Hi iaec,
In R16 the caps have a UV information, so yes it can be done for the cap. Note, there is a Preselection for the Cap C1 or C2 (just type this in the Texture Tag>Attribute Manager>Selection.
The following should work nicely if the “Rounding UVW Keep Shape” (New in R16) is not enabled, as it extend the UV Space, and things becomes more complicated ;o)
I use normally a square, as this represents in the best way the UV space. The larges dimension will determine the UV square (if the texture is a square). The widest distance in u or v will create the square of the UV. One of each UV sides will determine the zero point, for U and for V. Hence the problem to explain it. If you render a start, or even draw a new one in Photoshop, take the largest dimension X or Y (Z) and set that as the dimension for the square, then find the zero point. UV space goes from 0-1. Find out which side is 0, or use the offset in the Texture Tag.
Keep the square format for simplicity. Done.
There is another way to do it in Illustrator, but more steps. You just use the placement as described above, and draw your star in Illustrator. Export as Ai-8. The drawing in Ai needs to be exported as square, based on the instructions above. It should fit.
Besides that, a Sweep only a 0.01% longer with a smaller Star would do it, but it takes more render time, and clutters the set up, so I mention it, but well, not really…)
Alternative, the Fillet Caps and the Engraved set up would work, but not flat.
I can elaborate more on the Photoshop way, just let me know.
I’m not aware of a fast Shader version, as long as the Sweep is active (polygons—N-Gons—Proximal)
All the best
Sassi