“ In projective and conformal geometric algebra the line and sphere "at infinity" become concrete, and this permits rotations, translations and dilatons to all be described by rotor sandwich products. “
Plato was right and the world *is* made of sandwiches. Sandwich products sounds terribly like the quaternion math used in game dev. I hope the universe works this way for the reasons quats are used!
Yes indeed, well spotted! The quaternions are a (twisted) subalgebra of the Clifford algebra for N>3 space. Chris Doran and Joan Lasenby are active in game software research. They have some very fast algorithms, and tell me the geometric algebra is even faster than quaternions.... and of course more versatile, since in GA everything useful is a sandwich product. Yumyum.
Few know this, but the quaternions are unwittingly under-the-hood using a left-handed coordinate frame. The bivector even subalgebra is right-handed. So if I were Misha Gromov I'd say, "Quaterrrrniiiions are stuupeeed." (I can't do a good Russian accent.)
“ In projective and conformal geometric algebra the line and sphere "at infinity" become concrete, and this permits rotations, translations and dilatons to all be described by rotor sandwich products. “
Plato was right and the world *is* made of sandwiches. Sandwich products sounds terribly like the quaternion math used in game dev. I hope the universe works this way for the reasons quats are used!
Yes indeed, well spotted! The quaternions are a (twisted) subalgebra of the Clifford algebra for N>3 space. Chris Doran and Joan Lasenby are active in game software research. They have some very fast algorithms, and tell me the geometric algebra is even faster than quaternions.... and of course more versatile, since in GA everything useful is a sandwich product. Yumyum.
Few know this, but the quaternions are unwittingly under-the-hood using a left-handed coordinate frame. The bivector even subalgebra is right-handed. So if I were Misha Gromov I'd say, "Quaterrrrniiiions are stuupeeed." (I can't do a good Russian accent.)
Anything is better than gimbal lock! Although, GL is good for meme game videos (don't ask).
See, I am going to start in with the acronyms now. It will be a TLA arms race, all the way down.