```{-# OPTIONS_GHC -DFlt=Double -DVECT_Double #-}

-- | Classic 4x4 projective matrices, encoding the affine transformations of R^3.
-- Our convention is that they are intended for multiplication on
-- the /right/, that is, they are of the form
--
-- >     _____
-- > [  |     |  0  ]
-- > [  | 3x3 |  0  ]
-- > [  |_____|  0  ]
-- > [  p  q  r  1  ]
--
-- Please note that by default, OpenGL stores the matrices (in memory) by columns, while we
-- store them by rows; but OpenGL also use the opposite convention (so the OpenGL projective matrices
-- are intended for multiplication on the /left/). So in effect, they are the same when stored in the memory,
-- say with @poke :: Ptr Mat4 -> Mat4 -> IO ()@.
--
-- Warning: The naming conventions will probably change in the future.

module Data.Vect.Flt.Util.Projective where

import Data.Vect.Flt.Base
import Data.Vect.Flt.Util.Dim3

import qualified Data.Vect.Flt.Util.Dim4 as Dim4

--------------------------------------------------------------------------------

rotMatrixProj4' :: {- ' CPP is sensitive to primes -}  Flt -> Normal3 -> Proj4
rotMatrixProj4' angle axis = linear \$ rotMatrix3' axis angle

rotMatrixProj4 :: Flt -> Vec3 -> Proj4
rotMatrixProj4 angle axis = linear \$ rotMatrix3 axis angle

-- | synonym for "rotateAfterProj4"
rotateProj4 :: Flt -> Normal3 -> Proj4 -> Proj4
rotateProj4 = rotateAfterProj4

-- | Synonym for @\m -> m .*. rotMatrixProj4 angle axis@.
rotateAfterProj4 :: Flt -> Normal3 -> Proj4 -> Proj4
rotateAfterProj4 angle axis m = m .*. (rotMatrixProj4' angle axis)

-- | Synonym for @\m -> rotMatrixProj4 angle axis .*. m@.
rotateBeforeProj4 :: Flt -> Normal3 -> Proj4 -> Proj4
rotateBeforeProj4 angle axis m = (rotMatrixProj4' angle axis) .*. m

---------------

--scalingUniformProj3 :: Flt -> Proj3
--scalingUniformProj3 x = scaling (Vec2 x x)

scalingUniformProj4 :: Flt -> Proj4
scalingUniformProj4 x = scaling (Vec3 x x x)

-- | Equivalent to @\m -> scaling v .*. m@.
scaleBeforeProj4 :: Vec3 -> Proj4 -> Proj4
scaleBeforeProj4 (Vec3 u v w) p4 =
toProjectiveUnsafe \$
Mat4 (u*&a) (v*&b) (w*&c) t
where
Mat4 a b c t = fromProjective p4

-- | Equivalent to @\m -> m .*. scaling v@.
scaleAfterProj4 :: Vec3 -> Proj4 -> Proj4
scaleAfterProj4 v p4 =
toProjectiveUnsafe \$
Mat4 (a&!w) (b&!w) (c&!w) (t&!w)
where
w = extendWith 1 v
Mat4 a b c t = fromProjective p4

---------------

-- | Synonym for "translateAfter4"
translate4 :: Vec3 -> Proj4 -> Proj4
translate4 = translateAfter4

-- | Equivalent to @\m -> m .*. translation v@.
translateAfter4 :: Vec3 -> Proj4 -> Proj4
translateAfter4 v p4 =
toProjectiveUnsafe \$
Mat4 r1 r2 r3 (extendWith 0 v &+ r4)
where
Mat4 r1 r2 r3 r4 = fromProjective p4

-- | Equivalent to @\m -> translation v .*. m@.
translateBefore4 :: Vec3 -> Proj4 -> Proj4
translateBefore4 v p4 =
toProjectiveUnsafe \$
Mat4 r1 r2 r3 (extendWith 0 u &+ r4)
where
u = v .* (trim mat :: Mat3)
mat@(Mat4 r1 r2 r3 r4) = fromProjective p4

---------------

```