```-----------------------------------------------------------------------------
-- |
-- Module      :  Diagrams.Transform
-- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  diagrams-discuss@googlegroups.com
--
-- Some convenient functions related to transformations.
--
-----------------------------------------------------------------------------

module Diagrams.Transform
( conjugate, under

) where

import Diagrams.Core
import Data.Semigroup

-- | Conjugate one transformation by another. @conjugate t1 t2@ is the
--   transformation which performs first @t1@, then @t2@, then the
--   inverse of @t1@.
conjugate :: HasLinearMap v => Transformation v -> Transformation v -> Transformation v
conjugate t1 t2  = inv t1 <> t2 <> t1

-- | 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@.
under :: Transformable a => (a -> a) -> Transformation (V a) -> a -> a
f `under` t = transform (inv t) . f . transform t
```