How to print algebraic surfaces
Resources
I gave a talk at Notre Dame in May 2016 about this topic. The pdf of the slides is here. Note that the filesize is large, because of full-res images included. Eventually, this page hopes to replace this slideshow.
If you want to chat, send me an email!
Some advice
Briefly, here's how I print algebraic surfaces:
- Write Bertini input file. This contains the system, as well as setting for Bertini.
- Run Bertini,
tracktype: 1
. Produceswitness_data
file, which is used as input for Bertini_real. - Run Bertini_real. Produces the numerical cell decomposition.
- Gather data into
.mat
file, in Matlab. - Plot, verify looks good. If not, goto 2.
- Smooth, if desired. Run
sampler
. - Gather data again. Save to
.stl
. - In Blender, align normal vectors. If surface has no interior, add modifyer
Solidify
. - Because solidification routines assume some level of smoothness, and more importantly manifoldness, the solidification probably produced self-crossings and other garbage. Feed the model
.stl
through Microsoft's online fixer. - Slice. Generate
.gcode
. - Print small model.
- Print large model.
- ???
- Profit