cases of the sutherland hodgman polygon clipping

Question

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 Sutherland-Hodgman 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 sub-problem where a sub-problem 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 sub-problem of clip against the second window edge. Hence, identifying the output of the earlier sub-problem as the input, all of the sub-problems 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.