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ShearingTransform

ShearingTransform[Theta, v, n]
gives a TransformationFunction that represents a shear by Theta radians along the direction of the vector v, normal to the vector n, and keeping the origin fixed.
ShearingTransform[Theta, v, n, p]
gives 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 Theta 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.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Shearing by theta radians along the x axis:
Apply a 30° shearing along the x axis to the unit rectangle:
Shearing by theta radians along the x axis:
In[1]:=
Click for copyable input
Out[1]=
 
Apply a 30° shearing along the x axis to the unit rectangle:
In[1]:=
Click for copyable input
Out[1]=
Scope   (5)
Simple shearing along the x axis:
Simple shearing along the x axis in the x, y plane:
Shearing along the x axis in the plane z=1:
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:
Properties & Relations   (3)
The inverse of ShearingTransform[Theta, v, n]is given by ShearingTransform[-Theta, v, n]:
The inverse of ShearingTransform[Theta, v, n] is given by ShearingTransform[Theta, -v, n]:
Performing the shearing transform multiple times corresponds to a single shearing transform:
Possible Issues   (3)
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 a such that cos a=0:
For non-orthogonal vectors, the direction is determined by the projection of the direction vector:
Neat Examples   (1)
Transforming text:
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