module Cube
where
+import Data.List ( (\\) )
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
+
import Cardinal
import qualified Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
i :: Int,
j :: Int,
k :: Int,
- fv :: FunctionValues }
+ 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_" ++ subscript ++ "\n" ++
-- | Returns an empty 'Cube'.
empty_cube :: Cube
-empty_cube = Cube 0 0 0 0 empty_values
+empty_cube = Cube 0 0 0 0 empty_values 0
-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
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
-- | 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 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
+ 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
tetrahedron0 :: Cube -> Tetrahedron
tetrahedron0 c =
- Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+ 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'
+ 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'
+ 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'
+ 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'
+ 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'
+ 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'
+ 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)
+ 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'
+ 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'
+ 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))
+ fv' = rotate cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
+ vol = tetrahedra_volume c
tetrahedron9 :: Cube -> Tetrahedron
tetrahedron9 c =
- Tetrahedron fv' v0' v1' v2' v3'
+ 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)
+ 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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (back_face c)
$ rotate cwx
$ Tetrahedron.fv (tetrahedron0 c)
+ vol = tetrahedra_volume c
tetrahedron11 :: Cube -> Tetrahedron
tetrahedron11 c =
- Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (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'
+ 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'
+ 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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (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'
+ 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'
+ 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'
+ 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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (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'
+ 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'
+ 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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (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'
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (left_face c)
v3' = Face.v0 (left_face c)
fv' = rotate cwz $ rotate cwy
$ Tetrahedron.fv (tetrahedron0 c)
+ vol = tetrahedra_volume c
-tetrahedrons :: Cube -> [Tetrahedron]
-tetrahedrons c =
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra c =
[tetrahedron0 c,
tetrahedron1 c,
tetrahedron2 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 = tetrahedrons 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