3D cartesian coordinate system conversion

[light]

Hi all,

I have a 3d point in a Cartesian coordinate system "A" that I want to map to Cartesian coordinate system "B". Both systems have the same origin, but coordinate system B has been rotated around all three axes (in respect to system A).

As a very simple example, lets say I know a point in system "A" is at (3,0,0) and system "B" has been rotated around one of the axes by 180 degrees. What I would like to do is identify a formula that would tell me "in coordinate system B, this point is at (-3, 0, 0)."

I have thought about this problem in 2d and know I can solve it using the magnitude of the vector v (origin to point) and known rotation angle phi:
newx = cos(phi)*v
newy = sin(phi)*v

I haven't figured out how to do this in 3d coordinates yet. I would appreciate it if someone could point me in the right direction on how to accomplish this!

 

[Deleted member 4993]

Hi all,

I have a 3d point in a Cartesian coordinate system "A" that I want to map to Cartesian coordinate system "B". Both systems have the same origin, but coordinate system B has been rotated around all three axes (in respect to system A).

As a very simple example, lets say I know a point in system "A" is at (3,0,0) and system "B" has been rotated around one of the axes by 180 degrees. What I would like to do is identify a formula that would tell me "in coordinate system B, this point is at (-3, 0, 0)."

I have thought about this problem in 2d and know I can solve it using the magnitude of the vector v (origin to point) and known rotation angle phi:
newx = cos(phi)*v
newy = sin(phi)*v

I haven't figured out how to do this in 3d coordinates yet. I would appreciate it if someone could point me in the right direction on how to accomplish this!

For a quick tutorial - go to:

http://mathworld.wolfram.com/RotationMatrix.html

Finally, make google your friend .....

 

[light]

Thank you. Google is great, but if you don't know what terms to look for it can be awfully frustrating to find what you are looking for.

I actually skimmed over rotation matrices, but thought they were only useful for rotating a point vs. re-mapping them which is what I am trying to do.