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Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between and , between and , and between and ; the distance in terms of the original coordinates is the ...
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
MapQuest Find Me let users automatically find their location, access maps and directions and locate nearby points of interest, including airports, hotels, restaurants, banks and ATMs. Users also had the ability to set up alerts to be notified when network members arrive at or depart from a designated area.
The square root appearing above can be eliminated for such applications as ordering locations by distance in a database query. On the other hand, some methods for computing nearest neighbors, such as the vantage-point tree, require that the distance metric obey the triangle inequality, in which case the square root must be retained.
Pathfinding or pathing is the search, by a computer application, for the shortest route between two points. It is a more practical variant on solving mazes . This field of research is based heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph .
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.
Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol. 3 of The Art of Computer Programming (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post ...
Difference in longitude of the points on the auxiliary sphere; α 1, α 2: forward azimuths at the points; α: forward azimuth of the geodesic at the equator, if it were extended that far; s: ellipsoidal distance between the two points; σ: angular separation between points: σ 1: angular separation between the point and the equator: σ m
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