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  2. Geographical distance - Wikipedia

    en.wikipedia.org/wiki/Geographical_distance

    Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...

  3. Vincenty's formulae - Wikipedia

    en.wikipedia.org/wiki/Vincenty's_formulae

    As noted above, the iterative solution to the inverse problem fails to converge or converges slowly for nearly antipodal points. An example of slow convergence is (Φ 1, L 1) = (0°, 0°) and (Φ 2, L 2) = (0.5°, 179.5°) for the WGS84 ellipsoid. This requires about 130 iterations to give a result accurate to 1 mm. Depending on how the inverse ...

  4. Cost distance analysis - Wikipedia

    en.wikipedia.org/wiki/Cost_distance_analysis

    It is thus based on the fundamental geographic principle of Friction of distance. It is an optimization problem with multiple deterministic algorithm solutions, implemented in most GIS software. The various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two-dimensional space, meaning that a path could be ...

  5. Proximity analysis - Wikipedia

    en.wikipedia.org/wiki/Proximity_analysis

    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]

  6. Great-circle navigation - Wikipedia

    en.wikipedia.org/wiki/Great-circle_navigation

    For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R. Likewise, the vertex, the point on the great circle with greatest latitude, is found by substituting σ = + 1 ⁄ 2 π. It may be convenient to parameterize the ...

  7. Outline of trigonometry - Wikipedia

    en.wikipedia.org/wiki/Outline_of_trigonometry

    Hansen's problem; Snellius–Pothenot problem; Great-circle distance – how to find that distance if one knows the latitude and longitude. Resection (orientation) Vincenty's formulae; Geographic distance; Triangulation in three dimensions

  8. Position resection and intersection - Wikipedia

    en.wikipedia.org/wiki/Position_resection_and...

    Position resection and intersection are methods for determining an unknown geographic position (position finding) by measuring angles with respect to known positions.In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.

  9. Erdős distinct distances problem - Wikipedia

    en.wikipedia.org/wiki/Erdős_distinct_distances...

    In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 [ 1 ] [ 2 ] and almost proven by Larry Guth and Nets Katz in 2015.