GeoGridUnitDistance

GeoGridUnitDistance[proj,loc,α]

gives the actual geo distance corresponding to a unit distance on the geo grid obtained with projection proj, evaluated in the limit of small displacement from location loc in direction α.

Details and Options

  • The inverse of geo grid unit distance is also known as point scale or particular scale.
  • GeoGridUnitDistance combines the global nominal scale (the shrinking factor of the geo model to the reference model of the map, traditionally denoted as 1:125000 and similar) and the local distortion of scale induced by the geo projection.
  • The result of GeoGridUnitDistance[] corresponds to a ratio of Quantity geo distances on the geo model (of Earth or any other body) and dimensionless distances of the projected geo grid.
  • Points of maps including large regions ("large-scale maps") correspond to large values of geo distance scale, and points of "small-scale maps" correspond to small values of geo distance scale.
  • If geo grid unit distance is independent of azimuth at a point, then it is said to be isotropic at that point. A geo projection is conformal if and only if geo grid unit distance is isotropic at all points, though its value may still vary from point to point.
  • A geo projection can be given as a named projection "proj" with default parameters or as {"proj",params}, where "proj" is any of the entities of GeoProjectionData and params are parameter rules like "StandardParallels"->{33,60}. GeoProjectionData["proj"] gives the default values of the parameters for the projection "proj".
  • The location loc can be given as a coordinate pair {lat,lon} in degrees, a geo position object like GeoPosition[] or GeoGridPosition[] or as a geo entity Entity[].
  • The bearing or azimuthal direction α is an angle measured clockwise from true north. It can be given as a Quantity angle, as a number in degrees or as a named compass direction like "North", "NE" or "NEbE".
  • GeoGridUnitDistance threads over its location and direction arguments.
  • Possible options of GeoGridUnitDistance include:
  • GeoModelAutomaticmodel of Earth or a celestial body
    UnitSystem$UnitSystemunit system to use in the result

Examples

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Basic Examples  (2)

Compute the unit geo distance induced by the Mercator projection at Copenhagen in the northeast direction:

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Compute the final position of a geodesic of that length starting from Copenhagen in the northeast direction:

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Compare the geo path joining those locations with the map units and the scale bar:

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If map units are made to correspond to inches, the traditional scale notation is 1:2468243, as given by the following:

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Use the Mollweide projection to construct a flat map based on a reference sphere of radius 6371:

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Then a unit of projected distance at London corresponds to a geo distance between these two values:

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Scope  (9)

Options  (2)

Properties & Relations  (11)

Possible Issues  (1)

Neat Examples  (1)

Introduced in 2019
(12.0)