Clipping Polygons Dr Scott Schaefer 1 Clipping Polygons

Why Is Polygon Clipping Hard? n What happens to a triangle during clipping? -

Why Is Polygon Clipping Hard? Concave polygon Multiple polygons 7/86

Why Is Polygon Clipping Hard? n A really tough case 8/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually

Sutherland-Hodgman Clipping n Input/output for algorithm: - input: list of polygon vertices in order

Sutherland-Hodgman Clipping n Edge from S to E takes one of four cases: outside

Sutherland-Hodgman Algorithm Out In No output Out In Output E Out In Output I,

Sutherland-Hodgman Algorithm Out In No output b Out In Output E Out In Output

Sutherland-Hodgman Algorithm Easy to pipeline for parallel processing n Polygon from one boundary does

Weiler-Atherton Algorithm General polygon vs. polygon clipping n Handles non-convex shapes n Not as

Weiler-Atherton Algorithm n n Process the edges of the polygon in a counterclockwise order

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Clipping Polygons Dr. Scott Schaefer 1

Clipping Polygons 2/86

Clipping Polygons 3/86

Why Is Polygon Clipping Hard? n What happens to a triangle during clipping? - possible outcomes: triangle quad triangle 5 -gon 4/86

Why Is Polygon Clipping Hard? n What happens to a triangle during clipping? - possible outcomes: triangle quad triangle 5 -gon How many sides could a clipped triangle have? 5/86

How Many Sides? 7 6/86

Why Is Polygon Clipping Hard? Concave polygon Multiple polygons 7/86

Why Is Polygon Clipping Hard? n A really tough case 8/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 9/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 10/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 11/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 12/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 13/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 14/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 15/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 16/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation 17/86

Sutherland-Hodgman Clipping n Basic idea: - consider each edge of the view window individually - clip the polygon against the view window edge’s equation - after doing all edges, the polygon is fully clipped 18/86

Sutherland-Hodgman Clipping n Input/output for algorithm: - input: list of polygon vertices in order {abcdef} a b f e d c 19/86

Sutherland-Hodgman Clipping n Input/output for algorithm: - input: list of polygon vertices in order - output: list of clipped polygon vertices consisting of old vertices (maybe) and new vertices (maybe) 20/86

Sutherland-Hodgman Clipping n Edge from S to E takes one of four cases: outside inside outside E S E no output inside E output inside outside inside S E S I output E output 21/86

Sutherland-Hodgman Algorithm Out In No output Out In Output E Out In Output I, E 22/86

Sutherland-Hodgman Algorithm Out In No output Out In Output E Out In Output I, E 23/86

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Sutherland-Hodgman Algorithm Out In No output b Out In Output E Out In Output I, E 28/86

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Sutherland-Hodgman Algorithm Out In No output Out In Output E Out In Output I, E Possible error for nonconvex polygons 65/86

Sutherland-Hodgman Algorithm Easy to pipeline for parallel processing n Polygon from one boundary does not have to be complete before next boundary starts n n Leads to substantial performance gains 66/86

Weiler-Atherton Algorithm General polygon vs. polygon clipping n Handles non-convex shapes n Not as efficient as Sutherland-Hodgman n Not easy to parallelize n 67/86

Weiler-Atherton Algorithm n n Process the edges of the polygon in a counterclockwise order until an inside-outside pair of vertices is encountered Follow the window boundaries in a counterclockwise direction from the exitintersection point to another intersection point with the polygon Repeat until at a previously processed vertex Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order 68/86

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