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I have what is apparently called an equirectangular projection of the world. I can use the 3D functionality of Photoshop to use this as a texture for a globe, by creating a sphere mesh; or I can use "CC Sphere" in After Effects etc. This is great.

I now want to attach (flat) objects to the surface of that sphere (imagine some sort of sticker, an image frame, or text. Clearly, I cannot just add them to the original 2d-projection of the earth. They need to fit the projection. This is very effectually visualized here:

I have no idea how to approach this, or what tools to even use. I figure it might be necessary to design this in 3D to begin with, and then export it to a texture. Any ideas?

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The issue with the equirectangular map is the Tissot Indicatrix, which is the way the lines spread out towards the top and bottom of the map (the distortion when wrapping and unwrapping the texture on a shape). See:

  1. Tissot's indicatrix
  2. How does one calculate distortion on Equirectangular Projection?
  3. Equirectangular projection
  4. USGS Publications Warehouse Map Projections
  6. PanoToolsNG
  7. Panorama photo stitcher

I'm still working on trying to create an action or a set of actions that work with distorting maps to projection. I'll post something once I get it working.

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In the Photoshop versions that support 3D, you can paint directly on a 3D surface, independent of the existing texture. Try making a custom brush from one of these flat objects, and "painting" it on. If your objects are simple enough, that might be all you need to do.

An alternative approach (very much depends on the specifics of your application) might be to put your flat object(s) on its/their own layer(s), turn them into 3D objects, orient them correctly, then merge down (CS6 only).

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Yes, Alan is totally correct. Painting on the object itself (projection painting) will make the painting/cloning look proper based on the camera angle and the surface of the object, as opposed to painting directly on the texture map (which may not have a 1:1 pixel ratio). – Kevin Bomberry Aug 22 '12 at 4:55

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