module Cube
where

import Cardinal
import qualified Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
import Point
import Tetrahedron hiding (c)
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" ++
        " fv: " ++ (show (Cube.fv 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



-- Face stuff.

-- | The top (in the direction of z) face of the cube.
top_face :: Cube -> Face.Face
top_face c = Face.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.Face
back_face c = Face.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.Face
down_face c = Face.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.Face
front_face c = Face.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.Face
left_face c = Face.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.Face
right_face c = Face.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)


reorient :: Tetrahedron -> Tetrahedron
reorient t = t
--         | volume t > 0 = t
--         | otherwise = t { v2 = (v3 t),
--                           v3 = (v2 t) }

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

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

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

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

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

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

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

tetrahedron7 :: Cube -> Tetrahedron
tetrahedron7 c =
    reorient $ Tetrahedron fv' v0' v1' v2' v3'
    where
      v0' = center c
      v1' = center (top_face c)
      v2' = Face.v3 (top_face c)
      v3' = Face.v0 (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
    ]