Rigid transformation

A rigid transformation, also called a Euclidean transformation or Euclidean isometry, is a geometric transformation of Euclidean space that preserves the distance between every pair of points. The principal rigid transformations are rotations, translations and reflections; when handedness, or orientation, is also preserved, so reflections are excluded, a rigid transformation is instead called a rigid motion or a proper rigid transformation. Formally, a rigid transformation can be written as T(v) = Rv + t, where R is an orthogonal matrix representing a rotation or reflection component and t is a translation vector. Because rigid transformations preserve distance between every pair of points by definition, the terms Euclidean transformation and Euclidean isometry are used interchangeably with rigid transformation. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/