Why does my texture image join badly at the edges? Bad UV unwrapping?

Question

I added a Texture Image to a torus and when I started painting on the torus, I saw this undesired effect at the point where the edges of the underlying image join:

I can see this effect also in the underlying linked image (right-click on the image and open it in a new browser tab to see it at full-size where it's easier to see the issue):

The .blend file is here (I'm using Blender 2.92).

There's nothing fancy about the torus or how I linked the image. The torus has been just lightly deformed and I don't see anything unusual about the mesh at this join point:

I did no customization in the UV Editing workspace, in fact, I didn't go near that workspace at all.

I created the deformed torus in the Layout workspace, selected it, switched to the Texture Painting workspace. There in the Image Editor, I added a new image giving it the name "Torus_texture" and changed none of the other default image properties. I went to the Shading workspace, added a new Texture Image node, selected the "Torus_texture" and linked the node's Color output to the Base Color input of the material node for the torus. And that's it - the result has this odd anomaly shown above.

Clearly, I have done something wrong but I'd like to know what so I can correct it without starting from scratch again.

I know I've done something that introduced this issue as if I simply create a completely new undeformed torus, add a material and repeat the steps outlined above I don't see this problem:

The hard edge that you see is a stroke that I drew directly on the underlying image, rather than the torus, so that I could see the join point. Here there's no odd anomaly at the join point when I draw directly on the torus.

Its .blend file is here for comparison.

Answer 1

You are using the default UV Map for a torus, which should (and does work) provided you make a small change to the shader. Here's your original texture node:

In this case, the interesting setting is the 2nd one

This flat projection produces the torus you have in your question

If you change the type in the drop down menu from "Flat" to "Tube"

The problem goes away, but the project changes so that the UV map is on the other side of the Torus:

There ways I solve this later problem: simply reposition the torus so the part you want exposed is visible to the camera

The image texture is trying to map a 2D UV map onto a 3D object. If you give it guidance by marking seams then you've actually created a flat (almost) representation of your 3D object and "Flat" works. But if you count on the various smart UV unwrapping modes, they rely on you hinting the geometry of your object in the image texture settings.

There are a very long list of possible combinations, each requiring a slightly different approach to the settings, which is why most tutorials on UV mapping go directly to "mark seams, make flat". The problem with doing this with a Torus is that if I mark the obvious seams:

The resulting uwrap:

has several problems. It doesn't match you image texture. It doesn't use very much of the space available. You can cut the Torus into pieces to fix the later, but the only way to fix the former is to redo the texture painting.

This is why, by the way, the workflow for texturing is to first create the UV Map, then test it with a UV checker, and only then to create the image texture.