Thingiverse
Cube - smooth algebraic surface
von ofloveandhate
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Cube, a smooth algebraic surface of degree six. This is the set of real points for which
```
x^6 + y^6 + z^6 -1 = 0.
```
Is everywhere smooth! Not an actual cube; you get a cube if you replace the 6 in the equation by infinity, but then it's impossible to compute...
I have provided these files:
* `Cube_fixed_Blocky.stl` -- has the normal vectors fixed.
* `Cube_fixed_Med_Smooth.stl` -- the blocky version, normal vectors fixed
* `cube_raw_blocky.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for 4- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. The raw versions are not directly suitable for 3d printing.
* `cube_raw_med_smooth.stl` --ran through `sampler` with fairly loose tolerances. Incorrect normals.
* `input` -- the Bertini_real input file used to compute it.
This surface was sampled
```
x^6 + y^6 + z^6 -1 = 0.
```
Is everywhere smooth! Not an actual cube; you get a cube if you replace the 6 in the equation by infinity, but then it's impossible to compute...
I have provided these files:
* `Cube_fixed_Blocky.stl` -- has the normal vectors fixed.
* `Cube_fixed_Med_Smooth.stl` -- the blocky version, normal vectors fixed
* `cube_raw_blocky.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for 4- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. The raw versions are not directly suitable for 3d printing.
* `cube_raw_med_smooth.stl` --ran through `sampler` with fairly loose tolerances. Incorrect normals.
* `input` -- the Bertini_real input file used to compute it.
This surface was sampled
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