BUILT-IN MATHEMATICA SYMBOL

# RotationTransform

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

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

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

RotationTransform[, 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[, {u, v}, ...]
gives a rotation by radians in the hyperplane spanned by u and v.

## DetailsDetails

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

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

A 2D rotation transform by radians:

 Out[1]=

Rotate a vector:

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Rotate around the axis:

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 Out[2]=

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

 Out[1]=

Rotate around the axis:

 Out[2]= Play Animation ▪