...while beating the pinch! OK, let me admit it - there's just no way you are going to get a 2D texture map to fit a sphere without distortion. But the two characters above - Mr. Spherical and Mr. Cubic - aren't your only options. First, let's hope you own Photoshop - or some image editor that has a polar to rectangular filter function. This is your key to some alternatives.
As we can see above, both the spherical and cublic options are real give aways if you need to see more than a third or so of the surface. Add polar mapping to your repertoire and you'll gain a little more flexibility. Let's see what it can do with a worst case texture example - a grid. Here's how:
Open your texture in Photoshop. I'm using a texture in a 2:1 format here - as normal for single tile spherical mapping.
Open the Polar co-ordinates filter dialog. (Filters > Distort > Polar co-ordinates)
on! - don't press OK
Select Polar to rectangular (this is NOT the Photoshop default) - and OK
Save the texture and map spherically as a single tile
It's that simple. What a transformation! And here is a further variation:
Instead of working with a 2:1 format texture, as would be normal for spherical mapping (the horizontal has to wrap over 360 degrees, as oppossed to the vertical dimension which has to wrap over 180 [approximately] ); use a 1:1 (square) format.
Run the Polar co-ordinates filter - as above - remembering to use the Polar to rectangular option (Filters > Distort > Polar co-ordinates).
Select the top half of the resulting image, float (cmd c, cmd v), flip vertically - and move to the bottom of the image
Save and map spherically as normal. This is what you'll get: Mapping the sphere with just one seam and no significant pinch!
Happy texture mapping!
The techniques in this tutorial owe their birth to a (different) polar mapping idea originally floated by John Knoll of Photoshop and ILM fame.
Mapping the sphere
Polar mapping:
This is what you'll get:
Not suitable for every application, but certainly one for the tool box.
