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Inverse bilinear interpolation (pupil tracker)

I have build a eye tracking application using openCV and i wish to control the location of the mouse pointer using the location of the left eye pupil.

What i have is four points of the pupil that correspond to the four screen corners. Now i would like to map the current coordinate of the pupil given the four corner positions into a screen coordinate position.

Are there any build in functions in openCV that would let me do this? I already did some research and found that inverse bilinear interpolation would allow me to do this. However i can't seem to find this functionality in opencv for Point2f types.