Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they …

Rotation quaternions are closely related to the axis-angle representation of rotation. We will therefore start with an explanation of the axis-angle representation, and then show how to …

Both operators v⋆ and ⋆v define the same rotation angle, but the opposite rotation direction around the chosen axis. The rotation direction depends on the perspective of the rotation as …

Quaternions are very efficient for analyzing situations where rotations in R3 are involved. A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo …

Sep 21, 2024 · Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared …

Unit quaternions represent the mathematical space of rotations in three dimensions in a very straightforward way. The correspondence between rotations and quaternions can be …

Quaternions are used in computer graphics and related fields because they allow for compact representations of rotations in 3D space. This will be explained in this article. A pair of …

Also see Quaternions and spatial rotation for more information about modeling three-dimensional rotations using quaternions. See Hanson (2005) [42] for visualization of quaternions.

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they …

Quaternion rotation maintains vector magnitude. Quaternion rotation maintains angular deviation between two vectors. Quaternion rotation maintains the magnitude of the triple product. …