I could use some advise with the following problem: Lets say there is a cuboid that has two distinguished points - that is one of its vertexes ($A$) and the other one is somewhere on the surface ($B$).
There is an arbitrary point $X_B$ with coordinates $(a,b,c)$ if you take B as the origin. Now this cuboid gets moved (i.e. a translation and a rotation get applied), so that those two distinguished points on its surface are now at $A'$ and $B'$. The coordinates of $X$ for $B'$ being the origin can be calculated with a transformation matrix: $X_B' = M_B * X = (a', b', c')$
The same thing works for $A$ being the origin: $X_A = (e,f,g) \rightarrow X_A' = M_A * X_A$
Thing is: I know $M_B$ but not $M_A$ - but that is what I need to know. My feeling tells me that probably $M_A = M_B$, as the relationship between A and B stays the same. I've been trying to prove that or to find any other way to get $M_A$ out of $M_B$, but I couldn't find anything. Any help with this is highly appreciated!