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 types listed below:
Latitude Type | Description |
---|---|
| 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. |
| 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. |
| 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. |
| 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. |
| The isometric latitude is a nonlinear function of the geodetic latitude. |
| 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. |
| The rectifying latitude is used to map an ellipsoid to a sphere in such a way that distance is preserved along meridians. |
latin
has the angle units specified by units
:
either 'degrees'
or 'radians'
.
The output array, latout
, has the same size and
units as latin
.
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');
Version History
Introduced before R2006a
See Also
referenceEllipsoid
| referenceSphere
| oblateSpheroid
| rsphere