ShearingMatrix

ShearingMatrix[θ,v,n]

gives the matrix corresponding to shearing by θ radians along the direction of the vector v, and normal to the vector n.

Details

  • ShearingMatrix gives matrices corresponding to shearing with the origin kept fixed.
  • ShearingMatrix gives matrices with determinant 1, corresponding to area- or volume-preserving transformations.
  • In 2D, ShearingMatrix turns rectangles into parallelograms. ShearingMatrix[θ,{1,0},{0,1}] effectively slants by angle θ to the right.
  • In 3D, ShearingMatrix does the analog of shearing a deck of cards by angle θ in the direction v, with the cards being oriented so as to have normal vector n.

Examples

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Basic Examples  (2)

A shearing by θ radians along the axis:

In[1]:=
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Out[1]//MatrixForm=

Apply a 30° shear along the axis to a square:

In[1]:=
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Out[1]=

Scope  (5)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (3)

Neat Examples  (1)

See Also

ShearingTransform  ScalingMatrix  RotationMatrix

Tutorials

Introduced in 2007
(6.0)