In Euclidean geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. A rotation...

Charts on SO(3) Rotations and reflections in two dimensions CORDIC Squeeze mapping Infinitesimal rotation matrix Irrational rotation Orientation (geometry)...

describing more complex rotations in four-dimensional space and higher dimensions, where they can be used to break down the rotations into simpler parts....

rotation can be decomposed into a combination of principal rotations. The combination of any sequence of rotations of an object in three dimensions about...

and reflection is said to have improper rotation symmetry. In 3 dimensions, improper rotation is equivalently defined as a combination of rotation about...

(instead of +1). These combine proper rotations with reflections (which invert orientation). In other cases, where reflections are not being considered, the label...

groups are: ∞∞, K, or SO(3), all possible rotations. ∞∞m, Kh, or O(3), all possible rotations and reflections. As noted above for the infinite isometry...

a rotation matrix, as well as the ease of combining successive rotations, make the rotation matrix a useful and popular way to represent rotations, even...

(along composite rotations' associative property), the set of all rotations is a group under composition. Every non-trivial rotation is determined by...

including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal...