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translation matrix equation (2d / Basic)
P'=T+P
 x' = x + dx
 y' y dy

scale matrix equation (2d / Basic)
P'=S.P
 x' = sx 0 . x
 y' 0 sy y

rotation matrix equation (2d / Basic)
P'=R.P
 x' = cos# sin# . x
 y' sin# cos# y

Homogeneous Transformations

What is the homogeneous coordinate?
The last coordinate, called homogeneous coordinate. Used to project the scene onto the screen.

What is concatenation in the context of Transformation?
sequentially multiplying matrices to combine scaling, rotation and translation in just one step.
 e.g.
 Scale then Translate
 p' = T S p
 T S = 1 0 3 . 2 0 0 = 2 0 3
 0 1 1 0 2 0 0 2 1
 0 0 1 0 0 1 0 0 1
remember: AB != BA

Whats matrix inversion good for?
where V are coordinate systems

coordinate system transformation






3D rotation about arbitrary axis

View transformation detail

