A few days ago I asked how to slice three-dimensional surfaces:
How can we produce sliceforms?
The three outstanding answers make me believe that dicing parametric surfaces should also be possible. Blender - Python has a modifier called Remesh that does this automatically and iteratively.
We take a Catenoid as an example:
ParametricPlot3D[{ Cos[u] Cosh[v], Sin[u] Cosh[v], v}, {u, 0, 2 Pi}, {v, -Pi/2, Pi/2}, BoxRatios -> {1, 1, 0.6}]
A screenshot from my Blender-application after two nested cube operations (with a checker texture):
After three nestings (perforated):
After five nestings (colored by height):
A Ding-Dong surface as another example
ParametricPlot3D[{ Cos[u] Sqrt[1 - v] v, Sin[u] Sqrt[1 - v] v, v}, {u, 0, 2 Pi}, {v, -1, 1}]
After four nestings:
My request
I know how to dice with Blender and Lego bricks, but would prefer to see a solution with Mathematica. Thank you in advance for your answers and ideas.
