Title says it. Basically: how to turn concave areas into convex ones, and vice versa?

Any ideas of how to achieve this?

Not very clear what you want. If you want to simulate or just flip your normals, can you be more specific with a visual example, perhaps?

Spherical inversion is one way. You can do it with a similar method to stereographic projection.

https://en.wikipedia.org/wiki/Inversion_in_a_sphere [en.wikipedia.org]

Interesting, thank you!

Looks like it involves some quite complex math.

If its a shape with a clear volumetric center with equal distance to any point on the mesh surface, like a sphere, I was thinking if it would be possible to perhaps "mold" the inside of the mesh using some kind of boolean operation, and then apply a displacement attribute depending on the distance to the center. But I'll have to try.

@albinioni
I posted here files with Spherical inversion and other stuff, complex shapes and MATH ,that you can find also if you google MATH BERLIN HOUDINI. " vex codes"
https://forums.odforce.net/topic/44999-on-growth-and-form/?page=8 [forums.odforce.net]