1. There are four cases for line clipping: both endpoints inside, both outside, one inside one outside, and both endpoints outside but the line intersects the clipping area. 2. The midpoint subdivision algorithm divides lines into three categories - visible, not visible, and candidates for clipping - and recursively subdivides candidate lines until they are fully classified. 3. Polygon clipping processes polygon edges as line segments and handles four cases when a pair of vertices are passed to the clipper: both outside are discarded, first outside second inside saves intersection and second vertex, both inside saves second, first inside second outside saves intersection.