Log-Spherical Mapping in SDF Raymarching

In this post, I’ll describe a set of techniques for manipulating signed distance fields (SDFs) allowing the creation of self-similar geometries like the flower above. This is done by crafting distance functions based on the log-spherical mapping, which I’ll explain starting with basic tilings and building up to the recursive shell transformation. If we’re tiling spheres, this would give us the following distance function:

Distance functions made using this technique work well with raymarching:

Log-polar mapping applied to two dimensions of a 3D geometry.

Source: www.osar.fr