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The markings were then repeated by a second set at right angles to the first. Depending on usage, the marked scale numbers could refer to distance or speed. A second disc was marked with a circular scale all around the edge labelled in degrees, with radial lines from the centre of the disc stretching out every ten degrees.
The distance along the great circle will then be s 12 = Rσ 12, where R is the assumed radius of the Earth and σ 12 is expressed in radians. Using the mean Earth radius, R = R 1 ≈ 6,371 km (3,959 mi) yields results for the distance s 12 which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for details.
The contraction hierarchies (CH) algorithm is a two-phase approach to the shortest path problem consisting of a preprocessing phase and a query phase.As road networks change rather infrequently, more time (seconds to hours) can be used to once precompute some calculations before queries are to be answered.
Proximity analysis is a class of spatial analysis tools and algorithms that employ geographic distance as a central principle. [1] Distance is fundamental to geographic inquiry and spatial analysis, due to principles such as the friction of distance, Tobler's first law of geography, and Spatial autocorrelation, which are incorporated into analytical tools. [2]
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.