>> Problem: Given n lines, determine a point minimizing the summation of the
>> distances from the point to the n lines.
>>
>
> This is a Least Absolute Deviations problem, which are normally solved by
> simplex methods; see the Wikipedia page for more details. If an O(n^3)
> running time is acceptable to you, however, a minimal solution will always
> be found at the intersection of two of the lines, so you can just check
> all
> the intersection points if you like.
What if the lines are parallel? For two parallel lines, any point between or
on the lines will solve it, for three it'll be a point on the middle line,
etc.
Sounds like an odd thing to want, really - there's presumably often lots of
these points. Under what circumstances might one look for this rather than,
say, a least squared distance?
<relurk>
Danny
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