Oblique Mercator

 

images\sc_projections_oblique_mercator.gif

 

An oblique cylindrical projection that is conformal but not equal area. The Oblique Mercator for the sphere is equivalent to a regular Mercator projection that has been altered by wrapping a cylinder around the sphere so that it touches the surface along the great circle path chosen for the central line instead of along the Earth's Equator.

 

Manifold provides four forms of the Oblique Mercator:

 

·      Oblique Mercator (A)

·      Oblique Mercator (A, centered)

·      Oblique Mercator (B)

·      Oblique Mercator (B, centered)

 

All four projections use the same formulae, but their initialization rules differ as noted below.

 

Scale

 

True along chosen central line, a great circle at an oblique angle or along two straight lines parallel to central line.

 

Distortion

 

Rapidly increasing distortion away from the great circle central line.

 

Usage

 

Used to map regions, such as the Alaska panhandle, that lie along oblique paths or great circles as opposed to regions that are North-South or East-West in extent. Used for grids on maps of the Alaska panhandle, for mapping in Switzerland, Madagascar and Borneo and for atlas maps of areas with greater extent in an oblique direction.

 

Normally, the Oblique Mercator is used only to show the region near the central line and for a relatively short portion of the central line.

 

Origin

 

Developed in 1900 - 1950 by Rosenmund, Laborde, Hotine and others.

 

Limiting Forms

 

The regular Mercator is the limiting form using the Equator as the central line, while the Transverse Mercator is the limiting form using a meridian as the central line.

 

Options

 

There are four variations of Oblique Mercator in Manifold: A and B variations as well as centered and non-centered versions. These differ from one another in how their options are used to specify the projection.

 

·      A versions take a Center Latitude and two additional points defined by 1st and 2nd Latitude and Longitude.

 

·      B versions take a central point defined by a Center Latitude and Center Longitude together with a Center Line Azimuth.

 

·      Centered versions unproject 0,0 to the center of the projection, while non-centered versions unproject 0,0 to the intersection of the Equator and the Prime Meridian.

 

The Oblique Mercator (B, centered) version is conceptually easiest for many people. To use it, specify the Center Latitude and Center Longitude for the desired center of the map. Specify the Center Line Azimuth to be the bearing line that runs in the approximate line of the main features of the map.

 

For example, the illustration at the beginning of this topic was created using Oblique Mercator (B, centered) using Center Latitude 0 (the Equator), Center Longitude -90 and a Center Line Azimuth of -30. The central point defined by the Center Latitude and Center Longitude is approximately in the middle of the North American and South American landmasses near the Isthmus of Panama. An azimuth of -30 is approximately the angle made drawn through the center of masses of North and South America.

 

The graticule in this example was originally created in a latitude / longitude drawing for the region near North and South America. After projection into Oblique Mercator (B, centered) those portions of the graticule not reasonably near the central line of the projection were very distorted. They were selected and deleted by hand.