Hammer retroazimuthal projection

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The front hemisphere of the Hammer retroazimuthal projection. 15deg graticule; center point at 45degN, 90degW. Hammer retroazimuthal projection front SW.JPG
The front hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.
The back hemisphere of the Hammer retroazimuthal projection. 15deg graticule; center point at 45degN, 90degW. Hammer retroazimuthal projection back SW.JPG
The back hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.
The full Hammer retroazimuthal projection centered on Mecca, with Tissot's indicatrix of deformation. Back hemisphere has been rotated 180deg to avoid overlap. Hammer Retroazimuthal with Tissot's Indicatrices of Distortion.svg
The full Hammer retroazimuthal projection centered on Mecca, with Tissot's indicatrix of deformation. Back hemisphere has been rotated 180° to avoid overlap.

The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point. [1] Additionally, all distances from the center of the map are proportional to what they are on the globe. In whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function. The back hemisphere can be rotated 180° to avoid overlap, but in this case, any azimuths measured from the back hemisphere must be corrected.

Contents

Given a radius R for the projecting globe, the projection is defined as:

where

and

The latitude and longitude of the point to be plotted are φ and λ respectively, and the center point to which all azimuths are to be correct is given as φ1 and λ0.

See also

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References

  1. Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. Chicago: University of Chicago Press. pp. 228–229. ISBN   0-226-76747-7 . Retrieved 2011-11-14.