Hammer projection

The Hammer Aitov projection (also Hammer Aitoff projection or only called Hammer projection ) is a 1892 proposed by Ernst Hammer equal-area map projection showing the entire Earth as an ellipse. It is based on the Aitov projection of Dawid Aitow, but is in contrast to those areas instead of isometrically. Hammer used a Lambert Azimuthal instead of the mitt distance loyal Azimuthal.

Equator and central meridian are reproduced to scale and as a straight line, with increasing distance from this but so does the distortion to very strong. Usually, the zero meridian of the central meridian.

Other longitude and latitude circles are shown as curves. The central meridian the opposite meridian forms the outer edge of the map.

The distortions in the Polgegenden are not as strong as with the similar looking Mollweide.

Formulas

And wherein the x and y components of the true surface Lambertian are Azimuthal. Written out:

The inverse of projection is determined via an intermediate variable:

Longitude and latitude can be calculated as follows:

With the longitude and the latitude. The mapping space is in the range and. From the area of the resulting ellipse equation, this results in the area

As the imaging surface of the unit sphere. This corresponds to the result of the spherical surface equation with r = 1

To get real metric sizes, the x -and y- values ​​must be multiplied by the radius of the Earth.