Combo

This is the simplest one.

but one has to know about the other operations......

it simply combines all the operations together as

x_new=k_TX * x_translation + k_RX * x_rotation + k_SX * x_scaling

and similarly

Y_new=k_Ty * y_translation + k_Ry * y_rotation + k_Sy * y_scaling

where k is a linear or nonlinear operator

and its done...............simple na.