Library/Geometry/Plane geometry/Plane transformations/Movements/Rotation/Compositions of rotations

Compositions of rotations

Overview
Important

A composition of two or more rotations in the plane means performing one rotation after another. The result of composing two rotations depends on their centers and angles. If the centers are the same, the composition is a rotation about that center by the sum of the angles. If the centers are different, the composition is usually not a rotation, but can be a translation or another type of transformation.

Important properties

  • Composing two rotations with the same center results in a rotation with the same center and the sum of the angles.

  • Composing two rotations with different centers usually results in a transformation called a 'rotation-translation' or a 'glide rotation', which is not generally a pure rotation.

  • The order of rotations matters if the centers are different (composition is not commutative).