# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ShearingTransform

ShearingTransform[θ,v,n]
gives a TransformationFunction that represents a shear by θ radians along the direction of the vector v, normal to the vector n, and keeping the origin fixed.

ShearingTransform[θ,v,n,p]
gives a shear that keeps the point p fixed, rather than the origin.

## DetailsDetails

• ShearingTransform gives a TransformationFunction which can be applied to vectors.
• ShearingTransform works in any number of dimensions, and always gives area- or volume-preserving transformations.
• In 2D, ShearingTransform turns rectangles into parallelograms. ShearingTransform[θ,{1,0},{0,1}] effectively represents slanting by angle θ to the right.
• In 3D, ShearingTransform does the analog of shearing a deck of cards by angle θ in the direction v, with the cards oriented so as to have normal vector n, and the card that goes through the point p kept fixed.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Shearing by θ radians along the axis:

 Out[1]=

Apply a 30° shearing along the axis to the unit rectangle:

 Out[1]=

Apply a shearing transform in the plane:

 Out[2]= Play Animation