Given a set of points x 1 y 1 x 2 y 2 x n y n the convex hull is the smallest convex polygon containing all the points Convex Hulls Given a set of points x 1 y ID: 309603
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Slide1
Convex Hulls
Given a set of points (x
1,y1),(x2,y2),…,(xn,yn), the convex hull is the smallest convex polygon containing all the points.Slide2
Convex Hulls
Given a set of points (x
1,y1),(x2,y2),…,(xn,yn), the convex hull is the smallest convex polygon containing all the points.Slide3
Convex Hulls
Gift-wrapping algorithm
running in time O(n2), or, more precisely, O(nk) where k is the number of vertices on the hull.An O(n log n) algorithm ?Slide4
Convex Hulls
The
Graham Scan algorithm
Running time ?Slide5
Convex Hulls
A divide-and-conquer algorithm ?
Running time ?Slide6
Closest Pair of PointsInput: n points in the plane (x
1,y1),…,(xn,yn)Output: distance of the closest pair of points, i.e.,
mini,j (i j) distance of (xi,yi) and (xj,yj)Slide7
Closest Pair of PointsInput: n points in the plane (x
1,y1),…,(xn,yn)Output: distance of the closest pair of points, i.e.,
mini,j (i j) distance of (xi,yi) and (xj,yj)Slide8
Closest Pair of PointsInput: n points in the plane (x
1,y1),…,(xn,yn)Output: distance of the closest pair of points, i.e.,
mini,j (i j) distance of (xi,yi) and (xj,yj)