Problem on coordinate conversion

[tancm]

Set the coordinate system a, coordinate system b and coordinate system c coincident, they have common

origin of coordinate O. b and c rotate in accordance by OA modulus size along vector OA according to right-hand rule. A

with coordinate (xa, ya, za) was mapped to a. Then c rotate by OB modulus size along vector OB according to right-hand

rule. B with coordinate (xb, yb, zb) was mapped to b. Now the c can also be got once from the coincident position along

vector OC according to right-hand rule, rotating by OC modulus size, where C with coordinate (x1a, y1a, z1a) was mapped to

a. A (xa, ya, za) and B (xb, yb, zb) are known, How to get C (x1a, y1a, z1a)?

[Guest]

The easiest way is probably to use quaternions.
http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
Change your rotation vectors into quaternions, multiply them, then convert the quaternion back into a rotation vector.

Hope this helps,

R. Baber.