And there are coordinate system that are called as:
- left handed coordinate system
- right handed coordinate system
For some reasons I have observed ambiguousness in various rotation matrices.
Example: Rotation about y-axis by t could be written as:
$$
\begin{bmatrix}
cost & 0 & -sint & 0 \\
0 & 1 & 0 & 0 \\
sint & 0 & cost & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}
$$
Check 25:28 of the video and step numbered (3).
This is frying my brain since few days. I know getting free assistance in this huge topic is not possible. But even if you could display a small support, small guidance, that would be greatly push me through this phase.
References:
https://stackoverflow.com/questions/19747082/how-does-coordinate-system-handedness-relate-to-rotation-direction-and-vertices
shivajikobardan•5mo ago
https://www.cairographics.org/cookbook/matrix_conventions/
The reason behind this is called pre-multiplication vs post-multiplication technique of matrix transformation.
Post-multiplication
- transformation matrix appears after the position vector matrix
- position vector matrix in homogenous coordinates is represented as a row matrix.
Pre-multiplication
- transformation matrix appears before the position vector matrix
- here the position vectors in homogenous coordinates are represented in column matrix.
Textbook reference: Mathematical elements for computer graphics Rogers/Adams