Drawing the cap for a sphere.

It appears as though I’ve gotten the stencil buffer enabled, and I use glStencilOp(Replace, replace, invert) for my drawing to fill the buffer with 1’s(The defaults are all 0’s), however I’m not sure how to draw the caps themselves. If I draw something that “Covers the whole window” with glStencilFunc(GL_EQUALS,0x1,~0) should it “Fill” The portions that were clipped? I’m not quite sure how that makes sense, and I’m also not sure how to create a quadralateral that will fill the screen. The code I was working doesn’t draw anything even withou the stencil buffer.