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I don't know if I understand what you are looking to do.
When making an overlay I generaly use wood that is 1/4-1/2" thick, but it would be up to you. Then cut all of the pieces out and glue together. Sand and glue to the top of the box or whatever you are working on. I would probably use a bandsaw to cut the pieces, but there are a lot of ways you could do that.

Also, a compass rose is usually alternating colors in a star pattern, i think. So I would probably try to make two at once, one the mirror of the other. cutting and glueing alternating types of wood. but with the points needing to be nice and neat, it might not be the best method.
 

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3d compass rose huh? ok, I can not think anything off hand where you could use a table saw, or any sort of machine with out a complex jig arangment, and then making compass roses can be tricky enough with veneers so that all the point match in the middle, let alone making a 3d type.

you could start by cutting/milling your stock to match the "heighth" of your rose, then after making a 1:1 drawing to know where exatly the points meet and at what angle usually that would be the 360 divided by number of points (normally 8) times 2. I hope this is right, I have never attempted to calculate this before, I usually use a compass to do this, and draw the lines using a straight edge. but I think you get the idea… you can set this on your mitre gauge and cut the ends where the meet in the middle, but you still must cut the points to the wished angle. I think this could be the tricky part, draw this out and and cut out a wedged shaped piece on the table saw, and use the parallel fence to the table saw to cut the one side and then make another wedge shaped piece, but double the angle and use that to cute the other side of the point using the parallel fence.

I hope this is understandable. and I hope it helped out.
 

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John I just posted one on the project page. don't know if this what your looking for. let me know and I will try to explain it to you.
 
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