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,
tetrahedron :: Cube -> Int -> Tetrahedron
tetrahedron c 0 =
- Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol 0
+ Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (front_face c)
vol = tetrahedra_volume c
tetrahedron c 1 =
- Tetrahedron fv' v0' v1' v2' v3' vol 1
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (front_face c)
vol = tetrahedra_volume c
tetrahedron c 2 =
- Tetrahedron fv' v0' v1' v2' v3' vol 2
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (front_face c)
vol = tetrahedra_volume c
tetrahedron c 3 =
- Tetrahedron fv' v0' v1' v2' v3' vol 3
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (front_face c)
vol = tetrahedra_volume c
tetrahedron c 4 =
- Tetrahedron fv' v0' v1' v2' v3' vol 4
+ Tetrahedron fv' v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (top_face c)
vol = tetrahedra_volume c
tetrahedron c 5 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate cwy $ rotate cwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 6 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 7 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate cwy $ rotate ccwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 8 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate cwy $ rotate cwy $ fv c
vol = tetrahedra_volume c
tetrahedron c 9 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 10 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 11 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 12 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0))
+ fv' = rotate ccwy $ fv c
vol = tetrahedra_volume c
tetrahedron c 13 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate ccwy $ rotate ccwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 14 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 15 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate ccwy $ rotate cwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 16 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0))
+ fv' = rotate ccwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 17 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate ccwz $ rotate cwy $ fv c
vol = tetrahedra_volume c
tetrahedron c 18 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 19 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 20 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0))
+ fv' = rotate cwz $ fv c
vol = tetrahedra_volume c
tetrahedron c 21 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ fv' = rotate cwz $ rotate ccwy $ fv c
vol = tetrahedra_volume c
tetrahedron c 22 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ fv c
vol = tetrahedra_volume c
tetrahedron c 23 =
- Tetrahedron fv' v0' v1' v2' v3' vol 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 (tetrahedron c 0)
+ $ 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] ]
-
--- | All completely contained in the front half of the cube.
-front_half_tetrahedra :: Cube -> [Tetrahedron]
-front_half_tetrahedra c =
- [ tetrahedron c n | n <- [0,1,2,3,6,12,19,21] ]
-
--- | All tetrahedra completely contained in the top half of the cube.
-top_half_tetrahedra :: Cube -> [Tetrahedron]
-top_half_tetrahedra c =
- [ tetrahedron c n | n <- [4,5,6,7,0,10,16,20] ]
-
--- | All tetrahedra completely contained in the back half of the cube.
-back_half_tetrahedra :: Cube -> [Tetrahedron]
-back_half_tetrahedra c =
- [ tetrahedron c n | n <- [8,9,10,11,4,14,17,23] ]
-
--- | All tetrahedra completely contained in the down half of the cube.
-down_half_tetrahedra :: Cube -> [Tetrahedron]
-down_half_tetrahedra c =
- [ tetrahedron c n | n <- [12,13,14,15,2,8,18,22] ]
-
--- | All tetrahedra completely contained in the right half of the cube.
-right_half_tetrahedra :: Cube -> [Tetrahedron]
-right_half_tetrahedra c =
- [ tetrahedron c n | n <- [16,17,18,19,1,5,9,13] ]
-
--- | All tetrahedra completely contained in the left half of the cube.
-left_half_tetrahedra :: Cube -> [Tetrahedron]
-left_half_tetrahedra c =
- [ tetrahedron c n | n <- [20,21,22,23,3,7,11,15] ]
+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