Andrew's Monotone Chain Convex Hull Algorithm

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Presentation transcript:

Andrew's Monotone Chain Convex Hull Algorithm

Andrew's Monotone Chain Scan A left-to-right variant of Graham's scan Discovered by Andrew in 1979 Using a linear lexigraphic sort of the point set by the x- and y-coordinates This may be an advantage if this order is already known for a set which is often the case.

The Chain Method U1 U3 U2 U5 U6 U4 U8 U7 Definition : A chain C = ( u1, … , up ) is a planar straight-line graph with vertex set { u1, … , up } and edge set { (ui, ui+1) : i = 1, …, p-1 } U1 U2 U3 U4 U5 U6 U7 U8

The Monotone Chain U1 L U2 U3 U4 U5 Definition : A chain C = ( u1, …, up ) is said to be monotone with respect to a straight line L if a line orthogonal to L intersects C in exactly one point. L U1 U2 U3 U4 U5