There are two shear transformations: vertical and horizontal. The vertical shear transformation affects only the y-component of the coordinates of points in an object, and the horizontal shear transformation affects only the x-component.

If an application shears an object that contains two orthogonal vectors (two perpendicular lines), the vectors are no longer orthogonal.

A shearing transformation alters the shape of an object by translating its x-coordinates relative to its y-coordinates, or its y-coordinates relative to its x-coordinates. The amount by which the coordinates are translated is determined by the angle of the shear.

The equation for shearing an object to the left along the x axis by angle (theta) is:

x' = x - y tan (theta)

y' = y

To shear an object along the y-axis, the tangent of the angle of the shear is represented by constant B in the general equation.