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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 ...
However, in higher dimensions, variants of the obstacle problem of finding a minimum-energy surface above a given shape can have the convex hull as their solution. [5] For objects in three dimensions, the first definition states that the convex hull is the smallest possible convex bounding volume of the objects.
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.
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.
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 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.
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. One can build a convex hull in this manner so long as the order of points guarantees no point would fall within the triangle.
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).