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Can simple textures be controlled using just texture coordinate node? I'm using a simple texture for this experiment:
texture

which I'd like to place at the side of an experimental sphere(with the texture as it is), the first result that I would get is:
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the texture is distorted and so I would have to scale it down using the mapping node and the texture looks fine from top view:
top view
However, if we look at the bottom the texture appears reflected:
3

after a long time, I figured out that the texture is split into equal sizes and are mirrored as can be seen below:
mapped

I'd only like to keep one but I don't know how.
There could be work arounds using an empty or partly uv unwrapping the mesh, But I'd like to know if there is a solution for this particular sort of problem using only the mapping node.

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I believe you should be using the Generated coordinates for this rather than Object. The Generated coordinates range from 0.0 to 1.0 over the range of the object whereas the Object coordinates are in "object space" with 0 at the origin and positive values on one side of each axis and negative at the other - this is why you're seeing an oposite reflected image. You should then be able to scale it without seeing the reflected second image.

You should also set your Image Texture node Projection mode from Flat to Sphere.

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