Derivation of a Polynomial Equation for the Natural Earth projection

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Dušan Petrovič (University of Ljubljana)

Bernhard Jenny (ETH Zürich)

Lorenz Hurni (ETH Zürich)

University of Ljubljana, Faculty of Civil and Geodetic Engineering

ETH Zürich, Institute of Cartography and Geoinformation

31. August 2011

The original Natural Earth projection defines the length and spacing of parallels in a tabular form for every five degrees of increased latitude. To project all intermediate values, the piece-wise cubic spline interpolation is used.

This graduation thesis introduced alternative polynomial equations that are simpler to compute. The polynomial expression also smoothed the rounded corners where the meridians meet the horizontal pole lines, a distinguishing mark of the Natural Earth projection.