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The convex hull of a simple polygon is divided by the polygon into pieces, one of which is the polygon itself and the rest are pockets bounded by a piece of the polygon boundary and a single hull edge. Although many algorithms have been published for the problem of constructing the convex hull of a simple polygon, nearly half of them are ...
Input = a set S of n points Assume that there are at least 2 points in the input set S of points function QuickHull(S) is // Find convex hull from the set S of n points Convex Hull := {} Find left and right most points, say A & B, and add A & B to convex hull Segment AB divides the remaining (n − 2) points into 2 groups S1 and S2 where S1 are points in S that are on the right side of the ...
The closed convex hull of a set is the closure of the convex hull, and the open convex hull is the interior (or in some sources the relative interior) of the convex hull. [9] The closed convex hull of is the intersection of all closed half-spaces containing .
A demo of Graham's scan to find a 2D convex hull. Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original algorithm in 1972. [1] The algorithm finds all vertices of the convex hull ordered along its boundary.
The dynamic convex hull problem is a class of dynamic problems in computational geometry. The problem consists in the maintenance, i.e., keeping track, of the convex hull for input data undergoing a sequence of discrete changes, i.e., when input data elements may be inserted, deleted, or modified.
A 2D demo for Chan's algorithm. Note however that the algorithm divides the points arbitrarily, not by x-coordinate. In computational geometry, Chan's algorithm, [1] named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set of points, in 2- or 3-dimensional space.
Thus, using kinetic convex hull to maintain the upper and lower envelopes, a kinetic sorted list on these intervals to maintain the antipodal pairs, and a kinetic tournament to maintain the pair of maximum distance apart, the diameter of a moving point set can be maintained. This data structure is responsive, compact and efficient.
For the sake of simplicity, the description below assumes that the points are in general position, i.e., no three points are collinear.The algorithm may be easily modified to deal with collinearity, including the choice whether it should report only extreme points (vertices of the convex hull) or all points that lie on the convex hull [citation needed].