Shear Mapping

In mathematics, shear mapping or transvection is a particular kind of linear mapping. Linear mapping is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. A shear mapping's effect leaves all points on one axis fixed, while the other points are shifted parallel to the axis by a distance proportional to their perpendicular distance from that axis.

Shear mappings carry areas into equal areas and volumes into equal volumes, as they preserve the width, length, and etc. of parallelograms; see equi-areal mapping for the reason and for other linear mappings that have this property.

Read more about Shear Mapping:  Elementary Form, Advanced Form