If you want to just solve the problem make your map bigger as nextdesign suggests (4k x 4k should be sufficient).
On the other hand if you want to understand why you need to make the map bigger here is another attempt to explain lol.
What you have marked as 10x10 is actually 1 grid square and is 1 x 1.
The entire image you have is of the 0-1 UV space and has 10 x 10 grid squares. (you can see them; they are even marked 0.0 - 0.9 this is why this region is called the 0-1 UV space. In math terms it would be written [0,1) meaning from 0 (inclusive) to 1 (exclusive) or in other words from 0.0 to 0.999... which is easier to write as 0-1)
Therefore, if the texture map for the entire 0-1 UV space is 1024 x 1024 then each grid square is about 102 x 102 pixels.
On a 23" monitor with a 16:9 screen ratio the dimensions are about 20 x 18.4 in. So at a resolution of 1920 x 1080 there are about 96 pixels per inch in both x and y.
So as NextD says - You need more pixels in your texture map. If you go to to a 4K map each of those UV squares will be getting about 408 x 408 pixels or about 4 inches square on a 23 inch 16:9 screen before you get texture stretching.
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To compute the x and y size of a monitor given the screen ratio and the diagonal size...
screen ratio = xr:yr ... 16:9, 4:3,...etc
diagonal = d ........ 23,24,17,...etc
use the formula y = sqrt( (d^2 * yr^2) / (xr^2 + yr^2) )
then compute x = xr * y / yr
"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675
Last edited by ctbram; 25-09-2011 at 03:05 AM.