Quaternion type: Difference between revisions

(An exception to this need to normalize unit length quaternions after multiplication might be when quaternions are represented as an index into a [[wp:Geodesic_grid|geodesic grid]]. For example, a grid with 25x2016x20 faces would have <code>a total of 15 vertices for each face (5+4+3+2+1), 3 of those vertices would be from the original 20 vertices of the icosahedron, and 9 of those vertices (5+4+3-3) would be on the edge of the original face (and, thus, use for two faces), the remaining 3 vertices would be interior. This means we would have 170 vertices (20+(20*189%2</code> vertices)+20*3, which would allow a quaternion to be represented in a single byte index into a list of 200170 quaternions, and would allow quaternion multiplication to be represented as a 40kbyte29kbyte lookup table. In some contexts - where quaternion multiplication is needed in high volume for secondary or tertiary issues (where precision isn't vital), such low precision quaternions might be adequate or even an advantage...)