A New World Projection

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A New World Projection

How wonderful, my old mental Mercator must go!



https://www.sott.net/article/333120-Japanese-origami-cartography-leaves-design-world-spinning-world-map-accurate-in-2D-and-3D

"This original mapping method can transfer a spherical surface to a rectangular surface as a map of the world while maintaining correctly proportions in areas," according to the Good Design Award website. (https://www.g-mark.org/award/describe/44527)

But the AuthaGraph isn't absolutely perfect. According to the Good Design Awards: "The map needs a further step to increase a number of subdivision for improving its accuracy to be officially called an area-equal map."

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Wow...that's really cool.

Not sure what's happening here. This hasn't been an issue with modern UV-mapping since I started doing graphics, although the stretch factor is likely still in play. But his map doesn't line up in any way with the globe, as we know it. Quick comparison to a standard spherical globe-map. His poles don't even line up.




These four views per Earth-map are the two horizontals and the two poles. I understand he's trying to map it better, but his equator isn't even correct.

This projection converts spherical coordinates to rectangular coordinates. It is not supposed to wrap around a sphere. It is designed to reduce the difference in area caused by the math used when this type of coordinate transformation is performed.

For example, take 4 points on the globe expressed in latitude and longitude which are spherical coordinates. To view that area (or collate it with other spatial data), we need to map those coordinates into 2D rectangular coordinates that our map data is stored in. Those 4 points will look very different after conversion and the area expressed by them will be different. By how much is determined by the coordinate projection used. Mercator was good, this should be better.

Ah, gotcha. I mean, I suspected that this was the case - to remove spacial deformation caused by unwrapping. Honestly I just wanted to see it on a sphere and play with Maya a little.