rotation

A transform that turns every point the same angle around a fixed center, changing no distances.

A rotation is a linear transform represented by a rotation matrix $R$ that turns every point by the same angle $\theta$ about a fixed origin, preserving every distance and every angle between points -- unlike an affine transform in general (Chapter 6), which is allowed to change them. Composed with a translation, $R$ is exactly the "R" in a camera's extrinsic pose $[R\,|\,t]$ (Chapter 7): the rotation and position of the camera in the world.

Examples

Rotating a square $90°$ about its center produces an identical square in a different orientation -- every side length and every angle inside it is unchanged.