Is it possible to mapping a image around a ring shaped mesh? I would imagine there should be a way to curve/distort the image around the mesh. If not, how can I straighten out the mesh easily instead to fit the image?

mesh ring and texture

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    $\begingroup$ select_all, then select one face, then press U, select follow active quad $\endgroup$ – Chebhou Mar 26 '15 at 15:01

Using face select, select all the faces of the circle then have one face the active face (selected last, it will be lighter orange).

Press U > Follow Active Quads, then hit OK.

That will give you a straight line of the UV for the circular faces, which will deform your pattern around the edge perfectly.
animated gif

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