module Cube
where
-import Grid
+import Data.List ( (\\) )
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
+
+import Cardinal
+import qualified Face (Face(Face, v0, v1, v2, v3))
+import FunctionValues
import Point
+import Tetrahedron hiding (c)
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,
+ tetrahedra_volume :: 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
+ (Positive tet_vol) <- arbitrary :: Gen (Positive Double)
+ return (Cube h' i' j' k' fv' tet_vol)
+ 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)) ++
- " (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"
-
+ "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 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 0
+
-- | 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')
-
- 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
+ x = delta * i'
+ y = delta * j'
+ z = delta * k'
+
+ -- | 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)
+-- Face stuff.
- (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
- Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)
+-- | 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)
- 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) }
+-- | 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)
-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)
+-- 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)
- 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'
+-- | 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)
-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')
--- These next three functions basically form a 'for' loop, looping
--- through the xs, ys, and zs in that order.
-cubes_from_values :: Grid -> Int -> Int -> [Double] -> [Cube]
-cubes_from_values g i' j' vals =
- zipWith (reverse_cube g i' j') [0..] vals
+-- | 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)
-cubes_from_planes :: Grid -> Int -> [[Double]] -> [[Cube]]
-cubes_from_planes g i' planes =
- zipWith (cubes_from_values g i') [0..] planes
-cubes :: Grid -> [[[Cube]]]
-cubes g = zipWith (cubes_from_planes g) [0..] (function_values g)
+tetrahedron0 :: Cube -> Tetrahedron
+tetrahedron0 c =
+ Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol
+ where
+ v0' = center c
+ v1' = center (front_face c)
+ v2' = Face.v0 (front_face c)
+ v3' = Face.v1 (front_face c)
+ vol = tetrahedra_volume c
+
+tetrahedron1 :: Cube -> Tetrahedron
+tetrahedron1 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron2 :: Cube -> Tetrahedron
+tetrahedron2 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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
+ vol = tetrahedra_volume c
+
+tetrahedron3 :: Cube -> Tetrahedron
+tetrahedron3 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron4 :: Cube -> Tetrahedron
+tetrahedron4 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron5 :: Cube -> Tetrahedron
+tetrahedron5 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron6 :: Cube -> Tetrahedron
+tetrahedron6 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron7 :: Cube -> Tetrahedron
+tetrahedron7 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron8 :: Cube -> Tetrahedron
+tetrahedron8 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron9 :: Cube -> Tetrahedron
+tetrahedron9 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+tetrahedron10 :: Cube -> Tetrahedron
+tetrahedron10 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+
+ vol = tetrahedra_volume c
+
+tetrahedron11 :: Cube -> Tetrahedron
+tetrahedron11 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron12 :: Cube -> Tetrahedron
+tetrahedron12 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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))
+ vol = tetrahedra_volume c
+
+
+tetrahedron13 :: Cube -> Tetrahedron
+tetrahedron13 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron14 :: Cube -> Tetrahedron
+tetrahedron14 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron15 :: Cube -> Tetrahedron
+tetrahedron15 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron16 :: Cube -> Tetrahedron
+tetrahedron16 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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))
+ vol = tetrahedra_volume c
+
+
+tetrahedron17 :: Cube -> Tetrahedron
+tetrahedron17 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron18 :: Cube -> Tetrahedron
+tetrahedron18 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron19 :: Cube -> Tetrahedron
+tetrahedron19 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron20 :: Cube -> Tetrahedron
+tetrahedron20 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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))
+ vol = tetrahedra_volume c
+
+
+tetrahedron21 :: Cube -> Tetrahedron
+tetrahedron21 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron22 :: Cube -> Tetrahedron
+tetrahedron22 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume c
+
+
+tetrahedron23 :: Cube -> Tetrahedron
+tetrahedron23 c =
+ Tetrahedron fv' v0' v1' v2' v3' vol
+ 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)
+ vol = tetrahedra_volume 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]
+
+-- | All completely contained in the front half of the cube.
+front_half_tetrahedra :: Cube -> [Tetrahedron]
+front_half_tetrahedra c =
+ [tetrahedron0 c,
+ tetrahedron1 c,
+ tetrahedron2 c,
+ tetrahedron3 c,
+ tetrahedron6 c,
+ tetrahedron12 c,
+ tetrahedron19 c,
+ tetrahedron21 c]
+
+
+-- | All tetrahedra completely contained in the top half of the cube.
+top_half_tetrahedra :: Cube -> [Tetrahedron]
+top_half_tetrahedra c =
+ [tetrahedron4 c,
+ tetrahedron5 c,
+ tetrahedron6 c,
+ tetrahedron7 c,
+ tetrahedron0 c,
+ tetrahedron10 c,
+ tetrahedron16 c,
+ tetrahedron20 c]
+
+
+-- | All tetrahedra completely contained in the back half of the cube.
+back_half_tetrahedra :: Cube -> [Tetrahedron]
+back_half_tetrahedra c =
+ [tetrahedron8 c,
+ tetrahedron9 c,
+ tetrahedron10 c,
+ tetrahedron11 c,
+ tetrahedron4 c,
+ tetrahedron14 c,
+ tetrahedron17 c,
+ tetrahedron23 c]
+
+
+-- | All tetrahedra completely contained in the down half of the cube.
+down_half_tetrahedra :: Cube -> [Tetrahedron]
+down_half_tetrahedra c =
+ [tetrahedron12 c,
+ tetrahedron13 c,
+ tetrahedron14 c,
+ tetrahedron15 c,
+ tetrahedron2 c,
+ tetrahedron8 c,
+ tetrahedron18 c,
+ tetrahedron22 c]
+
+
+-- | All tetrahedra completely contained in the right half of the cube.
+right_half_tetrahedra :: Cube -> [Tetrahedron]
+right_half_tetrahedra c =
+ [tetrahedron16 c,
+ tetrahedron17 c,
+ tetrahedron18 c,
+ tetrahedron19 c,
+ tetrahedron1 c,
+ tetrahedron5 c,
+ tetrahedron9 c,
+ tetrahedron13 c]
+
+
+-- | All tetrahedra completely contained in the left half of the cube.
+left_half_tetrahedra :: Cube -> [Tetrahedron]
+left_half_tetrahedra c =
+ [tetrahedron20 c,
+ tetrahedron21 c,
+ tetrahedron22 c,
+ tetrahedron23 c,
+ tetrahedron3 c,
+ tetrahedron7 c,
+ tetrahedron11 c,
+ tetrahedron15 c]
+
+
+in_top_half :: Cube -> Point -> Bool
+in_top_half c (_,_,z) =
+ distance_from_top <= distance_from_bottom
+ where
+ distance_from_top = abs $ (zmax c) - z
+ distance_from_bottom = abs $ (zmin c) - z
+
+in_front_half :: Cube -> Point -> Bool
+in_front_half c (x,_,_) =
+ distance_from_front <= distance_from_back
+ where
+ distance_from_front = abs $ (xmin c) - x
+ distance_from_back = abs $ (xmax c) - x
+
+
+in_left_half :: Cube -> Point -> Bool
+in_left_half c (_,y,_) =
+ distance_from_left <= distance_from_right
+ where
+ distance_from_left = abs $ (ymin c) - y
+ distance_from_right = abs $ (ymax c) - y
+
+
+-- | Takes a 'Cube', and returns the Tetrahedra belonging to it that
+-- contain the given 'Point'. This should be faster than checking
+-- every tetrahedron individually, since we determine which half
+-- (hemisphere?) of the cube the point lies in three times: once in
+-- each dimension. This allows us to eliminate non-candidates
+-- quickly.
+--
+-- This can throw an exception, but the use of 'head' might
+-- save us some unnecessary computations.
+--
+find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
+find_containing_tetrahedron c p =
+ head containing_tetrahedra
+ where
+ candidates = tetrahedra c
+ non_candidates_x =
+ if (in_front_half c p) then
+ back_half_tetrahedra c
+ else
+ front_half_tetrahedra c
+
+ candidates_x = candidates \\ non_candidates_x
+
+ non_candidates_y =
+ if (in_left_half c p) then
+ right_half_tetrahedra c
+ else
+ left_half_tetrahedra c
+
+ candidates_xy = candidates_x \\ non_candidates_y
+
+ non_candidates_z =
+ if (in_top_half c p) then
+ down_half_tetrahedra c
+ else
+ top_half_tetrahedra c
+
+ candidates_xyz = candidates_xy \\ non_candidates_z
+
+ contains_our_point = flip contains_point p
+ containing_tetrahedra = filter contains_our_point candidates_xyz
projects / spline3.git / blobdiff