I have an image [1] of a spherical surface that I want to map onto a sphere, but
it is a Mollweide projection. I tried to convert it to a rectangular Mercator
projection (is that even the right one?) with Mathematica [2], but it doesn't
really work. I do get a rectangular image which kind of looks right, but when I
use the texture in Povray with

pigment { image_map { png "text.png" map_type 1 } }

the edges don't seem to match up and the texture looks distorted around the
poles. In the end, I want to create something similar to this [3]. What can I
do?

Adrian




[1] http://map.gsfc.nasa.gov/media/101080/101080_7yrFullSky_WMAP_1280B.png (I
cropped it properly, of course)

[2] invmerc[{x_, y_}] := {ArcTan[Sinh[y]], x};
theta2[phi_] := theta2[phi] =
   FindRoot[2 th + Sin[2 th] == Pi Sin[phi], {th, 0}][[1, 2]];
moll[{phi_, lambda_}] := {2 Sqrt[2] lambda Cos[theta2[phi]]/Pi,
   Sqrt[2] Sin[theta2[phi]]};
merc2moll[p_] := moll[invmerc[p]];
result = ImageTransformation[Import["text.png"], merc2moll,
   DataRange -> Sqrt[2] {{-2, 2}, {-1, 1}}];
Export["text-merc.png", result];

[3] http://particle.physics.ucdavis.edu/Graphics/rotate/wmap_movie.gif

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