A polynomial equation for the natural earth projection

Savric, B, Jenny, B, Patterson, T, Petrovic, D and Hurni, L 2011, 'A polynomial equation for the natural earth projection', Cartography and Geographic Information Science, vol. 38, no. 4, pp. 363-372.


Document type: Journal Article
Collection: Journal Articles

Title A polynomial equation for the natural earth projection
Author(s) Savric, B
Jenny, B
Patterson, T
Petrovic, D
Hurni, L
Year 2011
Journal name Cartography and Geographic Information Science
Volume number 38
Issue number 4
Start page 363
End page 372
Total pages 10
Publisher Taylor and Francis
Abstract The Natural Earth projection is a new projection for representing the entire Earth on small-scale maps. It was designed in Flex Projector, a specialized software application that offers a graphical approach for the creation of new projections. The original Natural Earth projection defines the length and spacing of parallels in tabular form for every five degrees of increasing latitude. It is a pseudocylindrical projection, and is neither conformal nor equal-area. In the original definition, piece-wise cubic spline interpolation is used to project intermediate values that do not align with the five-degree grid. This paper introduces alternative polynomial equations that closely approximate the original projection. The polynomial equations are considerably simpler to compute and program, and require fewer parameters, which should facilitate the implementation of the Natural Earth projection in geospatial software. The polynomial expression also improves the smoothness of the rounded corners where the meridians meet the horizontal pole lines, a distinguishing trait of the Natural Earth projection that suggests to readers that the Earth is spherical in shape. Details on the least squares adjustment for obtaining the polynomial formulas are provided, including constraints for preserving the geometry of the graticule. This technique is applicable to similar projections that are defined by tabular parameters. For inverting the polynomial projection the Newton-Raphson root finding algorithm is suggested.
Subject Cartography
Geospatial Information Systems
Keyword(s) Projections
Natural Earth projection
Flex Projector
DOI - identifier 10.1559/15230406384363
Copyright notice © 2011 Cartography and Geographic Information Society. All rights reserved.
ISSN 1523-0406
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Citation counts: TR Web of Science Citation Count  Cited 10 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 9 times in Scopus Article | Citations
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