Wolfram Language & System 10.4 (2016)|Legacy Documentation

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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.

gives a shear that keeps the point p fixed, rather than the origin.


  • 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:

Click for copyable input

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

Click for copyable input

Apply a shearing transform in the plane:

Click for copyable input
Click for copyable input
Out[2]=Play Animation
Introduced in 2007