Video: A new way to unfold the Earth’s surface produces a new kind of map

Unravelling the world in novel new ways (Image: J van Wijk/The Cartographic Journal/Maney Publishing)

A new technique for unpeeling the Earth’s skin and displaying it on a flat surface provides a fresh perspective on geography, making it possible to create maps that string out the continents for easy comparison, or lump together the world’s oceans into one huge mass of water surrounded by coastlines.

See a gallery of the new maps

“Myriahedral projection” was developed by Jack van Wijk, a computer scientist at the Eindhoven University of Technology in the Netherlands.


“The basic idea is surprisingly simple,” says van Wijk. His algorithms divide the globe’s surface into small polygons that are unfolded into a flat map, just as a cube can be unfolded into six squares.

Cartographers have tried this trick before; van Wijk’s innovation is to up the number of polygons from just a few to thousands. He has coined the word “myriahedral” to describe it, a combination of “myriad” with “polyhedron”, the name for polygonal 3D shapes.

Warping reality

The mathematical impossibility of flattening the surface of a sphere has long troubled mapmakers. “Consider peeling an orange and trying to flatten it out,” says van Wijk. “The surface has to distort or crack.”

Some solutions distort the size of the continents while roughly preserving their shape – the familiar Mercator projection, for instance, makes Europe and North America disproportionately large compared with Africa. Others, like the Peters projection, keep landmasses at the correct relative sizes, at the expense of warping their shapes.

An ideal map would combine the best properties of both, but that is only possible by inserting gaps into the Earth’s surface, resulting in a map with confusing interruptions. Van Wijk’s method makes it possible to direct those cuts in a way that minimises such confusion.

Maps of significance

When generating a map he assigns a “weighting” to each edge on the polyhedron to signal its importance, influencing the placement of the cuts or folds. All the maps are equally accurate, but tweaking the weightings gives dramatically different results.

Assigning more significance to landmass gives a map of all the continents in a line, similar to Buckminster Fuller’s Dymaxion map. Making oceans more important than land produces one giant sea surrounded by the world’s coastlines.

“Now and then you make an unexpected discovery,” says van Wijk. A map that separates land from sea as far as possible, leaving the continents marooned away from a sinuous watery mass, was one such serendipitous result of playing with the algorithm’s parameters.

Projection means prize

“His approach was fresh and innovative,” says Kenneth Field, editor of the British Cartographic Society’s The Cartographic Journal, which recently gave van Wijk the Henry Johns award, which recognises the best mapmaking research paper each year. “He managed to achieve a projection that reduces angular deformation to an absolute minimum and preserves area – not an easy trick,” adds Field, “it was a unanimous decision to give him the prize.”

Van Wijk attributes his success to being somewhat of an outsider. Cartographers typically seek single formulae that can be used to transform the entire globe, he says, while computer scientists look for algorithms that work in small steps and can be more adaptable.

Journal reference: The Cartographic Journal, DOI: 10.1179/000870408×276594