Mario
Posts:
4
Registered:
12/18/04


From distances to points
Posted:
Feb 17, 2013 8:20 AM


Hi
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?
Thanks Mario

