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:

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Out[2]=Play Animation

Scope  (5)

Applications  (2)

Properties & Relations  (3)

Possible Issues  (3)

Neat Examples  (1)

See Also

ShearingMatrix  GeometricTransformation  TransformationFunction  AffineTransform

Introduced in 2007
(6.0)