Rotation (geometry)

A transformation that turns points around a fixed center in a plane or an axis in space while preserving distances and angles. Its size and direction are specified by an angle.

Angle of rotation: The directed angle through which a figure or point turns around a fixed center or axis. It specifies the amount and direction of the transformation.
Euclidean distance: The straight-line distance between two points in Euclidean space. A rotation preserves the distance between every pair of points.
Quaternion: A four-component number system used to represent and compose rotations in three dimensions. Quaternions avoid several numerical and representational problems of three-dimensional rotation.
Reflection (mathematics): A transformation that flips points across a line, plane, or higher-dimensional subspace. Reflections preserve distances but reverse orientation, unlike rotations.
Center of rotation: The fixed point in a plane around which a rotation moves other points. Every point turns around this invariant location in a planar rotation.
Rigid transformation: A transformation that preserves distances between all pairs of points. Rotations are one type of distance-preserving transformation.
Gimbal lock: The loss of one rotational degree of freedom in a three-axis orientation representation. It exposes a limitation of representing rotations with Euler angles.
Translation (geometry): A transformation that shifts every point by the same displacement vector. Translations preserve distances without turning points around a center.
Rotation matrix: A matrix that represents a linear transformation rotating vectors around the origin. Multiplying coordinates by it computes a planar rotation.
Orientation (mathematics): A consistent distinction between the two possible directions around a space or coordinate frame. Rotations preserve orientation, unlike reflections.

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