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:

$x = 0.8707 \times l(\varphi) \times \lambda$,

$y = 0.8707 \times 0.52 \times d(\varphi) \times \pi$,

where

• $x$, $y$ are the Cartesian coordinates;
• $\lambda$ is the longitude from the central meridian;
• $\varphi$ is the latitude;
• $l(\varphi)$ is the length of the parallel at latitude $\varphi$;
• $d(\varphi)$ is the distance of the parallel from the equator at latitude $\varphi$.

$l(\varphi)$ and $d(\varphi)$ are given in this table:

$\varphi$ (degrees)	$l(\varphi)$	$d(\varphi)$
0	1	0
5	0.9988	0.062
10	0.9953	0.124
15	0.9894	0.186
20	0.9811	0.248
25	0.9703	0.31
30	0.957	0.372
35	0.9409	0.434
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	0.716	0.8936
80	0.6754	0.9394
85	0.627	0.9761
90	0.563	1

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

• Robinson projection
• Winkel tripel projection
• Kavrayskiy VII

References

• http://www.shadedrelief.com/NE_proj/
• http://cartography.oregonstate.edu/pdf/2011_Savric_etal_PolynomialNaturalEarth.pdf