How do I retopo this mess

It depends a bit on what you want to do with mesh afterwards:

  1. subdivision
  2. bevelling
  3. smooth shading
  4. autosmooth shading (with some sharp edges)

In the first three cases you’d want to have “triple fencing” around the sharp edges:

Far from perfect (won’t give good results with subdivision) and you’d need to use normal transfers or the like to get good shading.

The problem why this gets so messy is that the resolution of the sphere is much lower than that of the cut.

If you use a finer resolution you get something like this:


which is easier to clean up and gives better results:

sphere_cut_1_v01.blend (616.4 KB)

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I added a bevel around the groove and deleted most of the splicing edges on the sphere. The bevel really helps with the shading despite the ngons around the region.

Still not perfect but much less noticeable than before.