This tool deforms input geometry by the exponent of L^p-norm, so the result resembles superquadrics or superellipsoids.
Firstly i thought to use this deformation technique in conjunction with my other tool, the 2d curves generator, to just make rounded forms (kind of spirals) looks more "square-like". But then, I added third dimension and basis transform to the tool and try it on the head model... So, as I can see, it may also be used to roughly pre-deform a base mesh for sculpting or to 3d concept / form finding...
Of course, the deformation can be applied to a volumetric data (voxels), standard and VDB. Coming soon.
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The idea of L^p spaces is quite simple: when in Euclidean space, a vector length (or "norm") equals square root of the sum of the squares of it's components, why not replace those squares with arbitrary power "p". This replacement gives a range of metrics, including "Manhattan" (p = 1), Euclidean (p = 2), Chebyshev (p = inf).
For more information about L^p space and p-norm, see https://en.wikipedia.org/wiki/Lp_space#The_p-norm_in_finite_dimensions