Capping Spheres from two sides.

I am working on a program to display many spheres, and one feature is a “slice” to get the view into a different section of the spheres. This involves the possibility of a sphere being cut on both sides, so that you see a circle with a hole in it basically. I need to be able to cap both sides of the spheres and both clipping planes are always parallel. Using the standard “Cap” method, drawing back faces then front faces does not work because there are no faces at all where I need the caps to be. If anyone has any idea how to set up the stencil to be able to draw caps where there are no faces at all and still be able to rotate etc. it would be greatly appreciated.