module Cube
where
-import Face
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
+
+import Cardinal
+import qualified Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
---import Grid
import Point
+import Tetrahedron hiding (c)
import ThreeDimensional
data Cube = Cube { h :: Double,
deriving (Eq)
+instance Arbitrary Cube where
+ arbitrary = do
+ (Positive h') <- arbitrary :: Gen (Positive Double)
+ i' <- choose (coordmin, coordmax)
+ j' <- choose (coordmin, coordmax)
+ k' <- choose (coordmin, coordmax)
+ fv' <- arbitrary :: Gen FunctionValues
+ return (Cube h' i' j' k' fv')
+ where
+ coordmin = -268435456 -- -(2^29 / 2)
+ coordmax = 268435456 -- +(2^29 / 2)
+
+
instance Show Cube where
show c =
- "Cube_" ++ (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k 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)) ++ ")"
-
+ "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))
+
+
+-- | Returns an empty 'Cube'.
empty_cube :: Cube
empty_cube = Cube 0 0 0 0 empty_values
instance ThreeDimensional Cube where
-- | The center of Cube_ijk coincides with v_ijk at
- -- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
+ -- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
center c = (x, y, z)
where
delta = h c
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
+ -- | It's easy to tell if a point is within a cube; just make sure
+ -- that it falls on the proper side of each of the cube's faces.
+ contains_point c (x, y, z)
+ | x < (xmin c) = False
+ | x > (xmax c) = False
+ | y < (ymin c) = False
+ | y > (ymax c) = False
+ | z < (zmin c) = False
+ | z > (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'
+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)
+ v0' = (center c) + (delta, -delta, delta)
v1' = (center c) + (delta, delta, delta)
- v2' = (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'
+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)
+ v0' = (center c) + (delta, -delta, -delta)
v1' = (center c) + (delta, delta, -delta)
- v2' = (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'
+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)
+ v0' = (center c) + (-delta, -delta, -delta)
v1' = (center c) + (-delta, delta, -delta)
- v2' = (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'
+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)
+ v0' = (center c) + (-delta, -delta, delta)
v1' = (center c) + (-delta, delta, delta)
- v2' = (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'
+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)
+ 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'
+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)
+ 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' = Face.v0 (front_face c)
+ v3' = Face.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' = Face.v1 (front_face c)
+ v3' = Face.v2 (front_face c)
+ fv' = rotate ccwx (Cube.fv c)
+
+tetrahedron2 :: Cube -> Tetrahedron
+tetrahedron2 c =
+ 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 ccwx $ rotate ccwx $ Cube.fv c
+
+tetrahedron3 :: Cube -> Tetrahedron
+tetrahedron3 c =
+ 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 cwx (Cube.fv c)
+
+tetrahedron4 :: Cube -> Tetrahedron
+tetrahedron4 c =
+ 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 cwy (Cube.fv c)
+
+tetrahedron5 :: Cube -> Tetrahedron
+tetrahedron5 c =
+ 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 cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+
+tetrahedron6 :: Cube -> Tetrahedron
+tetrahedron6 c =
+ 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 cwy $ rotate cwz $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+
+tetrahedron7 :: Cube -> Tetrahedron
+tetrahedron7 c =
+ 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 cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
+
+tetrahedron8 :: Cube -> Tetrahedron
+tetrahedron8 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v0 (back_face c)
+ v3' = Face.v1 (back_face c)
+ fv' = rotate cwy $ rotate cwy $ (Tetrahedron.fv (tetrahedron0 c))
+
+tetrahedron9 :: Cube -> Tetrahedron
+tetrahedron9 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v1 (back_face c)
+ v3' = Face.v2 (back_face c)
+ fv' = rotate cwy $ rotate cwy $ rotate cwx $ Tetrahedron.fv (tetrahedron0 c)
+
+tetrahedron10 :: Cube -> Tetrahedron
+tetrahedron10 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v2 (back_face c)
+ v3' = Face.v3 (back_face c)
+ fv' = rotate cwy $ rotate cwy
+ $ rotate cwx
+ $ rotate cwx
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron11 :: Cube -> Tetrahedron
+tetrahedron11 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v3 (back_face c)
+ v3' = Face.v0 (back_face c)
+ fv' = rotate cwy $ rotate cwy
+ $ rotate ccwx
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron12 :: Cube -> Tetrahedron
+tetrahedron12 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v0 (down_face c)
+ v3' = Face.v1 (down_face c)
+ fv' = rotate ccwy (Tetrahedron.fv (tetrahedron0 c))
+
+tetrahedron13 :: Cube -> Tetrahedron
+tetrahedron13 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v1 (down_face c)
+ v3' = Face.v2 (down_face c)
+ fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron14 :: Cube -> Tetrahedron
+tetrahedron14 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v2 (down_face c)
+ v3' = Face.v3 (down_face c)
+ fv' = rotate ccwy $ rotate ccwz
+ $ rotate ccwz
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron15 :: Cube -> Tetrahedron
+tetrahedron15 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v3 (down_face c)
+ v3' = Face.v0 (down_face c)
+ fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron16 :: Cube -> Tetrahedron
+tetrahedron16 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v0 (right_face c)
+ v3' = Face.v1 (right_face c)
+ fv' = rotate ccwz (Tetrahedron.fv (tetrahedron0 c))
+
+
+tetrahedron17 :: Cube -> Tetrahedron
+tetrahedron17 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v1 (right_face c)
+ v3' = Face.v2 (right_face c)
+ fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron18 :: Cube -> Tetrahedron
+tetrahedron18 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v2 (right_face c)
+ v3' = Face.v3 (right_face c)
+ fv' = rotate ccwz $ rotate cwy
+ $ rotate cwy
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron19 :: Cube -> Tetrahedron
+tetrahedron19 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v3 (right_face c)
+ v3' = Face.v0 (right_face c)
+ fv' = rotate ccwz $ rotate ccwy
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron20 :: Cube -> Tetrahedron
+tetrahedron20 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v0 (left_face c)
+ v3' = Face.v1 (left_face c)
+ fv' = rotate cwz (Tetrahedron.fv (tetrahedron0 c))
+
+
+tetrahedron21 :: Cube -> Tetrahedron
+tetrahedron21 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v1 (left_face c)
+ v3' = Face.v2 (left_face c)
+ fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron22 :: Cube -> Tetrahedron
+tetrahedron22 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v2 (left_face c)
+ v3' = Face.v3 (left_face c)
+ fv' = rotate cwz $ rotate ccwy
+ $ rotate ccwy
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron23 :: Cube -> Tetrahedron
+tetrahedron23 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v3 (left_face c)
+ v3' = Face.v0 (left_face c)
+ fv' = rotate cwz $ rotate cwy
+ $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra 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,
+ tetrahedron22 c,
+ tetrahedron23 c]
+
+
+-- | Takes a 'Cube', and returns all Tetrahedra belonging to it that
+-- contain the given 'Point'.
+find_containing_tetrahedra :: Cube -> Point -> [Tetrahedron]
+find_containing_tetrahedra c p =
+ filter contains_our_point all_tetrahedra
+ where
+ contains_our_point = flip contains_point p
+ all_tetrahedra = tetrahedra c