This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ShearingTransform

 ShearingTransform gives a TransformationFunction that represents a shear by radians along the direction of the vector v, normal to the vector n, and keeping the origin fixed. ShearingTransformgives a shear that keeps the point p fixed, rather than the origin.
• ShearingTransform works in any number of dimensions, and always gives area- or volume-preserving transformations.
• In 3D, ShearingTransform does the analog of shearing a deck of cards by angle 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.
Shearing by radians along the axis:
Apply a 30° shearing along the axis to the unit rectangle:
Apply a shearing transform in the plane:
Shearing by 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 ▪
 Scope   (5)
Simple shearing along the axis:
Simple shearing along the axis in the plane:
Shearing along the axis in the plane :
Points in the shearing plane are not changed:
Points outside the shearing plane are moved in the shearing direction:
Transformation applied to a 2D shape:
Transformation applied to a 3D shape:
 Applications   (2)
Transforming the output of Plot:
Construct a slanted font from an upright font by shearing:
The inverse of ShearingTransform is given by ShearingTransform:
The inverse of ShearingTransform is given by ShearingTransform:
Performing the shearing transform multiple times corresponds to a single shearing transform:
The order in which shearings are applied is significant:
Applying the two shearings in different orders is not equivalent:
The transformation is not defined for angles such that :
For non-orthogonal vectors, the direction is determined by the projection of the direction vector:
Shear a 3D object about a point p:
In the plane:
In the plane:
In the plane:
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