Search results
Results from the WOW.Com Content Network
The lower bound on worst-case running time of output-sensitive convex hull algorithms was established to be Ω(n log h) in the planar case. [1] There are several algorithms which attain this optimal time complexity. The earliest one was introduced by Kirkpatrick and Seidel in 1986 (who called it "the ultimate convex hull algorithm"). A much ...
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. The algorithm takes O ( n log h ) {\displaystyle O(n\log h)} time, where h {\displaystyle h} is the number of vertices of the output (the convex ...
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 ...
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.
For many years the best algorithm of this type was that of Overmars and van Leeuwen (1981), which took time O(log 2 n) per update, but it has since been improved by Timothy M. Chan and others. In a number of applications finding the convex hull is a step in an algorithm for the solution of the overall problem.
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points. The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon . [ 1 ]
A particularly simple algorithm for this problem was published by Graham & Yao (1983) and Lee (1983). Like the Graham scan algorithm for convex hulls of point sets, it is based on a stack data structure. The algorithm traverses the polygon in clockwise order, starting from a vertex known to be on the convex hull (for instance, its leftmost point).
Animation of the gift wrapping algorithm. The red lines are already placed lines, the black line is the current best guess for the new line, and the green line is the next guess. In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.