I have this problem for some time already, and I can not find the solution or explanation of what is causing this.
Very simple mesh, top and bottom edges have equal amount of points. It is UV mapped so that the top edge is perfectly straight and the bottom edge is perfectly straight as well. Both, top and bottom points have exactly same X position on a UV map. I expect the texture to have nice smooth look, proportionally squeezed or extended. But I always get those wavy texture lines in the middle of the mesh, in the middle of the quad, where is no point, no line, nothing. It looks like the peaks of those waves occur on the diagonal lines, like the mesh would be triangulated. But its is not. Can somebody give me some ideas what could cause this?

linajakaite
It looks like the peaks of those waves occur on the diagonal lines, like the mesh would be triangulated. But its is not. Can somebody give me some ideas what could cause this?

The mesh is triangulated by the scene viewer, since the real time renderer can only draw triangles. Some raytracing renderers can render quads natively, such as Mantra, but others will triangulate, such as Karma.

Your object doesn't look like a rectangle, but its UVs are rectified. It seems there's not enough geometry to support (or compensate for) the difference between physical primitive shapes and their UV representations.
Add more vertical and/or horizontal spans. In other words: add more geometry to minimize the UV distortion.

Thanks to both!
And yes, adding more geometry helps.