General Oblique Transformation

Classification

Cylindrical

Available forms

Forward and inverse, spherical and ellipsoidal

Defined area

Global

Alias

ob_tran

Domain

2D

Input type

Geodetic coordinates

Output type

Projected coordinates

General Oblique Transformation

proj-string: +proj=ob_tran +o_proj=moll +o_lon_p=40 +o_lat_p=50 +lon_0=60

Usage

All of the projections of spherical library can be used as an oblique projection by means of the General Oblique Transformation. The user performs the oblique transformation by selecting the oblique projection +proj=ob_tran, specifying the translation factors, +o_lat_p, and +o_lon_p, and the projection to be used, +o_proj. In the example of the Fairgrieve projection, the latitude and longitude of the North pole of the unrotated geographic CRS, \(\alpha\) and \(\beta\) respectively, expressed in the rotated geographic CRS, are to be placed at 45°N and 90°W and the Mollweide projection is used. Because the central meridian of the translated coordinates will follow the \(\beta\) meridian it is necessary to translate the translated system so that the Greenwich meridian will pass through the center of the projection by offsetting the central meridian.

The final control for this projection is:

+proj=ob_tran +o_proj=moll +o_lat_p=45 +o_lon_p=-90 +lon_0=-90

Parameters

Required

+o_proj=<projection>

Oblique projection.

In addition to specifying an oblique projection, how to rotate the projection should be specified. This is done in one of three ways: Define a new pole, rotate the projection about a given point or define a new “equator” spanned by two points on the sphere. See the details below.

New pole

+o_lat_p=<latitude>

Latitude of the North pole of the unrotated source CRS, expressed in the rotated geographic CRS.

+o_lon_p=<longitude>

Longitude of the North pole of the unrotated source CRS, expressed in the rotated geographic CRS.

Rotate about point

+o_alpha=<value>

Angle to rotate the projection with.

+o_lon_c=<value>

Longitude of the point the projection will be rotated about.

+o_lat_c=<value>

Latitude of the point the projection will be rotated about.

New “equator” points

+o_lon_1=<value>

Longitude of first point.

+o_lat_1=<value>

Latitude of first point.

+o_lon_2=<value>

Longitude of second point.

+o_lat_2=<value>

Latitude of second point.

Optional

+lon_0=<value>

Longitude of projection center.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the “r” character.

Example: +lon_0=1.5708r

See Projection Units for more information.

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.

+x_0=<value>

False easting.

Defaults to 0.0.

+y_0=<value>

False northing.

Defaults to 0.0.