I need to draw a BufferedImage within a given quadrilateral. I want to do that:

I would like the cat to be deformed to be drawn within the quadrilateral.
Graphics objects have different methods to draw images, but only to stretch them along the X and Y axis (See Graphics.drawImage methods).
What I am dreaming of is a method Graphics.drawImage() where I specify the coordinates of the 4 quadrilateral points. Is there an easy way to do that?