Shane Celis on Nostr: npub14yqjk…vrfl3 But why multiply twice? Well, when you multiple a regular vector p ...

npub14yqjkzqkgv4a27egvq5xmh2ravemytg9g5kldqeqfts92uvh90sq2vrfl3 (npub14yq…rfl3) But why multiply twice? Well, when you multiple a regular vector p with a quaternion, you project it into quaternion space P = 0 + px i + py j + pz k. Notice the real part is zero. In general when you multiply a quaternion and a vector, you don’t get back a vector; you get another quaternion; its real part is not zero. However when you do q P q^-1, you’re guaranteed to get a vector; the real part will be zero. But it is effectively rotating it twice, so that’s why use half angles.