inverse

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

Syntax

phi = inverse(converter,lat)

phi = inverse(converter,lat,angleUnit)

Description

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.

Examples

Convert Conformal Latitude to Geodetic Latitude

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

Convert Isometric Latitude to Geodetic Latitude Using Radians

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

converter — Latitude converter

AuthalicLatitudeConverter, ConformalLatitudeConverter, IsometricLatitudeConverter, or RectifyingLatitudeConverter object

Latitude converter, specified as an AuthalicLatitudeConverter, ConformalLatitudeConverter, IsometricLatitudeConverter, or RectifyingLatitudeConverter object.

lat — Latitude coordinates to convert

numeric scalar, vector, matrix, or N-D array

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.

angleUnit — Unit of latitude coordinates

'degrees' (default) | 'radians'

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

Output Arguments

phi — Geodetic latitude coordinates

numeric scalar, vector, matrix, or N-D array

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