Bruteforce Search

Approximate Solutions:

"translate the square to cover the silhouette"
Approximate by folding on all edges of the convex hull of the silhouette (repeatedly).

Exact Solutions that are probably slow:

Exact search: unwrap faces from skeleton.
Will skeleton be provided as hint with all solutions?

Hard Problems:

lots of small faces during search

Research

http://erikdemaine.org/papers/CGTA2000/paper.pdf
- three general polynomial-time algorithms from strips of unlimited length, not a fixed square
  - the ring method (second one) could potentially be directly applicable
- a subroutine for convex polygons (Fig 2 & Theorem 2)
  - we should probably implement this. the example can be solved by this algorithm immediately.

Computational Geomotry

Rational numbers, use really long (greater than 64 bits) integers?
2D vector operations
Mirroring, line intersection, union of multiple polygons
- Clockwise or not? See Shoelace's formula https://en.wikipedia.org/wiki/Shoelace_formula

Other Properties

A valid solution is probably physically feasible. See http://erikdemaine.org/papers/PaperReachability_CCCG2004/paper.ps