Comments on: A Cody problem: simplify a polygon

By: Anton

Anton — Tue, 10 Jul 2012 17:48:57 +0000

I have posted a function on FEX a while ago that solves precisely this kind of problem. You can find it here:

http://www.mathworks.com/matlabcentral/fileexchange/34639-decimate-polygon

By: Steve Eddins

Steve Eddins — Tue, 10 Jul 2012 04:45:11 +0000

Sven, Richard—Thanks. I have updated test case #7, and the solutions are being rescored.

By: Richard Brown

Richard Brown — Tue, 10 Jul 2012 04:17:07 +0000

Hi Steve, there’s a problem in your test suite – problem 7 has a starting vertex that can be deleted, but that isn’t in your solution

i.e. P looks like this:

P = [1 2;
1 1;

\vdots

1 4;
1 3;
1 2 ];

The vertex [1 2] should be removed, but isn’t in your solution …

By: Sven

Sven — Tue, 10 Jul 2012 01:50:21 +0000

Hi Steve, nice little problem :)

Are you sure the test set at the moment is correct?

I’ve got a solution that fails only on the “Two rectangles separated by line segment” test. This test has:

P = [ ...
1 2
1 1
2 1
{snip}
1 4
1 3
1 2];

According to the criteria to “remove as many vertices as possible from P”, I think that the progression from [1 4] to [1 3] to [1 2] to [1 1] can be reduced to just [1 4] to [1 1]. However, you’ve kept [1 2] in the “correct” output… *scratches head quizically*

By: Steve Eddins

Steve Eddins — Tue, 10 Jul 2012 01:16:22 +0000

Cris—Thanks for pointing out a flaw in my test suite. I added a new test case and re-scored all the entries.

By: Cris Luengo

Cris Luengo — Mon, 09 Jul 2012 21:39:34 +0000

The problem with my solution, even though it passes the tests, is that the first point (and last, which are assumed to be equal) will never be deleted. If this point is in the middle of a straight line, the solution will be wrong. Fixing this somewhat complicates the code.

By: Steve Eddins

Steve Eddins — Mon, 09 Jul 2012 20:58:23 +0000

UPDATE: In a week or so, I’ll a pick the best solution (according to the well-known purple-seven multiphasic optimality criterion) and send out a prize (a hat or something similar) to the solver.