Polygon Clipping

• We will consider clipping convex polygons first.
  • These present much less challenge than concave polygons.
• Sutherland-Hodgman Polygon Clipping.
  • We will clip against a rectangle,
  • But it can be used to clip against an arbitrary convex clipping polygon.
  • And it can be done as a pipeline operation.
  • And it is what opengl uses (I think)
• Send successive pairs of line endpoints through a four stage pipeline
  • Each stage clips the point against one of the sides of the clip window.
  • Or in the case of a n-sided clip polygon, each side is against one of the sides.
• For any pair of vertexes against any side
  • If the first vertex is outside and the second is inside, pass along the intersection point and the second vertex are passed along to the next stage
  • If both vertexes are inside, only the second vertex is passed along.
  • If the first vertex is inside and the second is outside, pass the edge intersection along
  • If both are outside, no vertexes are passed along.
• Consider
  • 
  • Step 1, clip against the left.
    • Input {1,2} {2,3} {3,1}
    • Line {1,2} does not need clipped so send 2 on
    • Line {2,3} goes from inside to outside, so pass 2' along.
    • Line {3,1} goes from the outside to the inside, so pass along 3' and 1
    • 
  • Step two, clip against the right side.
    • Input {2,2'} {2',3'} {3',1} {1,2}
    • Line {2,2'} does not need clipped so send 2' on
    • Line {2',3'} does not need clipped so send 3' on
    • Line {3',1} does not need clipped so send 1 on
    • Line {1,2} does not need clipped so send 2 on
    • 
  • Step 3, clip against the bottom plane.
    • Input {2',3'} {3', 1} {1,2} {2,2'}
    • Line {2',3'} Goes from in to out so pass along 2"
    • Line {3',1} goes from out to out so pass along nothing
    • Line {1,2} goes from out to in, so pass along 1',2
    • Line {2,2'} goes from in to in so pass along 2'
    • 
  • Step 4, clip against the top plane
    • Input {2", 1'} {1',2} {2,2'} {2',2"}
    • There is no clipping at this stage
    • Each clip goes from in to in, so pass along the endpoint.
    • The output would be {1',2} {2,2'} {2', 2"} {2",1}
    • 
• A modification of this algorithm can work with concave polygons