In particular the order of the leaves of the tree (when read left to right for example) cannot change (another way to think of it is that the order that the leaves would be visited in an in-order traversal must be the same after the operation as before).

The key to understanding how a rotation functions is to understand its constraints. The inverse operation is the left rotation, which results in a movement in a counter-clockwise direction (the left rotation shown above is rooted at P). This operation results in a rotation of the tree in the clockwise direction. The right rotation operation as shown in the adjacent image is performed with Q as the root and hence is a right rotation on, or rooted at, Q. This article takes the approach of the directional movement of the rotating node. Some say that the direction of rotation reflects the direction that a node is moving upon rotation (a left child rotating into its parent's location is a right rotation) while others say that the direction of rotation reflects which subtree is rotating (a left subtree rotating into its parent's location is a left rotation, the opposite of the former). There exists an inconsistency in different descriptions as to the definition of the direction of rotations. It is used to change the shape of the tree, and in particular to decrease its height by moving smaller subtrees down and larger subtrees up, resulting in improved performance of many tree operations. A tree rotation moves one node up in the tree and one node down. In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements.

Rotate figures in pivot animator