Cases of the Sutherland Hodgman Polygon Clipping Algorithm
In order to clip polygon edges against a window edge we move from vertex V_{i} to the subsequent vertexV_{i+1} and choose the output vertex as per to four simple tests or rules or cases listed here in below:
Table: Cases of the SutherlandHodgman Polygon Clipping Algorithm
Case

Vi

Vi+1

Output Vertex

A

Inside window)

Inside

Vi+1

B

Inside

Outside

V'i i.e intersection of polygon and window edge

C

Outside

Outside

None

D

Outside

Inside

V'I ; Vi+1

Conversely, the 4 possible Tests listed above to clip any polygon conditions are as mentioned here:
1) If both Input vertices are within the window boundary then only second vertex is added to output vertex list.
2) If first vertex is within the window boundary and the 2nd vertex is outside then, merely the intersection edge along with boundary is added to output vertex.
3) If both Input vertices are outside the window boundary then nothing is added to the output list.
4) If the first vertex is outside the window and the 2nd vertex is within window, then both the intersection points of the polygon edge along with window boundary and second vertex are added to output vertex list.
Here, we can utilize the rules cited above to clip a polygon properly. The polygon should be tested against each edge of the clip rectangle; new edges should be added and existing edges must be discarded, retained or divided. In fact this algorithm decomposes the problem of polygon clipping against a clip window in the same subproblem where a subproblem is to clip all polygon edges that is pair of vertices in succession against a particular infinite clip edge. The output is a set of clipped edges or pair of vertices which fall in the visible side along w.r.t. clip edge. Such set of clipped edges or output vertices are taken as input for the subsequent subproblem of clip against the second window edge. Hence, identifying the output of the earlier subproblem as the input, all of the subproblems are solved in sequence, at last yielding the vertices which fall on or inside the window boundary. These vertices linked in order forms, the shape of the clipped polygon.