well see theres 2 planes perpendicular to each other. like this:
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now if you start to move subdivisions of that plane you get something like:
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which obviously form direction of a plane looks ok.
Because the planes are separate* it does not help how much you subidvide if your texture reports movement at the seams even by inetrpolation as the map must be 0 offset on both sides of the pilars uvmap edges so you must have some tetxure slack area outside the uv map taht does not move the texture or the edge wont line up.
However if you round the edge it doe snot really maytter since its a smooth surface and it aligns nevertheless.
*The fact that the 3d software reopots them being unison does not mean thay are inside the rasterisation step. because they are not. common sense of mathematics overrides whatever you think will happen