module Cube
where
+import Data.Maybe (fromJust)
+import qualified Data.Vector as V (
+ Vector,
+ findIndex,
+ map,
+ minimum,
+ singleton,
+ snoc,
+ unsafeIndex
+ )
+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 Tetrahedron (Tetrahedron(Tetrahedron))
import ThreeDimensional
data Cube = Cube { h :: Double,
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" ++
(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
+empty_cube = Cube 0 0 0 0 empty_values 0
-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
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)
+
+tetrahedron :: Cube -> Int -> Tetrahedron
-tetrahedron0 :: Cube -> Tetrahedron
-tetrahedron0 c =
- Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+tetrahedron c 0 =
+ 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 c 1 =
+ 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 (Cube.fv c) ccwx
+ fv' = rotate ccwx (Cube.fv c)
+ vol = tetrahedra_volume c
-tetrahedron2 :: Cube -> Tetrahedron
-tetrahedron2 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 2 =
+ 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 (Cube.fv c) (ccwx . ccwx)
+ fv' = rotate ccwx $ rotate ccwx $ Cube.fv c
+ vol = tetrahedra_volume c
-tetrahedron3 :: Cube -> Tetrahedron
-tetrahedron3 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 3 =
+ 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 (Cube.fv c) cwx
+ fv' = rotate cwx (Cube.fv c)
+ vol = tetrahedra_volume c
-tetrahedron4 :: Cube -> Tetrahedron
-tetrahedron4 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 4 =
+ 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 (Cube.fv c) cwy
+ fv' = rotate cwy (Cube.fv c)
+ vol = tetrahedra_volume c
-tetrahedron5 :: Cube -> Tetrahedron
-tetrahedron5 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 5 =
+ 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 (Tetrahedron.fv (tetrahedron4 c)) ccwz
+ fv' = rotate cwy $ rotate cwz $ fv c
+ vol = tetrahedra_volume c
-tetrahedron6 :: Cube -> Tetrahedron
-tetrahedron6 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 6 =
+ 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 (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz)
+ fv' = rotate cwy $ rotate cwz
+ $ rotate cwz
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron7 :: Cube -> Tetrahedron
-tetrahedron7 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 7 =
+ 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 (Tetrahedron.fv (tetrahedron4 c)) cwz
+ fv' = rotate cwy $ rotate ccwz $ fv c
+ vol = tetrahedra_volume c
-tetrahedron8 :: Cube -> Tetrahedron
-tetrahedron8 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 8 =
+ 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 (Tetrahedron.fv (tetrahedron4 c)) cwy
+ fv' = rotate cwy $ rotate cwy $ fv c
+ vol = tetrahedra_volume c
-tetrahedron9 :: Cube -> Tetrahedron
-tetrahedron9 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 9 =
+ 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 (Tetrahedron.fv (tetrahedron8 c)) ccwx
+ fv' = rotate cwy $ rotate cwy
+ $ rotate cwx
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron10 :: Cube -> Tetrahedron
-tetrahedron10 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 10 =
+ 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 (Tetrahedron.fv (tetrahedron8 c)) (ccwx . ccwx)
+ fv' = rotate cwy $ rotate cwy
+ $ rotate cwx
+ $ rotate cwx
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron11 :: Cube -> Tetrahedron
-tetrahedron11 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 11 =
+ 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 (Tetrahedron.fv (tetrahedron8 c)) cwx
+ fv' = rotate cwy $ rotate cwy
+ $ rotate ccwx
+ $ fv c
+ vol = tetrahedra_volume c
-
-tetrahedron12 :: Cube -> Tetrahedron
-tetrahedron12 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 12 =
+ 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 (Tetrahedron.fv (tetrahedron8 c)) cwy
-
+ fv' = rotate ccwy $ fv c
+ vol = tetrahedra_volume c
-tetrahedron13 :: Cube -> Tetrahedron
-tetrahedron13 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 13 =
+ 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 (Tetrahedron.fv (tetrahedron12 c)) ccwz
+ fv' = rotate ccwy $ rotate ccwz $ fv c
+ vol = tetrahedra_volume c
-
-tetrahedron14 :: Cube -> Tetrahedron
-tetrahedron14 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 14 =
+ 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 (Tetrahedron.fv (tetrahedron13 c)) (ccwz . ccwz)
-
+ fv' = rotate ccwy $ rotate ccwz
+ $ rotate ccwz
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron15 :: Cube -> Tetrahedron
-tetrahedron15 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 15 =
+ 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 (Tetrahedron.fv (tetrahedron12 c)) cwz
-
-
-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
- ]
+ fv' = rotate ccwy $ rotate cwz $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 16 =
+ 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 $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 17 =
+ 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 $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 18 =
+ 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
+ $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 19 =
+ 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
+ $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 20 =
+ 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 $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 21 =
+ 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 $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 22 =
+ 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
+ $ fv c
+ vol = tetrahedra_volume c
+
+tetrahedron c 23 =
+ 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
+ $ fv c
+ vol = tetrahedra_volume c
+
+-- Feels dirty, but whatever.
+tetrahedron _ _ = error "asked for a nonexistent tetrahedron"
+
+
+-- Only used in tests, so we don't need the added speed
+-- of Data.Vector.
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra c = [ tetrahedron c n | n <- [0..23] ]
+
+front_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_left_top_tetrahedra c =
+ V.singleton (tetrahedron c 0) `V.snoc`
+ (tetrahedron c 3) `V.snoc`
+ (tetrahedron c 6) `V.snoc`
+ (tetrahedron c 7) `V.snoc`
+ (tetrahedron c 20) `V.snoc`
+ (tetrahedron c 21)
+
+front_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_left_down_tetrahedra c =
+ V.singleton (tetrahedron c 0) `V.snoc`
+ (tetrahedron c 2) `V.snoc`
+ (tetrahedron c 3) `V.snoc`
+ (tetrahedron c 12) `V.snoc`
+ (tetrahedron c 15) `V.snoc`
+ (tetrahedron c 21)
+
+front_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_right_top_tetrahedra c =
+ V.singleton (tetrahedron c 0) `V.snoc`
+ (tetrahedron c 1) `V.snoc`
+ (tetrahedron c 5) `V.snoc`
+ (tetrahedron c 6) `V.snoc`
+ (tetrahedron c 16) `V.snoc`
+ (tetrahedron c 19)
+
+front_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_right_down_tetrahedra c =
+ V.singleton (tetrahedron c 1) `V.snoc`
+ (tetrahedron c 2) `V.snoc`
+ (tetrahedron c 12) `V.snoc`
+ (tetrahedron c 13) `V.snoc`
+ (tetrahedron c 18) `V.snoc`
+ (tetrahedron c 19)
+
+back_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_left_top_tetrahedra c =
+ V.singleton (tetrahedron c 0) `V.snoc`
+ (tetrahedron c 3) `V.snoc`
+ (tetrahedron c 6) `V.snoc`
+ (tetrahedron c 7) `V.snoc`
+ (tetrahedron c 20) `V.snoc`
+ (tetrahedron c 21)
+
+back_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_left_down_tetrahedra c =
+ V.singleton (tetrahedron c 8) `V.snoc`
+ (tetrahedron c 11) `V.snoc`
+ (tetrahedron c 14) `V.snoc`
+ (tetrahedron c 15) `V.snoc`
+ (tetrahedron c 22) `V.snoc`
+ (tetrahedron c 23)
+
+back_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_right_top_tetrahedra c =
+ V.singleton (tetrahedron c 4) `V.snoc`
+ (tetrahedron c 5) `V.snoc`
+ (tetrahedron c 9) `V.snoc`
+ (tetrahedron c 10) `V.snoc`
+ (tetrahedron c 16) `V.snoc`
+ (tetrahedron c 17)
+
+back_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_right_down_tetrahedra c =
+ V.singleton (tetrahedron c 8) `V.snoc`
+ (tetrahedron c 9) `V.snoc`
+ (tetrahedron c 13) `V.snoc`
+ (tetrahedron c 14) `V.snoc`
+ (tetrahedron c 17) `V.snoc`
+ (tetrahedron c 18)
+
+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 =
+ candidates `V.unsafeIndex` (fromJust lucky_idx)
+ where
+ front_half = in_front_half c p
+ top_half = in_top_half c p
+ left_half = in_left_half c p
+
+ candidates =
+ if front_half then
+
+ if left_half then
+ if top_half then
+ front_left_top_tetrahedra c
+ else
+ front_left_down_tetrahedra c
+ else
+ if top_half then
+ front_right_top_tetrahedra c
+ else
+ front_right_down_tetrahedra c
+
+ else -- bottom half
+
+ if left_half then
+ if top_half then
+ back_left_top_tetrahedra c
+ else
+ back_left_down_tetrahedra c
+ else
+ if top_half then
+ back_right_top_tetrahedra c
+ else
+ back_right_down_tetrahedra c
+
+ -- Use the dot product instead of 'distance' here to save a
+ -- sqrt(). So, "distances" below really means "distances squared."
+ distances = V.map ((dot p) . center) candidates
+ shortest_distance = V.minimum distances
+ lucky_idx = V.findIndex
+ (\t -> (center t) `dot` p == shortest_distance)
+ candidates
projects / spline3.git / blobdiff