Euclidean mapping

From Online Dictionary of Crystallography

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Transformation Euclidienne (Fr). Euklidische Abbildung (Ge). Transformazione Euclidiana (It). ユークリッド写像 (Ja). Transformación Euclidiana (Sp).


The Euclidean mapping or isometry is a special case of affine mapping that, besides collinearity and ratios of distances, keeps also distances and angles. Because of this, a Euclidean mapping is also called a rigid motion.

Euclidean mappings are of three types:

  • translations
  • rotations
  • reflections.

A special case of Euclidean mapping is a symmetry operation.