Opened 9 years ago

Last modified 2 years ago

#11564 new enhancement

Implement polyhedron unfolding (i.e net)

Reported by: QuantumKing Owned by: mhampton
Priority: major Milestone: sage-6.4
Component: geometry Keywords: unfolding, net
Cc: moritz Merged in:
Authors: QuantumKing Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:


An unfolding or a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. There is no overlap between the polygons.

I've attached code which does this. It will attempt to unfold without overlap a 3D polyhedron defined by the class <class 'sage.geometry.polyhedra.Polyhedron'>.


Attachments (2) (13.8 KB) - added by QuantumKing 9 years ago.
trac_11564_preliminary_effort.patch (12.1 KB) - added by mhampton 9 years ago.
Just for comparison with other effort, don't review

Download all attachments as: .zip

Change History (13)

Changed 9 years ago by QuantumKing

comment:1 Changed 9 years ago by mhampton

Funny timing, I was about to create a ticket with solution for this same issue. It was the outcome of an undergraduate research project. I will try to review your solution, maybe it is possible to merge the two approaches.

comment:2 Changed 9 years ago by novoselt

It would be great also to handle higher dimensions, i.e. unfolding a 4-d polytope into 3-d...

comment:3 Changed 9 years ago by QuantumKing

How does the code look? Any ideas to make it better would be appreciated

comment:4 Changed 9 years ago by mhampton

Sorry, I am traveling right now and its hard to find time for Sage development. I do have some comments though.

Not all the functions in your patch have documentation/doctests. These are mandatory for every function, so they need to be added.

I think it will make sense to merge our efforts. I haven't completely fixed up my student's effort but I am attaching the current state so you can take a look at what we did. There are different strengths and weaknesses in our efforts. Ours can handle tougher problems, but we don't have a function to check for overlaps.

If you haven't looked at the master's thesis of Schlickenrieder ( I highly recommend it. It was based on his work that my student choose to implement the steepest-edge algorithm.

A good test problem is what Schlickenrieder calls "turtles", for example:

tpoints = [[i,j,i^2+j^2] for i in srange(-5,6,1) for j in srange(-5,6,1)]
tp = Polyhedron(vertices=tpoints)

Changed 9 years ago by mhampton

Just for comparison with other effort, don't review

comment:5 Changed 7 years ago by QuantumKing

What's the status on this thing? I think it would be nice to have in sage...

comment:6 Changed 7 years ago by mhampton

My status is that I am too busy with other duties to finish this off, although I would really like to.

The code in my "trac_11564_preliminary_effort.patch" patch is from a student project. It works, but it could really use some refactoring.

Its possible I would find time to put more effort into this over my winter vacation, but don't count on it. Otherwise, if no one else works on it I would hope to tackle it in the spring or summer.

As I mentioned before, your code mainly needed full documentation (doctests). While it would be nice if it could handle some tough cases, for this kind of functionality something is better than nothing so feel free to finish your version up and I should be able to find time to review it.

comment:7 Changed 6 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:8 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:9 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:10 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:11 Changed 2 years ago by moritz

  • Cc moritz added
Note: See TracTickets for help on using tickets.