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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.All rigid transformations are examples of affine transformations. 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 kinematics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. According to Chasles' theorem, every rigid transformation can be expressed as a screw displacement.".
- Rigid_transformation wikiPageID "27832980".
- Rigid_transformation wikiPageLength "7350".
- Rigid_transformation wikiPageOutDegree "31".
- Rigid_transformation wikiPageRevisionID "649127814".
- Rigid_transformation wikiPageWikiLink Affine_transformation.
- Rigid_transformation wikiPageWikiLink Affine_transformations.
- Rigid_transformation wikiPageWikiLink Angular_displacement.
- Rigid_transformation wikiPageWikiLink Category:Euclidean_symmetries.
- Rigid_transformation wikiPageWikiLink Category:Functions_and_mappings.
- Rigid_transformation wikiPageWikiLink Category:Kinematics.
- Rigid_transformation wikiPageWikiLink Chasles_theorem_(kinematics).
- Rigid_transformation wikiPageWikiLink Determinant.
- Rigid_transformation wikiPageWikiLink Displacement_(vector).
- Rigid_transformation wikiPageWikiLink Dot_product.
- Rigid_transformation wikiPageWikiLink Euclidean_distance.
- Rigid_transformation wikiPageWikiLink Euclidean_geometry.
- Rigid_transformation wikiPageWikiLink Euclidean_group.
- Rigid_transformation wikiPageWikiLink Group_(mathematics).
- Rigid_transformation wikiPageWikiLink Improper_rotation.
- Rigid_transformation wikiPageWikiLink Isometry.
- Rigid_transformation wikiPageWikiLink Kinematics.
- Rigid_transformation wikiPageWikiLink Lie_group.
- Rigid_transformation wikiPageWikiLink Metric_space.
- Rigid_transformation wikiPageWikiLink Orientation_(mathematics).
- Rigid_transformation wikiPageWikiLink Orientation_(vector_space).
- Rigid_transformation wikiPageWikiLink Orthogonal_matrix.
- Rigid_transformation wikiPageWikiLink Orthogonal_transformation.
- Rigid_transformation wikiPageWikiLink Pythagorean_theorem.
- Rigid_transformation wikiPageWikiLink Reflection_(mathematics).
- Rigid_transformation wikiPageWikiLink Rigid_body.
- Rigid_transformation wikiPageWikiLink Rotation_(mathematics).
- Rigid_transformation wikiPageWikiLink Scalar_product.
- Rigid_transformation wikiPageWikiLink Screw_axis.
- Rigid_transformation wikiPageWikiLink Screw_displacement.
- Rigid_transformation wikiPageWikiLink Shape.
- Rigid_transformation wikiPageWikiLink Translation_(geometry).
- Rigid_transformation wikiPageWikiLink Translation_(mathematics).
- Rigid_transformation wikiPageWikiLinkText "Euclidean, or rigid, transformations".
- Rigid_transformation wikiPageWikiLinkText "Rigid transformation".
- Rigid_transformation wikiPageWikiLinkText "rigid transformation".
- Rigid_transformation wikiPageWikiLinkText "rigid".
- Rigid_transformation hasPhotoCollection Rigid_transformation.
- Rigid_transformation wikiPageUsesTemplate Template:Reflist.
- Rigid_transformation subject Category:Euclidean_symmetries.
- Rigid_transformation subject Category:Functions_and_mappings.
- Rigid_transformation subject Category:Kinematics.
- Rigid_transformation type Function.
- Rigid_transformation type Relation.
- 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 Euklidische_Transformation.
- Rigid_transformation sameAs m.0cc5hbp.
- Rigid_transformation sameAs Q7333813.
- Rigid_transformation sameAs Q7333813.
- Rigid_transformation wasDerivedFrom Rigid_transformation?oldid=649127814.
- Rigid_transformation isPrimaryTopicOf Rigid_transformation.