Active and passive transformation: Difference between revisions

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{{For|the concept of "passive transformation" in grammar|active voice|passive voice}}

[[File:PassiveActive.JPG|thumb|310px|In the active transformation (left), a point moves{{mvar|P}} fromis position Ptransformed to point {{mvar|{{′|P'}}}} by rotating clockwise by an [[angle]] {{mvar|θ}} about the [[origin (mathematics)|origin]] of thea fixed coordinate system. In the passive transformation (right), point {{mvar|P}} doesstays not movefixed, while the coordinate system rotates counterclockwise by an angle {{mvar|θ}} about its origin. The coordinates of {{mvar|{{′|P'}}}} inafter the active case (that is,transformation relative to the original coordinate system) are the same as the coordinates of {{mvar|P}} relative to the rotated coordinate system.]]

[[Geometric transformation]]s can be distinguished into two types: '''active''' or '''alibi transformations''' which change the physical position (''alibi'' means "elsewhere") of a set of [[point (geometry)|point]]s relative to a fixed [[frame of reference]] or [[coordinate system]]; and '''passive''' or '''alias transformations''' which leave points fixed but change the frame of reference or coordinate system relative to which they are described (''alias'' means "other name").<ref>Weisstein, Eric W. [http://mathworld.wolfram.com/AlibiTransformation.html "Alibi Transformation"], [http://mathworld.wolfram.com/AliasTransformation.html "Alias Transformation"]. ''Mathworld''.</ref><ref name= Davidson>{{cite book | title=Robots and screw theory: applications of kinematics and statics to robotics | author=Joseph K. Davidson, Kenneth Henderson Hunt | chapter=§4.4.1 The active interpretation and the active transformation | page=74 ''ff'' | chapter-url=https://books.google.com/books?id=OQq67Tr7D0cC&pg=PA74 | isbn=0-19-856245-4 |year=2004 | publisher=Oxford University Press}}</ref> By ''transformation'', [[mathematician]]s usually refer to active transformations, while [[physicist]]s and [[engineer]]s could mean either.{{cn}}