Natural Earth projection
This article is missing information about distortion, software support and the polynomial.(February 2017)
The natural Earth is defined by the following formulas:
- and are the Cartesian coordinates;
- is the longitude from the central meridian in radians;
- is the latitude in radians;
- is the length of the parallel at latitude ;
- is the distance of the parallel from the equator at latitude .
and are given as polynomials:
In the original definition of the projection, planar coordinates were lineally interpolated from a table of 19 latitudes and then multiplied by other factors. The authors of the projection later provided a polynomial representation that closely matches the original but improves smoothness at the "corners".
- Šavrič, Bojan; Jenny, Bernhard; Patterson, Tom; Petrovič, Dušan; Hurni, Lorenz (February 17, 2012). "A Polynomial Equation for the Natural Earth Projection" (PDF). Oregon State University. Archived from the original (PDF) on 2016-03-03. Retrieved January 24, 2020.
- Jenny, Bernhard; Patterson, Tom; Hurni, Lorenz (2008). "Flex Projector–Interactive Software for Designing World Map Projections". Cartographic perspectives. Retrieved January 24, 2020.
- "Natural Earth Projection: Home". www.shadedrelief.com. Archived from the original on 2012-04-07. Retrieved 2017-02-12.
It was originally designed in Flex Projector using graphical methods and now exists as a polynomial version.