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- Rigid_transformation abstract "In mathematics, a rigid transformation (isometry) of a vector space preserves distances between every pair of points. Rigid transformations of the plane R2, space R3, or real n-dimensional space Rn are termed a Euclidean transformation because they form the basis of Euclidean geometry.The Rigid transformations include rotations, translations, reflections, or their combination. Sometimes reflections are excluded from the definition of a rigid transformation by imposing that the transformation also preserve the handedness of figures in the Euclidean space (a reflection would not preserve handedness; for instance, it would transform a left hand into a right hand). To avoid ambiguity, this smaller class of transformations is known as proper rigid transformations (informally, also known as roto-translations). In general, any proper rigid transformation can be decomposed as a rotation followed by a translation, while any rigid transformation can be decomposed as an improper rotation followed by a translation (or as a sequence of reflections). Any object will keep the same shape and size after a proper rigid transformation, but not after an improper one.All rigid transformations are affine transformations. Rigid transformations which involve a translation are not linear transformations. Not all transformations are rigid transformations. An example is a shear, which changes two axes in different ways, or a similarity transformation, which preserves angles but not lengths. The set of all (proper and improper) rigid transformations is a group called the Euclidean group, denoted E(n) for n-dimensional Euclidean spaces). The set of proper rigid transformation is called special Euclidean group, denoted SE(n).In mechanics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies.".
- Rigid_transformation wikiPageID "27832980".
- Rigid_transformation wikiPageRevisionID "577798741".
- Rigid_transformation hasPhotoCollection Rigid_transformation.
- Rigid_transformation subject Category:Functions_and_mappings.
- Rigid_transformation type Abstraction100002137.
- Rigid_transformation type Function113783816.
- Rigid_transformation type FunctionsAndMappings.
- Rigid_transformation type MathematicalRelation113783581.
- Rigid_transformation type Relation100031921.
- Rigid_transformation comment "In mathematics, a rigid transformation (isometry) of a vector space preserves distances between every pair of points. Rigid transformations of the plane R2, space R3, or real n-dimensional space Rn are termed a Euclidean transformation because they form the basis of Euclidean geometry.The Rigid transformations include rotations, translations, reflections, or their combination.".
- Rigid_transformation label "Rigid transformation".
- Rigid_transformation sameAs m.0cc5hbp.
- Rigid_transformation sameAs Q7333813.
- Rigid_transformation sameAs Q7333813.
- Rigid_transformation sameAs Rigid_transformation.
- Rigid_transformation wasDerivedFrom Rigid_transformation?oldid=577798741.
- Rigid_transformation isPrimaryTopicOf Rigid_transformation.