How to print algebraic surfaces
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!
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. Produces
witness_datafile, which is used as input for Bertini_real.
- Run Bertini_real. Produces the numerical cell decomposition.
- Gather data into
.matfile, in Matlab.
- Plot, verify looks good. If not, goto 2.
- Smooth, if desired. Run
- Gather data again. Save to
- In Blender, align normal vectors. If surface has no interior, add modifyer
- Because solidification routines assume some level of smoothness, and more importantly manifoldness, the solidification probably produced self-crossings and other garbage. Feed the model
.stlthrough Microsoft's online fixer.
- Slice. Generate
- Print small model.
- Print large model.