Stretching a grid around a sphere...

[mr_malee]

a square area with a grid on it when looped horizontally and vertically becomes a torus, and you cant massage that into a sphere.

http://lab.andre-michelle.com/earth

that uses a flat bitmap and scrolls it horizontally, looks ok to me.

[xMCNUGGETx]

http://lab.andre-michelle.com/earth

From the comments on that page there was this link with some explanation.
http://makc.coverthesky.com/FlashFX/ffx.php?id=8
and here
http://blog.andre-michelle.com/2005/...mentmapfilter/

[rachil0]

a square area with a grid on it when looped horizontally and vertically becomes a torus, and you cant massage that into a sphere.

http://lab.andre-michelle.com/earth

that uses a flat bitmap and scrolls it horizontally, looks ok to me.

Actually the globe is a perfect example of what he is talking about. A 2D map of the earth surface (like a mercator projection) looks totally different when it's projected onto a sphere. Think how large Antarctica and Greenland look on the 2D map and how small they appear on the real globe - because they are both crowded near a singularity (pole) of the mapping function.

The globe looks ok in this case, because the original texture is already super distorted to compensate.

As for the OP, I think the best solution is the distorted cube mesh - you could define a square texture for each of the 6 deformed faces and then subdivide it in texture space to get a a tiny patch of texture mapped out to each tiny patch of sphere surface. Each patch can be filled using beginBitmapFill on two triangular regions and it should look pretty good.