I am facing a problem with the transformation from one coordinate system to another coordinate system. I have 2 coordinate systems and one 3D point in each coordinate system. For example in Coordinate System A, I have a 3D point (14, 23, 65 ) and if I transform it to Coordinate System B, that 3D point will be (-1, 2, 5). So whenever I have another 3D point in Coordinate System A, I want to transform it to Coordinate System B. I have tried to check on some affine transformation but I still can not understand it well. Is there any solution to this?
Thank you
If you have 3 linearly-independant points $p^1$, $p^2$ and $p^3$ corresponding to points $q^1$, $q^2$ and $q^3$. You need to solve for the unknown matrix in the following system:
$\begin{bmatrix} q^1_x&q^2_x&q^3_x\\ q^1_y&q^2_y&q^3_y\\ q^1_z&q^2_z&q^3_z \end{bmatrix} = \begin{bmatrix} a&d&g\\ b&e&h\\ c&f&i \end{bmatrix} \begin{bmatrix} p^1_x&p^2_x&p^3_x\\ p^1_y&p^2_y&p^3_y\\ p^1_z&p^2_z&p^3_z\\ \end{bmatrix}$
You have 9 unknowns and 9 equations.