GeoGridDirectionDifference
GeoGridDirectionDifference[proj,loc,β]
gives the difference between the angle from north to direction β on the geo grid obtained with projection proj and the actual angle from north to direction β at location loc.
GeoGridDirectionDifference[proj,loc,αβ]
gives the difference between projected and unprojected angles from direction α to direction β.
Details and Options
- Geo grid direction difference is a measure of how much angles between geo directions get expanded or contracted during map projection.
- GeoGridDirectionDifference[proj,loc,αβ] computes the difference angle (-)-(β-α) where α, β are azimuths defined on the Earth at the given location loc, and , are the respective projected bearings on the map.
- GeoGridDirectionDifference[proj,loc,α] is equivalent to GeoGridDirectionDifference[proj,loc,0α].
- GeoGridDirectionDifference[proj,loc] computes the largest absolute value of GeoGridDirectionDifference[proj,loc,αα+90] for any value of α.
- 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".
- GeoGridDirectionDifference threads over its location and direction arguments.
- Possible options of GeoGridDirectionDifference include:
-
GeoModel Automatic model of Earth or a celestial body
Examples
open allclose allBasic Examples (1)
Scope (9)
Compute the geo grid direction difference along the northeast direction for a geo projection at your current geo location:
These are the default values of the parameters of the "Albers" projection:
Specify other values for the parameters of the projection:
Compare any two initial directions with their projected versions:
Specify the azimuth as a number of degrees:
Specify the azimuth as a Quantity angle:
Specify a location using a pair {lat,lon} in degrees:
Use locations with geo position heads:
Specify a location using a geo Entity object:
Compute the geo grid direction difference for a list of different azimuths at the same location:
The input can also be given as a QuantityArray object:
Find the maximum absolute value of the angular difference of perpendicular directions:
Return the projected angular difference of a list of locations in different formats:
GeoGridDirectionDifference can efficiently process values for large numbers of locations:
Options (1)
GeoModel (1)
By default, GeoGridDirectionDifference returns values for a spherical geo model:
Using an ellipsoidal model of Earth produces a slightly different value:
The global scale of the reference model does not affect geo direction distortion:
Properties & Relations (6)
The geo grid direction difference varies periodically with the azimuth, with a period of 180 degrees:
Compute the azimuths of the minimal and maximal geo grid direction differences:
Compute the maximum value of the geo grid direction difference for perpendicular directions:
Check explicitly that the values agree when you compute them numerically:
Take the cylindrical projections, except for those requiring additional parameters or not given in normal aspect:
Choose 100 random geo locations:
Check that cylindrical projections do not distort the perpendicularity of the north and east directions:
Take the conformal projections, except for those requiring additional parameters:
Choose 100 random geo locations:
Check that the geo grid direction difference is zero at all the chosen points:
Flat polar projections have maximal geo grid angle difference at the poles if the azimuths define a meridian:
Possible Issues (1)
Text
Wolfram Research (2019), GeoGridDirectionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.
CMS
Wolfram Language. 2019. "GeoGridDirectionDifference." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.
APA
Wolfram Language. (2019). GeoGridDirectionDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html