UV maping a sphere to have stripes runing between both poles?

Question

I tried to map a country flag on a UV sphere, but I could not get it laid out the way how I wanted to see it. I used the Poland flag. I wanted to map it exactly as you can see in picture 1.

But what I got was a result as you can see in these pictures.

The flag was looped at least 8 times on each half side of the sphere.
I could double that, but I could not go half of that, or less. I wanted the flag to show up just 1 time at each half side of the sphere. or maybe twice at each side, but not 8 times. as you can see on the third picture, I tried to resize the UV map, but also then it would never go under 8 repeats. How can I change this?

Here is the Poland flag texture.

Answer 1

If you do it backwards, so instead of unwrapping an icosphere you create a plane and turn it into a sphere, you have a lot more control on the results. To turn a plane into a sphere see this answer

Unwrapping a plane will give you perfect UVs to do what you want:

.blend file

related:

What is the best way to unwrap a sphere? https://blender.stackexchange.com/a/13927/1853

Answer 2

While you could unwrap the sphere and then texture it, in this case it will be easier to just use a generated texture.

The first method simply differentiates the colors based on the selection. You can easily select the edge loops with the method in this answer. You will have to manually select the few faces at the poles.
Here I put a white material on the ball, selected the faces that should be red then added another material and hit Assign. You could also use vertex colors with this method.

The second method uses only one material, it creates the stripes with a gradient texture. Here are the nodes used to make the stripes in cycles.
Using object coordinates as the vector, a Gradient Texture node set to Radial creates the base for the stripes. The ColorRamp node set to Constant colors the stripes and makes the stripes distinct.

Here is an example ball rendered using the above nodes.

Answer 3

To to top view and unwrap using project from view (bounds)

Now what you are looking for is to invert the UV map for one half of the Sphere, so select only one half of the faces

and in the UV/Image editor window, rotate your UV map 180 degrees (R180)

Answer 4

i tried to find another way and simply deleted the poles , than made a UV map from this sphere without poles., then putting the poles back by E for extrude. en S size to "0" in this way you can repeat the texture as you desire,also less then 8 repeated loops , which was not possible before. you can even export this as an object and import it in other projects. the problem here is that it works for certain simple textures only , but for complex textures it would still look uncomfortably scrambled at the poles.