CSE167x Lecture3 Transforms 1

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

3D Rotations