module Cube
where
-import Data.List ( (\\) )
+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)
j' <- choose (coordmin, coordmax)
k' <- choose (coordmin, coordmax)
fv' <- arbitrary :: Gen FunctionValues
- return (Cube h' i' j' k' fv')
+ (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)
-- | 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,
v3' = (center c) + (-delta, delta, -delta)
-tetrahedron0 :: Cube -> Tetrahedron
-tetrahedron0 c =
- Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+tetrahedron :: Cube -> Int -> Tetrahedron
+
+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 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 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 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 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 cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+ 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)
v3' = Face.v3 (top_face c)
fv' = rotate cwy $ rotate cwz
$ rotate cwz
- $ Tetrahedron.fv (tetrahedron0 c)
+ $ 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 cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
+ 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 cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
+ 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)
v3' = Face.v2 (back_face c)
fv' = rotate cwy $ rotate cwy
$ rotate cwx
- $ Tetrahedron.fv (tetrahedron0 c)
+ $ 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)
fv' = rotate cwy $ rotate cwy
$ rotate cwx
$ rotate cwx
- $ Tetrahedron.fv (tetrahedron0 c)
+ $ 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)
v3' = Face.v0 (back_face c)
fv' = rotate cwy $ rotate cwy
$ rotate ccwx
- $ Tetrahedron.fv (tetrahedron0 c)
-
+ $ 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 ccwy (Tetrahedron.fv (tetrahedron0 c))
-
+ 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 ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
+ 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)
v3' = Face.v3 (down_face c)
fv' = rotate ccwy $ rotate ccwz
$ rotate ccwz
- $ Tetrahedron.fv (tetrahedron0 c)
-
+ $ 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 ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
-
+ fv' = rotate ccwy $ rotate cwz $ fv c
+ vol = tetrahedra_volume c
-tetrahedron16 :: Cube -> Tetrahedron
-tetrahedron16 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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 (Tetrahedron.fv (tetrahedron0 c))
+ fv' = rotate ccwz $ fv c
+ vol = tetrahedra_volume c
-
-tetrahedron17 :: Cube -> Tetrahedron
-tetrahedron17 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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 $ Tetrahedron.fv (tetrahedron0 c)
-
+ fv' = rotate ccwz $ rotate cwy $ fv c
+ vol = tetrahedra_volume c
-tetrahedron18 :: Cube -> Tetrahedron
-tetrahedron18 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 18 =
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (right_face c)
v3' = Face.v3 (right_face c)
fv' = rotate ccwz $ rotate cwy
$ rotate cwy
- $ Tetrahedron.fv (tetrahedron0 c)
-
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron19 :: Cube -> Tetrahedron
-tetrahedron19 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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
- $ Tetrahedron.fv (tetrahedron0 c)
+ $ fv c
+ vol = tetrahedra_volume c
-
-tetrahedron20 :: Cube -> Tetrahedron
-tetrahedron20 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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 (Tetrahedron.fv (tetrahedron0 c))
-
+ fv' = rotate cwz $ fv c
+ vol = tetrahedra_volume c
-tetrahedron21 :: Cube -> Tetrahedron
-tetrahedron21 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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 $ Tetrahedron.fv (tetrahedron0 c)
+ fv' = rotate cwz $ rotate ccwy $ fv c
+ vol = tetrahedra_volume c
-
-tetrahedron22 :: Cube -> Tetrahedron
-tetrahedron22 c =
- Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 22 =
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (left_face c)
v3' = Face.v3 (left_face c)
fv' = rotate cwz $ rotate ccwy
$ rotate ccwy
- $ Tetrahedron.fv (tetrahedron0 c)
-
+ $ fv c
+ vol = tetrahedra_volume c
-tetrahedron23 :: Cube -> Tetrahedron
-tetrahedron23 c =
- Tetrahedron fv' v0' v1' v2' v3'
+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
- $ Tetrahedron.fv (tetrahedron0 c)
+ $ fv c
+ vol = tetrahedra_volume c
+-- Feels dirty, but whatever.
+tetrahedron _ _ = error "asked for a nonexistent tetrahedron"
-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]
+-- 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) =
--
find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
find_containing_tetrahedron c p =
- head containing_tetrahedra
+ candidates `V.unsafeIndex` (fromJust lucky_idx)
where
- candidates = tetrahedra c
- non_candidates_x =
- if (in_front_half c p) then
- back_half_tetrahedra c
+ 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
- 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
+ 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