# Model the relationship between 3d points given two reference points

1. Nov 16, 2012

### dwelu

1. The problem statement, all variables and given/known data
Trying to figure out how to model the relationship between two 3D points, A and B. Both points have visibility to 2 common reference points, C and D. Bearing and angle readings are available from both A and B to the reference points C and D. The reference points C and D are at the same elevation. The goal is to spatially model these (relatively model in unitless 3d space) so the true distance between the points is not needed. Distances can be assumed in order to determine a 3d line equation that enables this modeling.

2. Relevant equations
Direction vector: (x-x0, y-y0, z-z0)
Parametric 3d line:
x = x1 + at
y = y1 + bt
z = z1 + ct

3. The attempt at a solution
I have assumed distances to the reference points in order to determine direction vectors, and therefore parametric line equations can be determined from A and B individually to points C and D. After that I’m not sure how to use this to relate the two points A and B.