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Convert authalic, conformal, isometric, or rectifying latitude to geodetic latitude



phi = inverse(converter,lat) returns the geodetic latitude coordinates corresponding to authalic, conformal, isometric, or rectifying latitude coordinates lat.


phi = inverse(converter,lat,angleUnit) specifies the units of output phi.


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Specify conformal latitude coordinates and create a conformal latitude converter. Then, convert the coordinates.

chi = [-90 -67.3637 -44.8077 -22.3643 0 22.3643 44.8077 67.3637 90];
conv = map.geodesy.ConformalLatitudeConverter(wgs84Ellipsoid);
phi = inverse(conv,chi)
phi = 1×9

  -90.0000  -67.5000  -45.0000  -22.5000         0   22.5000   45.0000   67.5000   90.0000

Specify isometric latitude coordinates and convert them to radians. Create an isometric latitude converter. Then, convert the coordinates by specifying the angle unit as 'radians'.

psi = [-Inf -1.6087 -0.87663 -0.40064 0 0.40064 0.87663 1.6087 Inf];
conv = map.geodesy.IsometricLatitudeConverter(wgs84Ellipsoid);
phi = inverse(conv,psi,'radians')
phi = 1×9

   -1.5708   -1.1781   -0.7854   -0.3927         0    0.3927    0.7854    1.1781    1.5708

Input Arguments

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Latitude coordinates to convert, specified as a numeric scalar, vector, matrix, or N-D array.

The interpretation of lat depends on the latitude converter. If the conversion is:

  • authalic, lat represents the variable β (beta).

  • conformal, lat represents χ (chi).

  • isometric, lat represents ψ (psi). lat is a dimensionless number and does not have an angle unit.

  • rectifying, lat represents μ (mu).

For authalic, conformal, and rectifying conversions, the values of lat must be consistent with angleUnit.

Units of latitude coordinates, specified as 'degrees' or 'radians'.

Output Arguments

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Geodetic latitude coordinates, specified as a numeric scalar value, vector, matrix, or N-D array. phi is the same size as lat. If angleUnit is not supplied, phi is in degrees. Otherwise, values of phi are consistent with the units of angleUnit.

Data Types: single | double

Version History

Introduced in R2013a

See Also