWmin) and (XWmax, YWmax), the given line has end-points (X1, Y1) and (X2, Y2).
• Calculate 
  
  

  
• Calculate pk, qk and rk for k = 1, 2, 3, 4 as:
  
• If pk=0 for some k, then the line is parallel to clipping boundary. Now test qk:

If one qk < 0 for these k, then the line is outside. 

If all qk ≥ 0 for these k, then some portion of the line is inside.

• For all pk < 0 (i.e. line proceeds from outside to inside the boundary), calculate 
  
  to determine intersection point with the possibly extended clipping boundary k and obtain a new starting point for the line at u1.
• For all pk > 0 (i.e. line proceeds from inside to outside the boundary), calculate 
  
  to determine intersection point with the possibly extended clipping boundary k and obtain a new end point for the line at u2.
• If
  
  discard the line. 
• Else, the line is now between
  
• Hence,
  
• Updated points are