3 ms·
You want geometric algebra. In 2D GA, you would have two unitary vectors, i and j, such that i * i = 1 and j * j = 1. The (non-commutative) product of between t
by yiyus 8y ago
You want geometric algebra. In 2D GA, you would have two unitary vectors, i and j, such that i * i = 1 and j * j = 1. The (non-commutative) product of between them (or their division) would be a bivector: i * j = ij = - j * i. You rotate 90 degrees the i and j vectors using the bivector.
The good thing about GA is that the same concept can be easily extended to 3D (quaternions), and in fact to 4D and nD.
- westoncb 8y agoThat does sound pretty close to what I had in mind. Are i and j from your example associated with orthogonal axes in a plane?
- yiyus 8y agoYes, they are. i would be the unitary vector in the horizontal direction, x, and j in the vertical one, y. In fact, geometric algebras are very general, and the one I briefly sketched is not the only possible interpretation. If you are interested, you can find many good introductions online, directed at different audiences. You can also search for the term "Clifford algebras" if you are interested in a more formal approach.