From Lines to Polygons

Clipping a polygon is harder than clipping a line because the result must remain a closed polygon, possibly with new vertices on the clip boundary. Sutherland-Hodgman clips a (convex) polygon against one clip edge at a time, sequencing through all clip edges.

Per-Edge Rule

Process each subject polygon edge (V_i, V_(i+1)) against one clip edge. Four cases:

The output of edge k is the input to edge k+1.

Algorithm Pseudocode

For each clipEdge in clipPolygon, build a fresh output list. For each consecutive pair (S, E) of subject vertices: if E is inside, then if S is also inside add E, else add the intersection of S-E with clipEdge and then E; if E is outside but S is inside, add only the intersection. After processing all clip edges, the surviving polygon is the result.

Walk-Through

Triangle (-2, 4), (6, 8), (4, -2) clipped against window [0,5] x [0,5]:

1. Left edge x=0: trim parts with x<0. Vertex 1 outside, vertex 2 inside, vertex 3 inside. Add intersections + insides.
2. Right edge x=5: trim parts with x>5. Vertex 2 outside now, etc.
3. Continue with bottom y=0 and top y=5. After all four edges, the result is the polygon clipped to the window.

Limitations

• Subject polygon may be concave; clip polygon must be convex.
• For concave subject vs convex clip windows the result is correct only if it remains a single polygon; otherwise spurious connecting edges appear ("dog-leg" artifact). Use Weiler-Atherton for arbitrary polygon-polygon clipping.

Why It Matters

This is the core of viewport clipping in classical software pipelines and the conceptual model behind GPU clipping against the homogeneous frustum.