# Homework Help: Finding a rotation matrix (difficult)

1. Jul 5, 2013

1. The problem statement, all variables and given/known data

There are two coordinate systems which have different euler angles. Approximately find the euler angles of the second coordinate system with respect to the first coordinate system. Do this by taking the fact that you are able to plot points and know the position of the points with an error of 1 mm in each coordinate system. Use as many points as it is necessary to get a result with an error of no more than 1 mm if the whole system of rotation is 0.25 meters.

2. Relevant equations

None that are relevent

3. The attempt at a solution

1) Find displacement vector between two coord systems.
2) Find multiple points in both coord systems
3) Find the plane that the two vectors span, corresponding to each individual point (there should be two vectors for each point since we have two coordinate systems).
4) Find the normal vector to the plane
5) From using the dot product, we can find the angle between the two vectors
6) I THINK (someone help me out here if I'm right or not) the angle that we have found between the two vectors should be the same magnitude angle (except the negative of the angle since we are going to rotate the coordinate system instead of vectors). The rotation axis of this angle I THINK, should be around the normal vector to the plane the two vectors spanned.
7) Well now I'm stuck...I figured what I was doing was on the right track but I'm not sure.

I have data for the points so I can start with that, but I dont want anyone to solve the exact solution for me. I am not sure what to do once I have the points. I thought I should find the vector of each point in the second coordinate system, then find the vector of the points in the first coordinate system (except subtract off the displacement vector between the two coordinate systems). Then somehow compare the orientation of the vectors.

Can someone help give an explanation as to how I can somehow find orientation between the two coordinate systems just by having a bunch of different points? I am not sure, but I think it may involve some sort of alogrithm that gets more accurate with more points.

Last edited: Jul 5, 2013