## Geocart Projections

What is a projection?

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Hotine

ellipsoidal oblique Mercator

Aspects of: Mercator

Parameters: Scale factor along central meridian

Classifications

Oblique aspect of Mercator projection
Cylindrical
Conformal

Graticule

Meridians and parallels: Two meridians 180° apart are straight lines. Other meridians and parallels are complex curves.
Poles: Points not on the central line

Scale

True along a chosen central line (a great circle at an oblique angle) or along two straight lines on the map parallel to the central line Constant along any straight line parallel to the central line (The scale for the projection of the ellipsoid varies slightly from these patterns.)
Increases with distance from the central line
Becomes infinite 90° from the central line

Other features

Conceptually projected onto a cylinder wrapped around the globe tangent to an oblique great circle or secant along two small circles equidistant from and on each side of the central great circle
Cannot be geometrically (or perspectively) projected
There are various means of adapting to the ellipsoid, but none can simultaneously maintain both perfect conformality and constant scale along the central line.

Usage

Large-scale mapping in Switzerland, Madagascar, and Borneo
Atlas maps of regions having greater extent in an oblique direction, such as Hawaii
Recommended for conformal mapping of regions having predominant extent in oblique direction, neither east-west nor north-south

Origin

Developed for various applications, chiefly large-scale mapping of the ellipsoid, by M. Rosenmund of Switzerland in 1903, J. Laborde of France in 1928, Martin Hotine of England in 1947, and others during the 20th century.

Other names

Rectified Skew Orthomorphic (when using Hotine's formulas)
Laborde (when using Laborde's formulas)
Hotine Oblique Mercator (when using Hotine's formulas)
Oblique Cylindrical Orthomorphic

Limiting forms

Mercator, if the Equator is the central line
Transverse Mercator, if a meridian is the central line

Description adapted from J.P. Snyder and P.M. Voxland, An Album of Map Projections, U.S. Geological Survey Professional Paper 1453. United States Government Printing Office: 1989.