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ConvexHullDef - Convex Hull most ubiquitous structure in...

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Convex Hull - most ubiquitous structure in computational geometry -useful to construct other structures -many applications: robot motion planning, shape analysis etc. - a beautiful object, one of the early success stories in computational geometry that sparked interest among Computer Scientists by the invention of O(nlogn) algorithm rather than a O(n**3) algorithm. - intimately related to sorting algorithm for both lower and upper bound.
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Convex hulls Preliminaries and definitions Intuitive definition 1 Given a set S = { p 1 , p 2 , …, p N } of points in the plane, the convex hull H ( S ) is the smallest convex polygon in the plane that contains all of the points of S . Imagine nails pounded halfway into the plane at the points of S . The convex hull corresponds to a rubber band stretch around them.
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Convex hulls Preliminaries and definitions Convex polygon A polygon is convex iff for any two points in the polygon (interior boundary) the segment connecting the points is entirely within the polygon. convex not convex
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Convex hulls Preliminaries and definitions Vertices A polygon vertex is convex if its interior angle ≤ π (180° 29. It is reflex if its interior angle > π (180° 29.
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