ellipsoidal oblique Mercator
Aspects of: Mercator
Parameters: Center scale factor
Geocart menu class: Cylindric
Oblique aspect of Mercator projection
Meridians and parallels: Two meridians 180° apart are straight lines. Other meridians and parallels are complex curves.
Poles: Points not on the central line
Symmetry: About either straight meridian
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
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.
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
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.
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
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.