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.
Introduced in 2007
(6.0)