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Leopold - smooth algebraic surface
door ofloveandhate
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Leopold, a smooth algebraic surface of degree six. This is the set of real points for which
```
1000*x^2*y^2*z^2+3*x^2+3*y^2+z^2-1 = 0.
```
No singularities! Smooth everywhere!
I have provided these files:
* `leopold_fixed.stl` -- has the normal vectors fixed.
* `leopold_raw.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.
* `input` -- the Bertini_real input file used to compute it.
This surface was sampled before I implemented cyclenumber > 1 sampling, so the surface is undersampled near critical points and singularities.
Computed with a Numerical Algebraic Geometry program I wrote, called [Bertini_real](https://bertinireal.com) and printed as part of my long-term project to
```
1000*x^2*y^2*z^2+3*x^2+3*y^2+z^2-1 = 0.
```
No singularities! Smooth everywhere!
I have provided these files:
* `leopold_fixed.stl` -- has the normal vectors fixed.
* `leopold_raw.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.
* `input` -- the Bertini_real input file used to compute it.
This surface was sampled before I implemented cyclenumber > 1 sampling, so the surface is undersampled near critical points and singularities.
Computed with a Numerical Algebraic Geometry program I wrote, called [Bertini_real](https://bertinireal.com) and printed as part of my long-term project to
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