---
title: "Ivory: With Jubilee And Circle Line"
---

> | Roam in grace, there's no frontier
> | There is life beyond the spheres
> | The long way home
> | Endless space
> | Proceed and carry on
> | The long way home
> | There is life beyond the spheres
— <cite>Blind Guardian, *Life Beyond the Spheres*</cite>

TODO:

 - Extend PGA to CGA
 - Grades represent circles, spheres, etc.
   - Lines, planes, etc. emerge when passing through infinity
 - Try to remain compatible with projective definitions
   - CGA is more general, so ideally PGA would be implemented in terms of CGA
     (just using a subset).
   - Seems tricky given that their signatures are different...