Clipping must account for all of the viewport's boundaries. The Cohen-Sutherland Method is used to clip lines to a viewport. An outcode is determined by the position of an endpoint and is a 4-bit value indicating whether it is outside of the viewport to the top (MSB), bottom, right, or left (LSB) side(s).
The algorithm can be summarized as follows:

1. Compute outcode for point P1
2. Compute outcode for point P0
3. Trivial accept? (both endpoints inside of viewport)

   Yes -- draw the line

4. Trivial reject? (both endpoints outside and on the same side of one of the viewport edges)

   Yes -- do not draw and exit

5. Is P0 inside the viewport?

   Yes -- swap P0 <--> P1

6. Is P0 > Ymax (top) ?

   Yes -- clip at intersection and move P0 to new point

7. Is P0 < Ymin (bottom) ?

   Yes -- clip at intersection and move P0 to new point

8. Is P0 > Xmax (right) ?

   Yes -- clip at intersection and move P0 to new point

9. Is P0 < Xmin (left) ?

   Yes -- clip at intersection and move P0 to new point

10. Branch back to Step 2

The worst case will iterate four times through the algorithm.

Clipping objects other than straight lines is rather difficult and/or computationally expensive. Clipping polygons involves ownership and adjacency problems as well as dealing with gaps formed when mesh surfaces are created and rotated.