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Flattening The World

 
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headus
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Posts: 2871
Joined: 24 Mar 2005
Location: Perth, Australia

PostPosted: Fri Mar 14, 2008 12:50 am    Post subject: Flattening The World Reply with quote

A long time UVLayout user sent me these images a while ago, but they're
still fascinating I think ... simple shape, but very interesting application.
Here's a summary of his detailed notes ...

"And here's another image, showing how circles projected on a sphere
and baked to the UVs created in UVLayout show very low distortion in
the flat map. The right side shows how circles drawn on the flat UV
template render as low distortion circles on the sphere.

It almost seems like magic that the quintessential curved surface
could be flattened with so little distortion. There's no projection in
cartography that can even come close, this is a centuries old quest
finally perfected.

Well, UVLayout deserves the credit anyway, and B. Fuller for figuring
out how to fit the continents into icosohedral face sections without
cutting them, and NASA's Blue Marble for the earth imagery. Actually,
Fuller's method doesn't quite work as well for an icosahedral sphere
mesh as it does for a planar faced icosahedron. After much adjustment,
I had to accept a slight cut somewhere, so settled on the coast of
China just south of Korea. In the Flattening the World image, I re-cut
the UVs so China remains inviolate and Korea gets its islands, but
this violates B. Fuller's geometry."


WikiPedia has more information on the Tissot diagram ...

http://en.wikipedia.org/wiki/Tissot's_Indicatrix

Phil



Flattening_the_World.jpg
 Description:
A UVLayout constructed map of the globe with minimal distortion of landmasses.
 Filesize:  81.61 KB
 Viewed:  25857 Time(s)

Flattening_the_World.jpg



Two_Way_Tissot.jpg
 Description:
"Tissot" analysis.
 Filesize:  119.43 KB
 Viewed:  25857 Time(s)

Two_Way_Tissot.jpg


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DJ Azot



Posts: 1
Joined: 13 Jul 2012

PostPosted: Fri Jul 13, 2012 6:39 am    Post subject: Reply with quote

I wana it!
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