Diagrams.Transform

Some convenient functions related to transformations.

Documentation

conjugate :: HasLinearMap v => Transformation v -> Transformation v -> Transformation v

Conjugate one transformation by another. conjugate t1 t2 is the transformation which performs first t1, then t2, then the inverse of t1.

under :: Transformable a => (a -> a) -> Transformation (V a) -> a -> a

Carry out some transformation "under" another one: f `under` t first applies t, then f, then the inverse of t. For example, scaleX 2 `under` rotationBy (-1/8 :: CircleFrac) is the transformation which scales by a factor of 2 along the diagonal line y = x.

Note that

 (transform t2) `under` t1 == transform (conjugate t1 t2)

for all transformations t1 and t2.