[R] shade overlapping portions of circles (or other shapes)

I'm making some illustrations and it would be convenient to automatically shade the overlapping portions of circles. These illustrations are for Social Choice theory, a field in political science and economics. I've wrestled together some examples so you can see what I mean, but have not

Re: [R] shade overlapping portions of circles (or other shapes)

A quick and simple way would be to fill both circles with a semi-transparent color (does not work on all devices), then the overlapping area will will show up as a different color/shade due to the alpha blending. You might want to redraw the circles without fill after the filled ones so that the