I am trying to create a program to automatically render planets and planetary rings. I want to use pycairo since it seems light and easy (however I do take suggestions). I am having a hard time understanding how I would hide only part of the ring that surrounds the planet. I am looking into the ninth line of this pycairo example.

Here is an example of what I envision (example is for inkscape).

My question is: How do I add rings that are tilted (similar to the aforementioned inkscape example) around the sphere depicted in the aforementioned pycairo example?