Identity returns a new matrix initialized to the identity.

Mul returns the transform T * U, which apply U then T.

Mul3 returns the transform R * S * T, which applies T, then S, then R.

Rotation returns a rotation.

Scaling returns the scaling by (sx, sy).

Skew returns a skew transformation.

Translation returns the translation by (tx, ty).

Transform encode a (2D) linear transformation The encoded transformation is given by : x_new = a * x + c * y + e y_new = b * x + d * y + f which is equivalent to the vector notation Y = AX + B, with A = | a c | ; B = | e | | b d | | f | Transformation may also be viewed as 3D matrices of the form T = | a c e | | b d f | | 0 0 1 | and P = | x | | y | | 1 | where | x_new | = T * P | y_new | | 1 |.