Decomposition of a 3D PGA Bivector

I've talked before about how non-simple bivectors can be written as the sum of simple commuting bivectors, making calculating exponentials much easier. But what does this mean geometrically? In this short, I show what this looks like in 3D PGA, which is one of the simplest cases where this is important.

Supporters:
David Johnston
Jason Killian
jerrud
Richard Penner
trb

[minerharry]

Looks like we’re already seeing ganim at work! Sick animations!

[DrDeuteron]

This is so weird. The algo. I read about bi quaterons and screws and now this? Idk, wtf was this about? And I do in fact have a phd in physics.but for real. Screws?

[ARBB]

Are you going to discuss geometric antiproducts and such eventually?

[mohammadeliousali]

Does this mean we can somehow write the exponential of sum of two non-commuting matrices as the product of exponential of some simmple commuting matrices? If yes, is there a paper or video where I can look this?

[raymondfrye]

Geometric Algebra?...or Algebraic Geometry?

[tinkeringtim]

Screw theory by Robert Ball. Worth citing where the ideas come from.