BUILT-IN MATHEMATICA SYMBOL

# ShearingTransform

ShearingTransform[, v, n]
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.

ShearingTransform[, 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[, {1, 0}, {0, 1}] effectively represents slanting by angle to the right.
• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

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 ▪