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Talk:Problem of Apollonius: Difference between revisions
→Meta error propagation: some comments to remind the brave ones who may want to fix the bug
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::: The problem is a division by zero, specifically when v11 is 0. AFAIK it's in all the examples. There may be other problems, for instance I wouldn't be surprised if all the solutions fail to handle some degenerate cases.
::: On a not quite related note, I do think line-by-line translations should be discouraged. Even if you have to pick up the algorithm from some existing examples, it's probably better to rewrite the code from semi-scratch, if only to make sure it's more idiomatic to your language. As to a solution -- I have no idea. --[[User:Ledrug|Ledrug]] 02:34, 15 September 2011 (UTC)
In searching of a proper fix, I scribbled many circles on a piece of paper, and reached the conclusion: I don't want any part of it. First off, the current problem of dividing by zero is just a minor annoyance. There are two fundamental problems:
# Circles can't always be represented by <code>[(x, y), r]</code>. Even if we ignore [[wp:Special cases of Apollonius' problem|degenerate input circles]], one still has to deal with degenerate solution circles, e.g. <code>[(0, -2), 1], [(0, 0), 1], [(0, 2), 1]</code> has two solutions that are straight lines.
# Touching each circle internally or externally isn't enough to identify a unique solution. <code>[(0, -3), 2], [(0, 0), 1], [(0, 3), 2]</code> has no solution that contains all circles inside, but has two solutions that's outside every circle. Essentially this involves whether solution is allowed to have negative radius: if it is, there's the risk of double counting; if not, there's the risk of missing solutions.
Besides the above, there are other special cases: <code>[(0, 0), 1], [(0, 0), 2], [(0, 0), 3]</code> has no solution; <code>[(0, 1), 1], [(0, 2), 2], [(0, 3), 3]</code> has infinitely many solutions, to name just two. Someone once said, "programming is all about special cases." Unfortunately, for Problem of Apollonius, there seem to be nothing ''but'' special cases. --[[User:Ledrug|Ledrug]]
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