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CompGeomIntro

# ch of ver tices of c hp in counterclockwise order

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Unformatted text preview: utput: a sequence L = (c1 , c2 , . . . ch ) of ver tices of C H(P ) in counterclockwise order Example: L = (p3 , p4 , p8 , p6 , p1 , p5 ) p6 p1 p8 p2 p7 p4 p5 p3 C H(P ) Introduction, Convex Hulls – p.13/40 CONVEX Characterizationization HULL - Character The directed edge (p, q ) is an edge of C H(P ) iff q p C H(P ) CONVEX CharacChaization tion HULL - ter racteriza The directed edge (p, q ) is an edge of C H(P ) iff q p r − all r ∈ P \ {p, q } lies to the left of line pq (oriented by →). pq CONVEX HULLrization Characte PROBLEM The directed edge (p, q ) is an edge of C H(P ) iff q p r ∀r ∈ P \ {p, q } the triangle (p, q , r) is oriented counterclock- wise. Introduction, Convex Hulls – p.16/40 OCONVEX HULL t rientation tes We denote C C W (p, q , r) = xp xq xr yp yq yr 111 = (xq − xp )(yr − yp ) − (xr − xp )(yq − yp ) Triangle (p, q , r) is counterclockwise iff C C W (p, q , r) > 0. How fast can we perform this test? 2 multiplications and 5 subtractions takes O(1) time CONVEX HULL - tNaive Aithrithm Firs algor lgo m Algorithm SlowConvexHull (P)...
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