# 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.

# Details

• 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.

# Examples

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## Basic Examples(3)

Shearing by θ radians along the axis:

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

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Apply a shearing transform in the plane:

 In[1]:=
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 Out[2]= PlayAnimation

## Neat Examples(1)

Introduced in 2007
(6.0)