A new technique for unpeeling the Earth鈥檚 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鈥檚 oceans into one huge mass of water surrounded by coastlines.
鈥淢yriahedral projection鈥� was developed by , a computer scientist at the Eindhoven University of Technology in the Netherlands.
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鈥淭he basic idea is surprisingly simple,鈥� says van Wijk. His algorithms divide the globe鈥檚 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鈥檚 innovation is to up the number of polygons from just a few to thousands. He has coined the word 鈥渕yriahedral鈥� to describe it, a combination of 鈥渕yriad鈥� with 鈥減olyhedron鈥�, the name for polygonal 3D shapes.
Warping reality
The mathematical impossibility of flattening the surface of a sphere has long troubled mapmakers. 鈥淐onsider peeling an orange and trying to flatten it out,鈥� says van Wijk. 鈥淭he surface has to distort or crack.鈥�
Some solutions distort the size of the continents while roughly preserving their shape 鈥� the familiar , for instance, makes Europe and North America disproportionately large compared with Africa. Others, like the , 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鈥檚 surface, resulting in a map with confusing interruptions. Van Wijk鈥檚 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 鈥渨eighting鈥� 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鈥檚 . Making oceans more important than land produces one giant sea surrounded by the world鈥檚 coastlines.
鈥淣ow and then you make an unexpected discovery,鈥� 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鈥檚 parameters.
Projection means prize
鈥淗is approach was fresh and innovative,鈥� says Kenneth Field, editor of the British Cartographic Society鈥檚 The Cartographic Journal, which recently gave van Wijk the , which recognises the best mapmaking research paper each year. 鈥淗e managed to achieve a projection that reduces angular deformation to an absolute minimum and preserves area 鈥� not an easy trick,鈥� adds Field, 鈥渋t was a unanimous decision to give him the prize.鈥�
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.
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