Re: Point with shortest distance to 3 lines
- From: "Larry Hammick" <larryhammick@xxxxxxxxx>
- Date: Tue, 05 Jun 2007 03:31:34 GMT
"Andrew" <chrisr34000@xxxxxxxxxxxxxx> wrote in message
news:1180991213.899304.259280@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi!
Let D_i:={(x,y) \el \IR^2 : y = a_i*x+b_i }, i=1,2,3 determine 3 lines
in |R^2.
I'm now looking for the point P(p_1,p_2) which has the shortest
distance to all these 3, given, lines.
If no two of the lines are parallel, the three lines chop up the plane into
7 regions. Write f(point) for the sum of the three distances. The gradient
of f, within any of the seven open regions, is a sum of three _constant_
unit vectors. I think you can work it all out from there.
For a scalene triangle whose three side lengths are distinct, there is a
unique minimizing point, namely the vertex which is opposite the longest
side.
LH
.
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