# Finding orientation of object in 3D space

Given the above constellation, I have to find the orientation of object B in the coordinate system of Object C. The objects A and B are fixed to a certain place and the object C can move in freely in 3D space.

I am given the following values:

• position of object B in the coordinate system of object A: $$Pos_B = (x_B, y_B, z_B)^T$$
• position of object C in the coordinate system of object A: $$Pos_C = (x_C, y_C, z_C)^T$$
• the orientation of object C in its own coordinate system : $$Rot_C = (\alpha_C, \beta_C, \gamma_C)^T$$
• A transformation matrix to move from (x,y,z)-coordinates (system A) to (m,n,o)-coordinates (system B): $$T_{xyz}$$

Additionally, I can always measure $$Pos_C$$ whenever object C moves.

Given the above information, does anyone have an idea how to get the orientation of object B?

Thanks in advance and if anything is unclear please let me know.

• The formulation "he orientation of object C in its own coordinate system" might be misleading. How can an object have an orientation relative to its own coordinate system. Could you specify more explicitly, what does this mean? Is it a translated CS with orientation parallel to A or B, relative to which the orientation is specified?
– 50k4
Nov 13 '20 at 16:32
• Is there an object C which moves away from its starting location? And you can read this offset?
– Ben
Nov 13 '20 at 18:31
• is this school work? Nov 14 '20 at 6:15