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# convertlat

Convert between geodetic and auxiliary latitudes

## Syntax

latout = convertlat(ellipsoid,latin,from,to,units)

## Description

latout = convertlat(ellipsoid,latin,from,to,units) converts latitude values in latin from type FROM to type TO. ellipsoid is a referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity].

latin is an array of input latitude values. from and to are each one of the latitude type strings listed below (or unambiguous abbreviations). latin has the angle units specified by units: either 'degrees', 'radians', or unambiguous abbreviations. The output array, latout, has the same size and units as latin.

Latitude Type

Description

geodetic

The geodetic latitude is the angle that a line perpendicular to the surface of the ellipsoid at the given point makes with the equatorial plane.

authalic

The authalic latitude maps an ellipsoid to a sphere while preserving surface area. Authalic latitudes are used in place of the geodetic latitudes when projecting the ellipsoid using an equal area projection.

conformal

The conformal latitude maps an ellipsoid conformally onto a sphere. Conformal latitudes are used in place of the geodetic latitudes when projecting the ellipsoid with a conformal projection.

geocentric

The geocentric latitude is the angle that a line connecting a point on the surface of the ellipsoid to its center makes with the equatorial plane.

isometric

The isometric latitude is a nonlinear function of the geodetic latitude.

parametric

The parametric latitude of a point on the ellipsoid is the latitude on a sphere of radius a, where a is the semimajor axis of the ellipsoid, for which the parallel has the same radius as the parallel of geodetic latitude.

rectifying

The rectifying latitude is used to map an ellipsoid to a sphere in such a way that distance is preserved along meridians.

To properly project rectified latitudes, the radius must also be scaled to ensure the equal meridional distance property. This is accomplished by rsphere.

## Examples

```% Plot the difference between the auxiliary latitudes
% and geocentric latitude, from equator to pole,
% using the GRS 80 ellipsoid. Avoid the polar region with
% the isometric latitude, and scale down the difference
% by a factor of 200.
grs80 = referenceEllipsoid('grs80');
geodetic = 0:2:90;
authalic = ...
convertlat(grs80,geodetic,'geodetic','authalic', 'deg');
conformal = ...
convertlat(grs80,geodetic,'geodetic','conformal', 'deg');
geocentric = ...
convertlat(grs80,geodetic,'geodetic','geocentric','deg');
parametric = ...
convertlat(grs80,geodetic,'geodetic','parametric','deg');
rectifying = ...
convertlat(grs80,geodetic,'geodetic','rectifying','deg');
isometric = ...
convertlat(grs80,geodetic(1:end-5), ...
'geodetic','isometric','deg');
plot(geodetic, (authalic - geodetic),...
geodetic, (conformal - geodetic),...
geodetic, (geocentric - geodetic),...
geodetic, (parametric - geodetic),...
geodetic, (rectifying - geodetic),...
geodetic(1:end-5), (isometric - geodetic(1:end-5))/200);
title('Auxiliary Latitudes vs. Geodetic')
xlabel('geodetic latitude, degrees')
ylabel('departure from geodetic, degrees');
legend('authalic','conformal','geocentric', ...
'parametric','rectifying', 'isometric/200',...
'Location','NorthWest');```