Question: Algebra for computational geometry and graphics

I would like to experiment with this in my line of work.
What basis/algebra do I need for 3D navigation algorithms / computer graphics?

like:
1) finding the line intersection of two planes
2) finding the point intersection of 3 planes.
3) translation and rotation of points, rotation of vectors.
4) barycentric coordinates of a point in a 3D polytope

No file, test, or entry point is named, and the issue asks for guidance rather than a defined change. First review the repository's geometric-algebra, linear-algebra, quaternion, and computational-geometry scope, then clarify whether the desired outcome is documentation, examples, or an implementation; done is a specifically scoped contribution with an agreed audience and acceptance criteria.

Written by the indexing model from the issue text.