The Loximuthal projection is a pseudocylindrical projection that is neither conformal nor equal area. It was presented by Karl Siemon in 1935, and independently as “Loximuthal” by Waldo R. Tobler. This projection has the special feature that loxodromes (rhumb lines) from the central point (the intersection of the central meridian and central latitude) are shown straight, true to scale, and correct in azimuth from the center. The azimuths with respect to other points along a rhumb line, however, are not shown correctly, due to angular distortion on the map projection.
The central meridian in the Loximuthal projection is a straight line generally over half as long as the Equator (depending on the central latitude). Other meridians are depicted as equally spaced complex curves that are concave toward the central meridian and which intersect at the poles. The parallels are equally spaced straight parallel lines running perpendicular to the central meridian. The poles are represented as points. The projection in symmetrical about the central meridian, and around the Equator in the case where the central latitude is the Equator. Scale is true along the central meridian, and is constant along any given latitude. Distortion varies from moderate to extreme, and is absent only at the intersection of the central latitude and central meridian.
The "Loximuthal" Projection has the following Parameters:
Parameter Name 
Parameter String 
Units 
Longitude of the Center of the Projection 
central_meridian 

Latitude of the Origin of the Projection 
latitude_of_origin 

False Easting 
false_easting 

False Northing 
false_northing 
NOTE: Only a spherical form of this projection is used. The semimajor axis of the ellipsoid (sphere) is used for forward and inverse projection from grid to geodetic coordinates within the system wherein this projection is incorporated.