I don't use Maya (I use Blender), but you should be able to leave your UVs outside the "box" and it will work fine, for your textures. For your lightmap UVs, you want to keep them inside though.
If you want to Keep the UVs inside the box without it being blurred and stretched you could increase the UV tiling on the checker shader. To do this you need to go to the attribute editor for the shader and increase both the x and y UV tiling.
It's stretched because your UVs are wrong. For one, the model is long and skinny, you have your UVs short and kind of fat, so nothing will look right because the texture is stretching. Second, it will be blurry because you don't have high quality rendering turned on in your viewport AND the UVs are so small that your mesh has very little resolution to work with. Use a planar projection on it to get the right shape of the UVs and scale it as large as you can/want to.
I have use the Planar Mapping for my Uv map.U mean the Repeat UV in Atribute editor?And what you mean with my UV are false?Do have a example?
I explained it already. If a face on your UV map isnt as close as possible to the shape of the actual polygon face on your model, there will be some texture stretching or compression. And switching to high quality mode makes the Trcture less blurry. You also need to scale the UVs to fit as much ofthe UV space as you can and either use a texture or adjust the tiling settings for the checker material to make that half black and half white.
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