Rotacionin

Rotacionin, the Albanian term for rotation, denotes the geometric transformation that rotates a figure or set of points about a fixed axis by a given angle. It is a rigid motion: distances and angles between points are preserved, and, in three dimensions, orientation is preserved as well (no reflections). In two dimensions, rotation is about a point; in three dimensions it is about a line, the rotation axis.

Mathematically, rotations are represented by orthogonal matrices with determinant 1, forming the special orthogonal groups SO(2) and SO(3) in 2D and 3D, respectively. Common parameterizations include Euler angles (three angles), axis–angle form (an axis vector and an angle), Rodrigues' rotation formula, and unit quaternions. In many applications, the axis–angle form is convenient for intuition, while quaternions avoid some drawbacks of Euler angles, such as gimbal lock.

Rotations can be composed by matrix multiplication; the order of composition matters, so turning first around one axis and then another generally differs from reversing the order. The right-hand rule determines the direction of the rotation axis.

Applications span computer graphics and animation, robotics and control, aviation and spacecraft attitude, crystallography, and geophysics. Practical considerations include numerical accuracy, the non-commutative nature of 3D rotations, and parameterization-induced singularities.