i use my plugin UV splinemapper for this, we extra made this for curved or polygonal folder elements in building streets, furniture etc:
https://3dtools.info/shop/spline-uv-mapper/
it generates a UVW map tag, that can be rendered in any engine and the result can be also rendered in other c4ds that not have this plugin.
one controlls the fow of the UV via a simple c4d spline. no unfolding or bodypaint needed;)