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Topic: From distances to points
Replies: 3   Last Post: Feb 18, 2013 4:02 AM

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Posts: 4
Registered: 12/18/04
From distances to points
Posted: Feb 17, 2013 8:20 AM
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I have given the measured distances between N points in space. I'm looking for the coordinates of these points.

For example there are 5 points P1,.., P5. The distances could be written as

P1 P2 P3 P4 P5
P1 0 r12 r13 r14 r15
P2 r21 0 r23 r24 r24
P3 r31 r32 0 r34 r35
P4 r41 r42 r43 0 r45
P5 r51 r52 r53 r54 0

As these values are measured r21!=r12.

I'm looking for an algorithm to find the points P1 (x1,y1,z2) .. P5 (x5,y5,z5) such that their positons are 'optimal'. A good criteria for optimal could be the following:

sum( (rij - Rij)^2 ) -> min where rij are measured dist, Rij optimized

To start I know that I have to fix some points, eg P1=(0,0,0) P2=(0,0,z) P3=(0,u,v)

Any ideas?


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