Sutherland Hodgeman polygon  clipping

The Sutherland-Hodgman polygon clipping algorithm is a method for clipping a polygon against an arbitrary convex clip window. It works by iteratively clipping each edge of the polygon against the clip window to produce a new, smaller polygon that lies completely inside the clip window.

The algorithm works as follows:

1. Initialize an empty list to hold the vertices of the clipped polygon.

2. For each edge of the clip window, clip the current polygon against that edge using the following steps:

   a. Initialize a new empty list to hold the vertices of the clipped polygon for this edge.

   b. Iterate over each vertex of the current polygon.

   c. If the vertex lies inside the clip window, add it to the new list.

   d. If the vertex lies outside the clip window, but the previous vertex lies inside, compute the intersection point between the edge of the clip window and the line segment between the current and previous vertices, and add it to the new list.

   e. If the vertex lies outside the clip window and the previous vertex lies outside or on the edge, discard it.

   f. When all vertices have been processed, set the new list of vertices as the current polygon and proceed to the next clip window edge.

3. When all edges of the clip window have been processed, the final list of vertices represents the clipped polygon.

Note that the Sutherland-Hodgman algorithm can handle concave polygons and multiple disjoint polygons, as long as the clip window is convex. However, it is computationally expensive for complex polygons or large numbers of vertices, as each edge of the polygon must be clipped against each edge of the clip window.