Thank you Puppeteer for the explanation. The site of Iņigo Quilez is also very informative and entertaining at the same time; I read his presentation:
Rendering Worlds with Two Triangles with raytracing on the GPU in 4096 bytes, now I think I have understood it.
As Superku said, I think regular meshes are nicer for certain things. I want for example hard edges like in this image:
and I am not 100% sure if I can achieve this easily with distance fields.
Other than that, I see also the possibilities for soft shadow rendering and collision detection. Maybe I will try a distance field for shadow computation; otherwise I would have used raytracing instead. I would then calculate a distance field that matches the polygonal ring. In the pixel shader I would evaluate then the shadow factor.
