Hi Yasmin - sorry, I'd like to try to be more help but that picture has lost me a bit I'm afraid!
I think maybe you're thinking of an unconventional mapping of the image such that the middle of the image is the origin, and a point on the cylinder (z, w) where z is the distance from an end (normalized to 0,1 range) and w is the angle around the cylinder, will map directly to a point (r, a) in the image where r is the distance from the middle and a is the angle relative to, say, the +x axis.
While that is a valid mapping, it suffers one significant issue: the area of the cylinder surface that a given image pixel maps to is massively different depending on the value of z, the distance along the cylinder. In effect, for large z (i.e. at one end of the cylinder) you will get a high resolution texture *around* the cylinder, while at low z (the other end, mapping to the centre of the image) you will have a very low res texture. In the limit, the end of the cylinder at z=0 will have no angular resolution because all those points map to the same image pixel regardless of angle.
Anyway, sorry if I've completely misunderstood your image. In general, for consistent results across a model you should usually prefer texture mappings that are close to isotropic and constant resolution.