Search results
Results from the WOW.Com Content Network
The algorithm will always correctly determine the closest pair, because it maps any pair closer than distance to the same grid point or to adjacent grid points. The uniform sampling of pairs in the first step of the algorithm (compared to a different method of Rabin for sampling a similar number of pairs) simplifies the proof that the expected ...
Consider, for example, the Closest pair problem: Given n points in the plane, find the two with the smallest distance from each other. One could compute the distances between all the pairs of points, of which there are n(n-1)/2, then pick the pair with the smallest distance.
The closest pair of points corresponds to two adjacent cells in the Voronoi diagram. If the setting is the Euclidean plane and a discrete set of points is given, then two points of the set are adjacent on the convex hull if and only if their Voronoi cells share an infinitely long side.
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects.. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, [1] although the term "closest point problem" is also used synonymously to the nearest neighbor search.
For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbor interpolation, by assigning the function value at the given point to all the points inside the cell. [3]
Closest pair of points problem, the algorithmic problem of finding two points that have the minimum distance among a larger set of points; Euclidean distance, the minimum length of any curve between two points in the plane; Shortest path problem, the minimum length of a path between two points in a graph
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Choose an interior point and draw edges to the three vertices of the triangle that contains it. Continue this process until all interior points are exhausted. [6] Incremental Algorithm : Sort the points of according to x-coordinates. The first three points determine a triangle.