UV mapping curved circle objects

Hi, everyone!

I was making this product visualization and struggled with the correct UV mapping inside those cut holes. Real wood behave somehow similar to what I’ve got, but I’m wondering, is there a correct way of mapping to force the texture to follow the surface?
I’ve tried to project from the front, but this stretches the texture on the inside circle (perpendicular to the camera). Tri-planar projection is wierd on the edges.

P.S. Geometry is messy, the production needs to be fast.


Holder.blend (1.64 MB)