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Difference between revisions of "Euclidean mapping"

From Online Dictionary of Crystallography

(Tidied translations and added German (U. Mueller))
 
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<font color="blue">Transformation Euclidienne</font> (''Fr''). <font color="black">Transformazione Euclidiana</font> (''It''). <font color="purple">ユークリッド写像</font> (''Ja'')
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<font color="blue">Transformation Euclidienne</font> (''Fr''). <font color="red">Euklidische Abbildung</font> (''Ge''). <font color="black">Transformazione Euclidiana</font> (''It''). <font color="purple">ユークリッド写像</font> (''Ja''). <font color="green">Transformación Euclidiana</font> (''Sp'').
  
  
The '''Euclidean mapping''' 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''.
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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:
 
Euclidean mappings are of three types:

Latest revision as of 09:45, 13 November 2017

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.