Natural Earth projection
Natural Earth projection of the world.
The Natural Earth projection is a pseudocylindrical map projection designed by Tom Patterson. It is neither conformal nor equal-area.
Definition
The Natural Earth is defined by the following formulas:
- ,
where
- x, y are the Cartesian coordinates;
- λ is the longitude from the central meridian;
- φ is the latitude;
- l(φ) is the length of the parallel at latitude φ;
- d(φ) is the distance of the parallel from the equator at latitude φ.
l(φ) and d(φ) are given in this table:
| φ (degrees) | l(φ) | d(φ) |
|---|---|---|
| 0 | 1.0000 | 0.0000 |
| 5 | 0.9988 | 0.0620 |
| 10 | 0.9953 | 0.1240 |
| 15 | 0.9894 | 0.1860 |
| 20 | 0.9811 | 0.2480 |
| 25 | 0.9703 | 0.3100 |
| 30 | 0.9570 | 0.3720 |
| 35 | 0.9409 | 0.4340 |
| 40 | 0.9222 | 0.4958 |
| 45 | 0.9006 | 0.5571 |
| 50 | 0.8763 | 0.6176 |
| 55 | 0.8492 | 0.6769 |
| 60 | 0.8196 | 0.7346 |
| 65 | 0.7874 | 0.7903 |
| 70 | 0.7525 | 0.8435 |
| 75 | 0.7160 | 0.8936 |
| 80 | 0.6754 | 0.9394 |
| 85 | 0.6270 | 0.9761 |
| 90 | 0.5630 | 1.0000 |
The values of the above functions for other latitudes are calculated by interpolation. The values for the southern hemisphere are calculated by changing the sign of the corresponding values for the northern hemisphere.
See also
References
- http://www.shadedrelief.com/NE_proj/
- http://cartography.oregonstate.edu/pdf/2011_Savric_etal_PolynomialNaturalEarth.pdf
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