Difference between Change of Basis and Rotation

[nhfoley]

This is probably more of a general math question than a rhino.python specific question... but if both input frames are unitized and orthonormal, what is the difference between an XformRotation4(frame1, frame2) and a ChangeBasis2(frame1, frame2) transform?


Or more generally - given two sets of 3 orthonormal frame vectors, what is the difference between a change of basis and a pure rotation between the two?


They are giving me different results when applied. Should they be identical? I'm trying to figure out if it's my logic or my implementation that is flawed.

[Goswin]

I struggeled with the same topic.
They are certainly not identical.
If you want to remap from one plane to another use Rotation.
You can think of Change of Basis as the reverse of Rotation without the translation.

so if you use the World Plane they are exactly the revers:
world=rs.WorldXYPlane()
rs.XformChangeBasis(anyplan,world) equals rs.XformRotation1(world,anyplane)