Coordinate System Transformations

[phil0stine]

Lets say I have Coordinate Frame's A and B.

and...

I have the coordinates of the 3 principle axes of B in terms of Frame A,

So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A:

X_A -> -Y_B
Y_A -> X_B
Z_A -> Z_B

My question is: Given a slightly more complex mapping, but without knowledge of euler rotations, how could a Rotation Matrix be calculated?

Thanks in advance

 

[JeSuisConf]

Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)

 

[phil0stine]

Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)

Clean and simple, with the added bonus of triggering a very faint memory of learning that once.

Thanks so much for clearing it up, this is what I need for my application.