Thingiverse
Geisha -- singular algebraic surface
door ofloveandhate
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Geisha, a singular algebraic surface of degree four. This is the set of real points for which
```
x^2*y*z + x^2*z^2 -(y^3*z + y^3) = 0.
```
Two singular lines, and two singular points on those lines!
I have provided these files:
* `geisha_thickened.stl` -- has the normal vectors fixed, and is thickened for printing.
* `geisha_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. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. 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
```
x^2*y*z + x^2*z^2 -(y^3*z + y^3) = 0.
```
Two singular lines, and two singular points on those lines!
I have provided these files:
* `geisha_thickened.stl` -- has the normal vectors fixed, and is thickened for printing.
* `geisha_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. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. 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
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