Notes about CSE167 of UCSD on Edx.
Slices available at https://is.gd/6iQ1hZ
Basic 2D Transform
scale
shear
rectangular shape -> parallelogram
$X’ = X + aY$
Y coordinate is equal to original, in other words, $Y’ = Y$
rotation
R(X+Y) = R(X) + R(Y)
- Linear: Rotation is a linear operation.
- Commutative: In 2D, it is commutative(可交换的), while in 3D, it is not.
Conclusion:
$\begin{bmatrix} x’ \ y’ \end{bmatrix} = \begin{bmatrix} \cos { \theta } & -\sin { \theta } \ \sin { \theta } & \cos { \theta } \end{bmatrix}\begin{bmatrix} x \ y \end{bmatrix}$
Composing transforms
Not commutative!! Order matters
Inverting Composite Transforms
