Interactive Design of World Map Projections

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Map Projection Design with Flex Projector

Flex Projector is a software application for designing new map projections for world maps. The design of new map projections has until now required mathematical expertise that limited this activity to a small group of specialists. Flex Projector enables cartographers to easily design new world map projections. A new projection is designed interactively in an iterative process, which allows the designer to graphically and numerically assess the representation of the continents and the graticule (the network of lines of latitude and longitude upon which a map is drawn).

The length and vertical distribution of parallels, as well as the concave or convex bending of parallels, and the distribution of meridians can be adjusted interactively. New projections can be generated from scratch, or existing ones can be changed.

A projection mixer allows for blending two projections to create a new projection. Flex Projector also offers complementary visualizations and numerical evaluation methods that illustrate the distribution and amount of the inevitable areal and angular distortion and help the projection designer optimize a projection.

Šavrič, B., Jenny, B., White, D. and Strebe D. R. (2015).
User preferences for world map projections.
Cartography and Geographic Information Science, 42-5, p. 398–409.
DOI: 10.1080/15230406.2015.1014425

Jenny, B., Patterson, T. and Hurni, L. (2011)
Graphischer Netzentwurf für Weltkarten mit Flex Projector – Graphic map projection [design] for world maps with Flex Projector.
Kartographische Nachrichten, 61-3, p. 133–139 [German].

Jenny, B. and Patterson, T. (2013)
Blending world map projections.
Cartography and Geographic Information Science, 40-4, p. 289–296.

Jenny, B., Patterson, T. and Hurni, L. (2010)
Graphical design of world map projections.
International Journal of Geographical Information Science, 24-11, p. 1687–1702.

Jenny, B., Patterson, T. and Hurni L. (2008)
Flex Projector—Interactive software for designing world map projections.
Cartographic Perspectives, 59, p. 12–27.

Natural Earth I and II Projections

The Natural Earth projection is a pseudocylindrical projection with a balanced appearance of major landmasses. The corners, where the pole lines and bounding meridians meet, were given a rounded appearance. The rounded corners suggest that the projection represents a spherical earth, and reduce the size of polar areas, thereby reducing the areal exaggeration of Antarctica.

The Natural Earth Projection was designed by Tom Patterson, US National Park Service using Flex Projector. Bojan Šavrič derived a polynomial equation. This equation is very simple to implement and fast to evaluate.
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Natural Earth

Šavrič, B., Patterson, T. and Jenny, B. (2015).
The Natural Earth II world map projection.
International Journal of Cartography, 1(2), 123–133.
DOI: 10.1080/23729333.2015.1093312

Natural Earth Projection Tool for ArcMap is a free toolbox for ArcMap that projects shapefiles to the Natural Earth or Natural Earth II projection.

Šavrič, B., Jenny, B., Patterson, T., Petrovič, D. and Hurni, L. (2011)
A polynomial equation for the Natural Earth projection.
Cartography and Geographic Information Science, 38-4, p. 363–372.

Hufnagel’s Pseudcylindric Map Projection Family

In 1989, Herbert Hufnagel introduced a generalization of the Mollweide projection, resulting in a family of pseudocylindrical equal-area projections. The Mollweide, Eckert Ⅳ and Wagner Ⅳ projections are members of this family. Explore Hufnagel’s projection with this interactive tool at

Jenny, B., Šavrič, B. and Strebe, D. R. (2017).
A computational method for the Hufnagel pseudocylindric map projection family.
Cartography and Geographic Information Science, 44(1), 86–94.
DOI: 10.1080/15230406.2015.1128853
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Code Libraries


The Java Map Projection Library JMapProjLib, a Java port of the popular PROJ.4 map projection library, was developed as part of this project. JMapProjLib was initiated by Jerry Huxtable. Most projections of PROJ.4 are implemented.


CanvasMap is JavaScript library for experimenting with map projection equations. It reads shapefiles and renders world maps with HTML5 Canvas. It is used to illustrate projection transformations here. Code is available on GitHub.