From: Danny Kodicek <dragon@we...>  20090825 22:33:21

>> 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 