module Cube
where
-import Grid
+import Cardinal
+import Face (Face(Face, v0, v1, v2, v3))
+import FunctionValues
import Point
+import Tetrahedron (Tetrahedron(Tetrahedron), fv)
import ThreeDimensional
-class Gridded a where
- back :: a -> Cube
- down :: a -> Cube
- front :: a -> Cube
- left :: a -> Cube
- right :: a -> Cube
- top :: a -> Cube
-
-
-data Cube = Cube { grid :: Grid,
+data Cube = Cube { h :: Double,
i :: Int,
j :: Int,
k :: Int,
- datum :: Double }
+ fv :: FunctionValues }
deriving (Eq)
instance Show Cube where
show c =
"Cube_" ++ (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c)) ++
- " (Grid: " ++ (show (grid c)) ++ ")" ++
" (Center: " ++ (show (center c)) ++ ")" ++
" (xmin: " ++ (show (xmin c)) ++ ")" ++
" (xmax: " ++ (show (xmax c)) ++ ")" ++
" (ymin: " ++ (show (ymin c)) ++ ")" ++
" (ymax: " ++ (show (ymax c)) ++ ")" ++
" (zmin: " ++ (show (zmin c)) ++ ")" ++
- " (zmax: " ++ (show (zmax c)) ++ ")" ++
- " (datum: " ++ (show (datum c)) ++ ")\n\n"
+ " (zmax: " ++ (show (zmax c)) ++ ")"
empty_cube :: Cube
-empty_cube = Cube empty_grid 0 0 0 0
-
--- TODO: The paper considers 'i' to be the front/back direction,
--- whereas I have it in the left/right direction.
-instance Gridded Cube where
- back c = cube_at (grid c) ((i c) + 1) (j c) (k c)
- down c = cube_at (grid c) (i c) (j c) ((k c) - 1)
- front c = cube_at (grid c) ((i c) - 1) (j c) (k c)
- left c = cube_at (grid c) (i c) ((j c) - 1) (k c)
- right c = cube_at (grid c) (i c) ((j c) + 1) (k c)
- top c = cube_at (grid c) (i c) (j c) ((k c) + 1)
+empty_cube = Cube 0 0 0 0 empty_values
+
-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmin c = (2*i' - 1)*delta / 2
where
i' = fromIntegral (i c) :: Double
- delta = h (grid c)
+ delta = h c
-- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmax c = (2*i' + 1)*delta / 2
where
i' = fromIntegral (i c) :: Double
- delta = h (grid c)
+ delta = h c
-- | The front boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymin c = (2*j' - 1)*delta / 2
where
j' = fromIntegral (j c) :: Double
- delta = h (grid c)
+ delta = h c
-- | The back boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymax c = (2*j' + 1)*delta / 2
where
j' = fromIntegral (j c) :: Double
- delta = h (grid c)
+ delta = h c
-- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmin c = (2*k' - 1)*delta / 2
where
k' = fromIntegral (k c) :: Double
- delta = h (grid c)
+ delta = h c
-- | The top boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmax c = (2*k' + 1)*delta / 2
where
k' = fromIntegral (k c) :: Double
- delta = h (grid c)
+ 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 (grid c)
+ 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')
+ x = delta * i'
+ y = delta * j'
+ z = delta * k'
contains_point c p
| (x_coord p) < (xmin 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)
+-- 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)
- (Cube g1 i1 j1 k1 d1) - (Cube _ i2 j2 k2 d2) =
- Cube g1 (i1 - i2) (j1 - j2) (k1 - k2) (d1 - d2)
+-- recip (Cube g1 i1 j1 k1 d1) =
+-- Cube g1 i1 j1 k1 (recip d1)
- (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
- Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)
+-- fromRational q = empty_cube { datum = fromRational q }
- 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) }
+-- | 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'
-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 }
-reverse_cube :: Grid -> Int -> Int -> Int -> Double -> Cube
-reverse_cube g k' j' i' datum' = Cube g i' j' k' datum'
-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 =
- Cube g i' j' k' ((((function_values g) !! i') !! j') !! k')
+-- 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)
--- These next three functions basically form a 'for' loop, looping
--- through the xs, ys, and zs in that order.
--- | The cubes_from_values function will return a function that takes
--- a list of values and returns a list of cubes. It could just as
--- well be written to take the values as a parameter; the omission
--- of the last parameter is known as an eta reduce.
-cubes_from_values :: Grid -> Int -> Int -> ([Double] -> [Cube])
-cubes_from_values g i' j' =
- zipWith (reverse_cube g i' j') [0..]
--- | The cubes_from_planes function will return a function that takes
--- a list of planes and returns a list of cubes. It could just as
--- well be written to take the planes as a parameter; the omission
--- of the last parameter is known as an eta reduce.
-cubes_from_planes :: Grid -> Int -> ([[Double]] -> [[Cube]])
-cubes_from_planes g i' =
- zipWith (cubes_from_values g i') [0..]
+-- | 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)
--- | Takes a grid as an argument, and returns a three-dimensional list
--- of cubes centered on its grid points.
-cubes :: Grid -> [[[Cube]]]
-cubes g = zipWith (cubes_from_planes g) [0..] (function_values g)
+
+-- 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
+ ]
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