This design was inspired by henryseg's Stereographic projection.
I fell in love with the Hilbert curve and after seeing what Henry made I decided to make my own projection.
In my opinion, only a SLS printer would be able to print this design.
But maybe a dual extruder 3D printer with PVA supports could pull it up ... maybe
Using Fusion 360 I created the stereographic projection the Hilbert curve. To do so, I joined each corner of the curve to the north pole of the sphere creating a 3D sketch. (Fig. 1)
Then I used the patch workspace to transform this 3D sketch into a solid body with the boundary fill command.
- Once I had a solid body of the projection I used the combine command to create the intersection between the sphere and the projection. (Fig. 2)
Whilst this was fun to draw by hand the next step is to create a script able to do the same thing from any imported .svg sketch.
Projection of half of the Hilbert curve
Intersection between the sphere and the completed projection