This year's ICFP Contest involved origami. The idea was to "fold" sheets of origami paper in such a way that they would match the (two-dimensional) silhouettes of completed origamis. Points were awarded based on how closely the solutions matched the problem silhouettes.
There was another dimension to the contest, which involved submitting your own problems for others to try and solve, but we didn't get that far!
We finished at position #84 on the leaderboard (out of 293 registered teams, 201 of which actually scored points). This was the best-ever showing for Team K&R (although that was with the leaderboard freeze several hours before the end of the contest; we might end up at a higher or lower place than that).
After solving a few problems manually, we started out by trying to
simply "drop" an unfolded sheet of origami paper to cover the
silhouette. We were able to score some points this way, especially
because some of the problems were themselves simply an unfolded sheet
of paper! Then we tried folding in half once vertically, which
allowed us to more closely match the silhouette of narrower origamis.
The files paper_drop_solution.py and fold_in_half_solution.py
implement these initial experiments.
In hv_folds.py we attempted a more general solution. Here, our
approach was to repeatedly fold the paper in half both horizontally
and vertically until we were close to the bounding box of the
silhouette, then move the resulting folded-up rectangle to fit over
the silhouette. This worked well for problems with a tight
rectilinear bounding box whose width and height was close to 1 divided
by a power of two. For others, it didn't work so well.
Then we added the ability to fold the paper once horizontally less than halfway, and once vertically less than halfway. This allowed us to do reasonably well on problems with tight bounding boxes that were between 0.5 and 1 on a side.
At some point, we figured out that we would be better able to match a
lot of silhouettes if we could rotate our folded-up rectangle to match
the diameter of the points of the silhouette. calipers.py
implements diameter-finding. Unfortunately, we ran into a lot of
trouble here with numerical instability. Our rotation code worked
well for, for example, problems 5 and 6 (with judicious use of
limit_denominator from Python's fractions module), but for problem
7 the server complained that our solution's destination facets weren't
congruent with its source facets. We think the calls to math.cos
and math.sin in the rotate_polygon function are at fault.
We also implemented a quick-and-dirty JavaScript visualizer in
visualizer.js. Open visualizer.html in your browser to try it
out. It displays problems and solutions by generating an SVG image.
parse_problem.py and solution_to_json.py convert problems and
solutions, respectively, to a JSON format that the visualizer can
understand.
Thanks to the organizers for making this contest possible! We had a lot of fun this year -- with feline assistance, of course:
