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Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science.. In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities.
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 ...
Convex hull, alpha shape and minimal spanning tree of a bivariate data set. In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel (1983).
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 .
Pages in category "Convex hull algorithms" The following 11 pages are in this category, out of 11 total. This list may not reflect recent changes. ...
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.
Sweephull [21] is a hybrid technique for 2D Delaunay triangulation that uses a radially propagating sweep-hull, and a flipping algorithm. The sweep-hull is created sequentially by iterating a radially-sorted set of 2D points, and connecting triangles to the visible part of the convex hull, which gives a non-overlapping triangulation.
The convex hull of a simple polygon can be subdivided into the given polygon itself and into polygonal pockets bounded by a polygonal chain of the polygon together with a single convex hull edge. Repeatedly reflecting an arbitrarily chosen pocket across this convex hull edge produces a sequence of larger simple polygons; according to the Erdős ...