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
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_" ++ subscript ++ "\n" ++
(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
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
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 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
v1' = center (front_face c)
v2' = Face.v1 (front_face c)
v3' = Face.v2 (front_face c)
- fv' = rotate (Cube.fv c) ccwx
+ fv' = rotate ccwx (Cube.fv c)
tetrahedron2 :: Cube -> Tetrahedron
tetrahedron2 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)
+ fv' = rotate ccwx $ rotate ccwx $ Cube.fv c
tetrahedron3 :: Cube -> Tetrahedron
tetrahedron3 c =
v1' = center (front_face c)
v2' = Face.v3 (front_face c)
v3' = Face.v0 (front_face c)
- fv' = rotate (Cube.fv c) cwx
+ fv' = rotate cwx (Cube.fv c)
tetrahedron4 :: Cube -> Tetrahedron
tetrahedron4 c =
v1' = center (top_face c)
v2' = Face.v0 (top_face c)
v3' = Face.v1 (top_face c)
- fv' = rotate (Cube.fv c) cwy
+ fv' = rotate cwy (Cube.fv c)
tetrahedron5 :: Cube -> Tetrahedron
tetrahedron5 c =
v1' = center (top_face c)
v2' = Face.v1 (top_face c)
v3' = Face.v2 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz
+ fv' = rotate cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron6 :: Cube -> Tetrahedron
tetrahedron6 c =
v1' = center (top_face c)
v2' = Face.v2 (top_face c)
v3' = Face.v3 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz)
+ fv' = rotate cwy $ rotate cwz
+ $ rotate cwz
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron7 :: Cube -> Tetrahedron
tetrahedron7 c =
v1' = center (top_face c)
v2' = Face.v3 (top_face c)
v3' = Face.v0 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz
+ fv' = rotate cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron8 :: Cube -> Tetrahedron
tetrahedron8 c =
v1' = center (back_face c)
v2' = Face.v0 (back_face c)
v3' = Face.v1 (back_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwy
+ fv' = rotate cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron9 :: Cube -> Tetrahedron
tetrahedron9 c =
v1' = center (back_face c)
v2' = Face.v1 (back_face c)
v3' = Face.v2 (back_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwx
+ fv' = rotate cwy $ rotate cwy
+ $ rotate cwx
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron10 :: Cube -> Tetrahedron
tetrahedron10 c =
v1' = center (back_face c)
v2' = Face.v2 (back_face c)
v3' = Face.v3 (back_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) (ccwx . ccwx)
+ fv' = rotate cwy $ rotate cwy
+ $ rotate cwx
+ $ rotate cwx
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron11 :: Cube -> Tetrahedron
v1' = center (back_face c)
v2' = Face.v3 (back_face c)
v3' = Face.v0 (back_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwx
+ fv' = rotate cwy $ rotate cwy
+ $ rotate ccwx
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron12 :: Cube -> Tetrahedron
v1' = center (down_face c)
v2' = Face.v0 (down_face c)
v3' = Face.v1 (down_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwy
+ fv' = rotate ccwy (Tetrahedron.fv (tetrahedron0 c))
tetrahedron13 :: Cube -> Tetrahedron
v1' = center (down_face c)
v2' = Face.v1 (down_face c)
v3' = Face.v2 (down_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) ccwz
+ fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron14 :: Cube -> Tetrahedron
v1' = center (down_face c)
v2' = Face.v2 (down_face c)
v3' = Face.v3 (down_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron13 c)) (ccwz . ccwz)
+ fv' = rotate ccwy $ rotate ccwz
+ $ rotate ccwz
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron15 :: Cube -> Tetrahedron
v1' = center (down_face c)
v2' = Face.v3 (down_face c)
v3' = Face.v0 (down_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) cwz
+ 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)
-tetrahedrons :: Cube -> [Tetrahedron]
-tetrahedrons c =
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra c =
[tetrahedron0 c,
tetrahedron1 c,
tetrahedron2 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
- ]
+ 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