I have a grid in a 2D system like the one in the before image where all points A,B,C,D,A',B',C',D' are given (meaning I know the respective x- and y-coordinates).

I need to calculate the x- and y-coordinates of A(new), B(new), C(new) and D(new) when the grid is distorted (so that A' is moved to A'(new), B' is moved to B'(new), C' is moved to C'(new) and D' is moved to D'(new)).

The distortion happens in a way in which the lines of the grid are each divided into sub-lines of equal length (meaning for example that AB is divided into 5 parts of the equal length |AB|/5 and A(new)B(new) is divided into 5 parts of the equal length |A(new)B(new)|/5).

The distortion is done with the DistortImage class of the Sandy 3D Flash engine. (My practical task is to distort an image using this class where the handles are not positioned at the corners of the image like in this demo but somewhere within it).