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I want to apply a UV - texture just to the side of a mesh, without it covering the whole model. When using the Image texture nodes, the texture distorts on the actual model. Example of the texture:enter image description here

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I think what you're looking for is "Project From View". First, pick the angle you want to capture it from - in your case, the sides. I find the best way is to use an orthographic side view using Numpad 1 or 3 keys.

Then, in edit mode, select all the faces on the side of the "airplane" (you can use circle select to get them all quickly since you are in side orthographic - However, if there are un-viewable sides/crevices, make sure to manually inspect to make sure they're all selected - as you can see in my second image, I was lazy and only circle selected so there are some pieces missing.). Once you have the angle, and the faces selected, press U and select "Project from view". Do the same thing for the other side if desired (to quickly switch view to the other side, press Numpad 9).

ProjectView1

On your UV map, you will have both sides selected (there will be other pieces too, but the sides will be captured "intact"). Move the other pieces as necessary (or give them a different material). You will then be free to align your "sides" with your image.

ProjectView2

Note that if there is significant curvature in the selection you unwrap together, some areas could come out warped. If this is the case, you can select the whole section, while keeping a rectangle (or square) shape as the "active" selection, then pressing U to unwrap again, but this time select "Follow Active Quads". this will straighten out the section according to the shape of the quad you had active. Do this in the 3D viewport, not the UV viewport. The closer to a rectangle shape that is aligned both vertically and horizontally (ie ideally a perfect rectangle with 0 rotation - this is not always a realistic expectation), the better the results of this operation.

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