module Cube
where

import Cardinal
import Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
import Point
import Tetrahedron (Tetrahedron(Tetrahedron), fv)
import ThreeDimensional

data Cube = Cube { h :: Double,
                   i :: Int,
                   j :: Int,
                   k :: Int,
                   fv :: FunctionValues }
            deriving (Eq)


instance Show Cube where
    show c =
        "Cube_" ++ subscript ++ "\n" ++
        " h: " ++ (show (h c)) ++ "\n" ++
        " Center: " ++ (show (center c)) ++ "\n" ++
        " xmin: " ++ (show (xmin c)) ++ "\n" ++
        " xmax: " ++ (show (xmax c)) ++ "\n" ++
        " ymin: " ++ (show (ymin c)) ++ "\n" ++
        " ymax: " ++ (show (ymax c)) ++ "\n" ++
        " zmin: " ++ (show (zmin c)) ++ "\n" ++
        " zmax: " ++ (show (zmax c)) ++ "\n"
        where
          subscript =
              (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c))


empty_cube :: Cube
empty_cube = Cube 0 0 0 0 empty_values


-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
xmin :: Cube -> Double
xmin c = (2*i' - 1)*delta / 2
    where
      i' = fromIntegral (i c) :: Double
      delta = h c

-- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
xmax :: Cube -> Double
xmax c = (2*i' + 1)*delta / 2
    where
      i' = fromIntegral (i c) :: Double
      delta = h c

-- | The front boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
ymin :: Cube -> Double
ymin c = (2*j' - 1)*delta / 2
    where
      j' = fromIntegral (j c) :: Double
      delta = h c

-- | The back boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
ymax :: Cube -> Double
ymax c = (2*j' + 1)*delta / 2
    where
      j' = fromIntegral (j c) :: Double
      delta = h c

-- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
zmin :: Cube -> Double
zmin c = (2*k' - 1)*delta / 2
    where
      k' = fromIntegral (k c) :: Double
      delta = h c

-- | The top boundary of the cube. See Sorokina and Zeilfelder,
--   p. 76.
zmax :: Cube -> Double
zmax c = (2*k' + 1)*delta / 2
    where
      k' = fromIntegral (k c) :: Double
      delta = h c

instance ThreeDimensional Cube where
    -- | The center of Cube_ijk coincides with v_ijk at
    --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
    center c = (x, y, z)
           where
             delta = h c
             i' = fromIntegral (i c) :: Double
             j' = fromIntegral (j c) :: Double
             k' = fromIntegral (k c) :: Double
             x = delta * i'
             y = delta * j'
             z = delta * k'

    contains_point c p
        | (x_coord p) < (xmin c) = False
        | (x_coord p) > (xmax c) = False
        | (y_coord p) < (ymin c) = False
        | (y_coord p) > (ymax c) = False
        | (z_coord p) < (zmin c) = False
        | (z_coord p) > (zmax c) = False
        | otherwise = True


-- instance Num Cube where
--     (Cube g1 i1 j1 k1 d1) + (Cube _ i2 j2 k2 d2) =
--         Cube g1 (i1 + i2) (j1 + j2) (k1 + k2) (d1 + d2)

--     (Cube g1 i1 j1 k1 d1) - (Cube _ i2 j2 k2 d2) =
--         Cube g1 (i1 - i2) (j1 - j2) (k1 - k2) (d1 - d2)

--     (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
--         Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)

--     abs (Cube g1 i1 j1 k1 d1) =
--         Cube g1 (abs i1) (abs j1) (abs k1) (abs d1)

--     signum (Cube g1 i1 j1 k1 d1) =
--         Cube g1 (signum i1) (signum j1) (signum k1) (signum d1)

--     fromInteger x = empty_cube { datum = (fromIntegral x) }

-- instance Fractional Cube where
--     (Cube g1 i1 j1 k1 d1) / (Cube _ _ _ _ d2) =
--         Cube g1 i1 j1 k1 (d1 / d2)

--     recip (Cube g1 i1 j1 k1 d1) =
--         Cube g1 i1 j1 k1 (recip d1)

--     fromRational q = empty_cube { datum = fromRational q }



-- | Return the cube corresponding to the grid point i,j,k. The list
--   of cubes is stored as [z][y][x] but we'll be requesting it by
--   [x][y][z] so we flip the indices in the last line.
-- cube_at :: Grid -> Int -> Int -> Int -> Cube
-- cube_at g i' j' k'
--         | i' >= length (function_values g) = Cube g i' j' k' 0
--         | i' < 0                          = Cube g i' j' k' 0
--         | j' >= length ((function_values g) !! i') = Cube g i' j' k' 0
--         | j' < 0                                  = Cube g i' j' k' 0
--         | k' >= length (((function_values g) !! i') !! j') = Cube g i' j' k' 0
--         | k' < 0                                          = Cube g i' j' k' 0
--         | otherwise =
--             (((cubes g) !! k') !! j') !! i'






-- Face stuff.

-- | The top (in the direction of z) face of the cube.
top_face :: Cube -> Face
top_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (delta, delta, delta)
      v1' = (center c) + (delta, -delta, delta)
      v2' = (center c) + (-delta, -delta, delta)
      v3' = (center c) + (-delta, delta, delta)



-- | The back (in the direction of x) face of the cube.
back_face :: Cube -> Face
back_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (delta, delta, delta)
      v1' = (center c) + (delta, delta, -delta)
      v2' = (center c) + (delta, -delta, -delta)
      v3' = (center c) + (delta, -delta, delta)


-- The bottom face (in the direction of -z) of the cube.
down_face :: Cube -> Face
down_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (delta, delta, -delta)
      v1' = (center c) + (-delta, delta, -delta)
      v2' = (center c) + (-delta, -delta, -delta)
      v3' = (center c) + (delta, -delta, -delta)



-- | The front (in the direction of -x) face of the cube.
front_face :: Cube -> Face
front_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (-delta, -delta, delta)
      v1' = (center c) + (-delta, delta, delta)
      v2' = (center c) + (-delta, delta, -delta)
      v3' = (center c) + (-delta, -delta, -delta)


-- | The left (in the direction of -y) face of the cube.
left_face :: Cube -> Face
left_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (-delta, -delta, delta)
      v1' = (center c) + (delta, -delta, delta)
      v2' = (center c) + (delta, -delta, -delta)
      v3' = (center c) + (-delta, -delta, -delta)


-- | The right (in the direction of y) face of the cube.
right_face :: Cube -> Face
right_face c = Face v0' v1' v2' v3'
    where
      delta = (1/2)*(h c)
      v0' = (center c) + (-delta, delta, -delta)
      v1' = (center c) + (delta, delta, -delta)
      v2' = (center c) + (delta, delta, delta)
      v3' = (center c) + (-delta, delta, delta)



tetrahedron0 :: Cube -> Tetrahedron
tetrahedron0 c =
    Tetrahedron (Cube.fv c) v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (front_face c)
      v2' = v0 (front_face c)
      v3' = v1 (front_face c)

tetrahedron1 :: Cube -> Tetrahedron
tetrahedron1 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (front_face c)
      v2' = v1 (front_face c)
      v3' = v2 (front_face c)
      fv' = rotate (Cube.fv c) ccwx

tetrahedron2 :: Cube -> Tetrahedron
tetrahedron2 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (front_face c)
      v2' = v2 (front_face c)
      v3' = v3 (front_face c)
      fv' = rotate (Cube.fv c) (ccwx . ccwx)

tetrahedron3 :: Cube -> Tetrahedron
tetrahedron3 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (front_face c)
      v2' = v3 (front_face c)
      v3' = v1 (front_face c)
      fv' = rotate (Cube.fv c) cwx

tetrahedron4 :: Cube -> Tetrahedron
tetrahedron4 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (top_face c)
      v2' = v0 (front_face c)
      v3' = v1 (front_face c)
      fv' = rotate (Cube.fv c) cwy

tetrahedron5 :: Cube -> Tetrahedron
tetrahedron5 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (top_face c)
      v2' = v1 (top_face c)
      v3' = v2 (top_face c)
      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwx

tetrahedron6 :: Cube -> Tetrahedron
tetrahedron6 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (top_face c)
      v2' = v2 (top_face c)
      v3' = v3 (top_face c)
      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) (ccwx . ccwx)

tetrahedron7 :: Cube -> Tetrahedron
tetrahedron7 c =
    Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (top_face c)
      v2' = v3 (top_face c)
      v3' = v1 (top_face c)
      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwx

tetrahedrons :: Cube -> [Tetrahedron]
tetrahedrons c =
    [tetrahedron0 c,
     tetrahedron1 c,
     tetrahedron2 c,
     tetrahedron3 c,
     tetrahedron4 c,
     tetrahedron5 c,
     tetrahedron6 c,
     tetrahedron7 c
                -- ,
                --  tetrahedron8 c,
                --  tetrahedron9 c,
                --  tetrahedron10 c,
                --  tetrahedron11 c,
                --  tetrahedron12 c,
                --  tetrahedron13 c,
                --  tetrahedron14 c,
                --  tetrahedron15 c,
                --  tetrahedron16 c,
                --  tetrahedron17 c,
                --  tetrahedron18 c,
                --  tetrahedron19 c,
                --  tetrahedron20 c,
                --  tetrahedron21 c,
                --  tetrahedron21 c,
                --  tetrahedron22 c,
                --  tetrahedron23 c,
                --  tetrahedron24 c
    ]