Quaternions and spatial rotation of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented
Six degrees of freedom on each hand. The SpaceOrb 360 is a 6DOF computer input device released in 1996 originally manufactured and sold by the SpaceTec IMC company (first bought by Labtec, which itself was later bought by Logitech). The controllers sold with HTC VIVE provide 6DOF information by the lighthouse, which adopts Time of Flight (TOF) technology to determine the position of controllers. Six degrees of freedom Six degrees of freedom (6DoF) refers to the freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three