jzhao.xyz

Search

Search IconIcon to open search

Computer Graphics

Last updated Jan 23, 2023 Edit Source

# Coordinate Frames

Let $A$ be the original coordinate frame and $B$ be the target coordinate frame

$$\begin{bmatrix}x \\ y \\ 1 \end{bmatrix}_B = \begin{bmatrix}a & b & c \\ d & e & f \\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}x \\ y \\ 1\end{bmatrix}_A$$

Then:

Overall,

The translation from $P_A$ to $P_B$ can be represented as $P_B = O_A + x_Ai_A + y_Aj_A$