Shear mapping

Common card · No. 368204

In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction. This type of mapping is also called shear transformation, transvection, or just shearing. The transformations can be applied with a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and replacing one of the zero elements with a non-zero value. An example is the linear map that takes any point with coordinates ( x , y ) {\displaystyle (x,y)} to the point ( x + 2 y , y ) {\displaystyle (x+2y,y)} . In this case, the displacement is horizontal by a factor of 2 where the fixed line is...

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