ShearingMatrix

, v, n]
gives the matrix corresponding to shearing by

radians along the direction of the vector v, and normal to the vector n.

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[, {1, 0}, {0, 1}] effectively slants by angle to the right.

In 3D, ShearingMatrix does the analog of shearing a deck of cards by angle in the direction v, with the cards being oriented so as to have normal vector n.

A shearing by

radians along the x axis:

Out[1]//MatrixForm=

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

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