[[Affine Transformations|Affine]] version of [[Shear Transformation]]. #### With shear factor $\vec v$, $\huge A = I+ \frac{1}{\norms{n}}\vec v \vec n ^ \intercal$ $\huge \vec b = \frac{- c}{\norms{\vec n}} \vec v $ #### Moves $P\mapsto Q$ $\huge\begin{align*} A&= I + \frac{1}{{\vec n^{\intercal}\vec P - c}}\vector{PQ}\vec n^{\intercal} \\ \vec b &= \frac{-c}{{\vec n^{\intercal} \vec P - c}} \vec v \end{align*}$ ### [[Homogeneous Coordinates]] #### With shear factor $\vec v$ $\huge A = I + \frac{1}{ \norms{\vec n} } \tilde v \tilde N^\intercal $ #### Moves $P\mapsto Q$ $ \huge A = I + \frac{1}{\tilde N ^\intercal \tilde P} \tilde{PQ} \tilde N^\intercal $