Loximuthal is a compromise pseudocylindrical projection. Loxodromes, or rhumb lines, are shown as straight lines with the correct azimuth and scale from the intersection of the central meridian and the central parallel.
The loximuthal projection was first presented by Karl Siemon in 1935. Waldo R. Tobler independently introduced the projection in 1966 and named it loximuthal. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
The subsections below describe the loximuthal projection properties.
Loximuthal is a pseudocylindric projection. The meridians are regularly distributed complex curves. They are concave toward the central meridian, which is projected as a straight line. The parallels are equally distributed straight lines perpendicular to the central meridian. The poles are presented as points. For most central parallels, the projection outline forms a pumpkin shape. The graticule is symmetric across the central meridian.
The loximuthal projection is neither conformal nor equal area. It generally distorts shapes, areas, distances, directions, and angles. Scale is true along the central meridian, and it is constant along a latitude. Only the point of intersection of the central meridian and the central parallel is free of distortion. As the value of the central parallel increases from the equator, the overall shape of the world becomes more distorted. Distortion values are symmetric only across the central meridian.
The loximuthal projection is useful to show loxodromes only.
The loximuthal projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius.
Loximuthal parameters are as follows:
- False Easting
- False Northing
- Central Meridian
- Central Parallel 1
Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.
Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.