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How would you unwrap this if you wish to keep the uv in one island, normally I would unwrap this as you see below, however if I wanted to have a texture without any seams this would not work due to the edges.

How I usually do it

Original shape

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  • $\begingroup$ One island? Each island corresponds one face. If you want one island, you'd have to texture a plain... well, plane. One thing you could do however, is add the UV islands on top of each other. This way you would get a repeated texture on all faces, meaning you only have to make the texture for one island. $\endgroup$
    – FreemoX
    Jul 31, 2017 at 21:01
  • $\begingroup$ Oh sorry, I thought a uv island corresponded to a collection faces. I don't follow how that would look though, wouldn't that mean the texture tiles on each face? $\endgroup$
    – Olle
    Jul 31, 2017 at 21:17
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    $\begingroup$ If unwrapping you have to define at least one seam to allow 2d texture to be wrapped on the surface of the mesh. UV island can be several faces, can be consisting only of one face, it depends on how unwrap was made (e.g. if you run Lightmap Pack unwrap method each island will consist only of one face, other methods will provide other results). $\endgroup$
    – Mr Zak
    Jul 31, 2017 at 21:27
  • $\begingroup$ Ah, yeah, sorry, haven't slept much. An island can also be a collection of faces, my bad. You can unwrap using "Follow active quads", this will make each face into a square on your UV. Just make sure you seam correctly for the ring $\endgroup$
    – FreemoX
    Jul 31, 2017 at 21:42
  • $\begingroup$ Can you spend a few more words about the final result you expect? Where should the UV map different from what you have currently achieved? Could you clarify the role of the seams? $\endgroup$
    – Carlo
    Jul 31, 2017 at 22:33

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I would mark two seam rings. One around the outside of the donut, and another cutting across a small ring of the donut: torus seams

The problem is that the quality of the unwrap you get from blender's default logic can be pretty variable. A plain unwrap sort of pinched the ends of the rectangular island. The "follow active quads" depends on the state of the uv map when it starts (the screenshot shows one of the less disastrous outcomes).

The best uv unwrap seems to be when you do a Reset (which makes every quad cover the entire image) and then a Follow Active Quads. Then you can scale it to fit in the image, or leave it huge to tile a texture.

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