Convert Google Maps Polygons, Circles, and Squares to PHP GD Drawing

I want to create polygons, squares, and circles using google maps api v3 drawing manager library and replicate those shapes in php's gd library. I want to submit a form with all the shapes drawn, their vertices to store later in mysql (I will take care of all that if the form submits the coordinates, radius, etc for each shape), and redraw the shapes in the php gd library and save the image or simply echo the headers and image (I will clean it up later, no need to be fancy). jQuery can be used to inject hidden form elements with the shape information for saving after the drawing is complete, etc. I believe the easiest way would be to convert the vertices of the shapes to pixel position to redraw them in php but I'm having trouble creating a new dummy overlay, getting the projection, and getting it to all work. I've included an html file to start from