Lenticular Projections

AITOFF

The Aitoff projection is a modified azimuthal projection that is neither conformal nor equal area. It was developed by David Aitoff (or Altow) in 1889. The central meridian is a straight line half the length of the Equator. Other meridians are equally spaced along the Equator and concave toward the central meridian. The Equator is straight. Other parallels are equally spaced along the central meridian and concave toward the nearest pole. The poles are represented by points. This projection is symmetrical about the Equator and the central meridian. Scale is true along the Equator and the central meridian. This projection is supported on spheres only.

Parameters: 

Usage:
World maps.

Notes:

Only a spherical form of this projection is used. The semi-major axis of the ellipsoid specified in the coordinate system datum definition is used as sphere radius.

HAMMER AITOFF

The Hammer Aitoff (or simply Hammer) projection is a modified azimuthal projection that is equal area.

H.H. Ernst von Hammer developed it in 1892.

The central meridian is depicted as a straight line half the length of the Equator. Other meridians are depicted as complex curves, unequally spaced along the Equator and concave toward the central meridian. The Equator is straight. Other parallels are depicted as complex curves, unequally spaced along the central meridian and concave toward the nearest pole. The poles themselves are represented by points. This projection is symmetrical about the central meridian and the Equator. Scale decreases along the central meridian and the Equator as you move away from the centre.

This projection has moderate distortion, with less shearing action on the outer meridians near the poles than may be found in pseudocylindrical projections.

Parameters: 

Usage:
Thematic world maps.

Notes:

Only a spherical form of this projection is used. The semi-major axis of the ellipsoid specified in the coordinate system datum definition is used as sphere radius.

WINKEL TRIPEL

The Winkel Tripel projection is a modified azimuthal projection that is neither conformal nor equal area. Oswald Winkel developed it in 1921 as the average of the Aitoff and Equidistant Cylindrical (Equirectangular) projections.

In this projection, the central meridian is a straight line. Other meridians are equally spaced along the Equator and are concave toward the central meridian. The Equator and the poles are straight lines, while all other parallels are curves, equally spaced along the central meridian and concave toward the nearest pole. Scale is true along the central meridian and constant along the Equator. Distortion is moderate, except near the outer meridians in the polar regions.

Parameters: 

Usage:
World maps.

Notes:

Only a spherical form of this projection is used. The semi-major axis of the ellipsoid specified in the coordinate system datum definition is used as sphere radius.