# RotationTransform

gives a TransformationFunction that represents a rotation in 2D by θ radians about the origin.

RotationTransform[θ,p]

gives a 2D rotation about the 2D point p.

RotationTransform[θ,w]

gives a 3D rotation around the direction of the 3D vector w.

RotationTransform[θ,w,p]

gives a 3D rotation around the axis w anchored at the point p.

RotationTransform[{u,v}]

gives a rotation about the origin that transforms the vector u to the direction of the vector v.

RotationTransform[{u,v},p]

gives a rotation about the point p that transforms u to the direction of v.

RotationTransform[θ,{u,v},]

gives a rotation by θ radians in the plane spanned by u and v.

# Details • RotationTransform gives a TransformationFunction that can be applied to vectors.
• or θ° specifies an angle in degrees.
• RotationTransform[θ,{u,v},p] can be used to specify any rotation about any point p, in any number of dimensions.
• Positive θ in RotationTransform[θ,{u,v},p] corresponds to going from the direction of u toward the direction of v.
• is equivalent to RotationTransform[θ,{{1,0},{0,1}}].
• RotationTransform[θ,w] is equivalent to RotationTransform[θ,{u,v}], where uw, vw, and u,v,w form a right-handed coordinate system.
• RotationTransform[θ,{u,v}] can effectively specify any element of the -dimensional rotation group . RotationTransform[θ,{u,v},p] can effectively specify any element of the -dimensional special Euclidean group.

# Examples

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## Basic Examples(4)

A 2D rotation transform by θ radians:

 In:= Out= Rotate a vector:

 In:= Out= Rotate around the axis:

 In:= Out= In:= Out= Rotate a 2D graphic by 30° about the origin:

 In:= Out= Rotate around the axis:

 In:= In:= Out= PlayAnimation ## Neat Examples(1)

Introduced in 2007
(6.0)