Thanks for the example, Ben.
There is no rule for an absolute number. It depends always on the final render size. With this size you can define the needed size of the object texture. Camera-position and field of view as well the position of the object and the way the texture is applied (scaled or via UV, tiled etc) are part of that equation
First of all, if the render is 1000 pixels and the visible texture is 1500 you are just fine. This is the rule of thumb, 1.5 times higher, as a pixel can rotate, etc. I guess the minimum number is base on Square root of two [1.414_]
Since the texture and the final result/render are not in the same size, you have to check how much of your texture is really in the final image. The cube in your scene has only ~500 pixels from the psd file in use. So the size of the psd file doesn’t matter if you show only a part of it. I have a 5K screen and the cube (filling the screen) looks pixelated [heavily], as you have mentioned.
If you move the camera toward the cube, it magnifies the texture even more.
You have to find the highest magnification of the texture. Given the “crop” of the texture, you can then estimate how large it should have been, times 1.5 at least. Your scene-file had the default render size, so I can’t use it, as I do not think that’s the final.
Have a look at the screenshot I have attached. I placed a 100x100 patter there, if you use this, you can easily count he squares and get the right numbers then.
Example: to render at HD with a hight of 1080 pixels. The texture shows [for example!] two of the squares in hight = 200 pixels. In the example we assume as well that whole texture is 2048x2048. So, it uses only 10% of it! The visible texture to fill 1080 needs to be roughly/min 1600 for the visible area, eight times higher. The way the texture is set up and shown is resulting in a size of 32Kx32K. This is quite large, so the question is, why using only 10% to start with?
Taken your example, the file uses only a fraction of the texture, roughly a third. There is lots of unused space. See the three images from UV-Edit. These six squares should fill the texture perhaps with a little seam.
I hope the math has become clear. It has a few variables, and the camera might move in closer—later on, so perhaps chose wisely.
If you need only on one side text, do it on an additional material, which might be only as large as the text. This would make sense if the texture on the object is less detailed.
Again, the Freeze texture is not able to increase that part of the texture.
Let me know if there is something unclear.
All the best
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