One interesting, but awkward possibility -- that may never occur, but has to be dealt with in case it does -- is if all three points of a triangle are equal.

Then the plane is flat and 'my angle' could cross it with any orientation. I'd have to look to the triangles adjoining the other two sides of the triangles that adjoin at my boundary to see how the potential flows through this boundary segment. Does your vector math cater to that?

Thinking about it more, if a triangle is flat, then it is either a local peak or trough and the potential will flow around, but not through it.

And that leads to the fact that if any segment on my boundary is formed by a pairs of points with equal height, then the potential will not cross the boundary through that segment at all, but rather will flow through the adjoining triangles, parallel to it; or not at all in the flat triangle case.

It may be too late, but I found another good reference on Wikipedia: it appears that AM was basically describing the Meandering Triangle variant of the Marching Squares algorithm.

To handle the case of vertices being equal, that article uses isobands instead of isobars (contour lines): label each point in the triangle (0 for points less than your level, 1 for points equal to your level, and 2 for points greater than your level), and then follow their lookup table for the shape of the isoband.

Thanks for that. Actually, as I'm only looking to discover the angle at which the lines would cross the triangles -- rather than actually plotting the lines which the simulation software already does -- AM's limited observations were all I required to code that part of the problem. It's still good to know some background though.

A harder part of the task was hacking the software's input and results files; but they are plain text files with a fairly obvious if not well documented structure.

The hardest part of the entire problem was waiting for the 60+ hours between setting the problem running and getting the results. Especially when as soon as I viewed them, it was blatantly obvious I had made a trivial mistake in the specification of one of the boundary conditions and would need to wait another 60+ hours for the correction :(

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With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I knew I was on the right track :)

In the absence of evidence, opinion is indistinguishable from prejudice.

Cheat. Put a new point of slightly different height in the middle of the triangle to form three new triangles that don't have this problem. :)

Not so fast. All that would do is create a local closed loop that still doesn't cross the boundary:

----------------------------------------------------
 \---____                                  ____---/
   \     ----_***********************__----     /
     \         * ----____  ____----*          /
       \         *       +       *          /
         \         *     |     *          /
           \         *   |   *          /
             \         * | *          /
               \         *          /
                 \       |        /
                   \     |      /
                     \   |    /
                       \ |  /
                         \/
[download]

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With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I knew I was on the right track :)

In the absence of evidence, opinion is indistinguishable from prejudice.