Mapping Flat Tiles to Round(duh) Spheres, HELP Please!

I’m attempting to create a sphere with a tile that’s mapped in a fashion that appears like it has no break. I started using an image that was perfectly square and selected all the faces on one half of the sphere. I then unwrapped them and used the image editor to map the unwrapped circles to the hemisphere. I did that for both sides and got the results I was looking for. However when I tried to create a tile that (in 2D) would be continuous and tried the same mapping technique I got distortions(?) I guess to the parts of my square file that were outside of the circle where the two hemispheres meet. Here’s a render that shows the first and second mapping attempts. I’m also attaching the two files that I’ve used for the texture mapping in hopes that someone can help me figure this out!! Thanks in advance!

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Use imported image as a plane, subdivide and Warp in edit mode: placing cursor approx 2 BU under plane from side ortho view warp 180deg, then from ortho front - 360deg (3d cursor set as a pivot both times). Spacebar search for Warp. Remove doubles as a final touch.

http://www.pasteall.org/blend/41320

Alternatively -map image to Cube sides, apply (modifier Apply button as ‘apply’) Subsurf lvl 2 and in edit mode To Sphere, 1 to all selected vertices.

And… What exactly was the question here… Could you clarify one more time please?

Thanks for the example. The problem I’m having is mapping my images to the sphere in a distortion free way that tiles seamlessly. In the example you’ve shown you can see that the image has been pinched at the top and stretched at the equator. I’m looking to do what I’ve shown in my render sample, but have the tile continue across the equator in the same way it does anywhere else on the sphere. Not in the reflected look that it has now. I need to be able to view the sphere from any angle and have the pattern continue unbroken and not distorted, aka. the circles on the sphere have to appear circular. I’m not sure that this is possible. I don’t know Blender or 3D rendering well enough to know. Mapping each hemisphere separately is as close as I’ve come but it’s still not there. Thanks again.

Have you checked polysphere yet? Cube, U -> Reset, Subsurf applied, to sphere?
http://www.pasteall.org/pic/show.php?id=101842

Eppo, that’s really cool. And thanks for the instruction. I didn’t know about the To Sphere command. I think this looks good, but I’m not sure it get’s to where my client wants me to be. I’m really not sure if it’s even possible. Primarily I see the point where the 3 sides of the cube come together and create a triangle sort of effect as the problem. I guess in the end I need something that will be able to distort my 2D file in a fashion similar to the way that maps are distorted so that I can then seamlessly wrap it back on to the 3D sphere. For instance I can take this image from NASA and wrap in onto the sphere so that it doesn’t have any distortion, but someone took the file and distorted it so that it would fit onto a rectangular image.

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It’s easy. You just have to choose what fits your bill.
http://math.rice.edu/~polking/cartography/cart.pdf
First sentence tells you all.