- Always be aware that whether your transformation is intrinsic or extrinsic.
- Multiplication order of quaternions or transformation matrices is inverted between the two.
In this article, right-handed system is used.
Let’s think of composite transformation $T_c$, which applies $T_1$ first, and then $T_2$.
- $T_1$: Rotate 90 deg around x-axis
- $T_2$: Rotate 180 deg around z-axis
Which is correct, $T_c = T_1 T_2$ or $T_c = T_2 T_1$ ?
Actually both can be true, we are missing something to identify $T_c$.