Thanks, Edward, that helped a lot.
I was confused because of the way the Layer Map is displayed inside the 3D Invigorator interface (the preview is a color bar graphic) and I was thinking it was mandatory to fill the entire object with the layer map.
This is what I learned:
I created a square precomp, placed the logo and info there and made them fill all the width of the comp. Then, I assigned the precomp to a Layer Map and got myself inside the Invigorator interface.
Now I was able to adjust the rotation, scale and position using the mapping controls you mentioned, Edward, and it was really easy once I figured out that I can turn the tiling to none. The image was not distorted and it didn’t matter the actual shape of the object (a lathe).
That was it! No distortion and no weird calculations for the aspect ratio of the layer map.
Thanks again