Natural Earth projection

From Wikipedia
https://en.wikipedia.org/wiki/Natural_Earth_projection
Natural Earth projection of the world.
The natural Earth projection with Tissot's indicatrix of deformation

The Natural Earth projection is a pseudocylindrical map projection designed by Tom Patterson and introduced in 2012. It is neither conformal nor equal-area, but a compromise between the two.

It was designed in Flex Projector, a specialized software application that offers a graphical approach for the creation of new projections. [1] [2]

Definition

The natural Earth is defined by the following formulas:

,

where

  • x∈[-2.73539, 2.73539] and y∈[-1.42239, 1.42239] are the Cartesian coordinates;
  • 𝜆∈[-π, π] is the longitude from the central meridian in radians;
  • φ∈[-π/2, π/2] is the latitude in radians;
  • 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 as polynomials: [3]

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". [1]

See also

References

  1. ^ a b 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.
  2. ^ Jenny, Bernhard; Patterson, Tom; Hurni, Lorenz (2008). "Flex Projector–Interactive Software for Designing World Map Projections". Cartographic perspectives. Retrieved January 24, 2020.
  3. ^ "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.