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Steps 1-2: Divide the points into two subsets. The 2-dimensional algorithm can be broken down into the following steps: [2] Find the points with minimum and maximum x coordinates, as these will always be part of the convex hull. If many points with the same minimum/maximum x exist, use the ones with the minimum/maximum y, respectively.
Incremental convex hull algorithm — O(n log n) Published in 1984 by Michael Kallay. Kirkpatrick–Seidel algorithm — O(n log h) The first optimal output-sensitive algorithm. It modifies the divide and conquer algorithm by using the technique of marriage-before-conquest and low-dimensional linear programming.
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.
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.
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
The Kirkpatrick–Seidel algorithm, proposed by its authors as a potential "ultimate planar convex hull algorithm", is an algorithm for computing the convex hull of a set of points in the plane, with () time complexity, where is the number of input points and is the number of points (non dominated or maximal points, as called in some texts) in the hull.
The lower convex hull of points in the plane appears, in the form of a Newton polygon, in a letter from Isaac Newton to Henry Oldenburg in 1676. [71] The term "convex hull" itself appears as early as the work of Garrett Birkhoff , and the corresponding term in German appears earlier, for instance in Hans Rademacher's review of Kőnig .
A kinetic convex hull data structure is a kinetic data structure that maintains the convex hull of a set of continuously moving points. [1] It should be distinguished from dynamic convex hull data structures, which handle points undergoing discrete changes such as insertions or deletions of points rather than continuous motion.