module Cube
where
+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" ++
v1' = center (front_face c)
v2' = Face.v1 (front_face c)
v3' = Face.v2 (front_face c)
- fv' = rotate (Cube.fv c) cwx
+ 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) (cwx . cwx)
+ 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) ccwx
+ 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) ccwy
+ 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)) cwz
+ 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)) (cwz . cwz)
+ 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)) ccwz
+ 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)) ccwy
+ 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)) cwx
+ 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)) (cwx . cwx)
+ 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)) ccwx
+ 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)) ccwy
+ 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)) cwz
+ 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)) (cwz . cwz)
+ 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)) ccwz
+ fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron16 :: Cube -> Tetrahedron
v1' = center (right_face c)
v2' = Face.v0 (right_face c)
v3' = Face.v1 (right_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwz
+ fv' = rotate ccwz (Tetrahedron.fv (tetrahedron0 c))
tetrahedron17 :: Cube -> Tetrahedron
v1' = center (right_face c)
v2' = Face.v1 (right_face c)
v3' = Face.v2 (right_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) cwy
+ fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron18 :: Cube -> Tetrahedron
v1' = center (right_face c)
v2' = Face.v2 (right_face c)
v3' = Face.v3 (right_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) (cwy . cwy)
+ fv' = rotate ccwz $ rotate cwy
+ $ rotate cwy
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron19 :: Cube -> Tetrahedron
v1' = center (right_face c)
v2' = Face.v3 (right_face c)
v3' = Face.v0 (right_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) ccwy
+ fv' = rotate ccwz $ rotate ccwy
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron20 :: Cube -> Tetrahedron
v1' = center (left_face c)
v2' = Face.v0 (left_face c)
v3' = Face.v1 (left_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwz
+ fv' = rotate cwz (Tetrahedron.fv (tetrahedron0 c))
tetrahedron21 :: Cube -> Tetrahedron
v1' = center (left_face c)
v2' = Face.v1 (left_face c)
v3' = Face.v2 (left_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) cwy
+ fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron22 :: Cube -> Tetrahedron
v1' = center (left_face c)
v2' = Face.v2 (left_face c)
v3' = Face.v3 (left_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) (cwy . cwy)
+ fv' = rotate cwz $ rotate ccwy
+ $ rotate ccwy
+ $ Tetrahedron.fv (tetrahedron0 c)
tetrahedron23 :: Cube -> Tetrahedron
v1' = center (left_face c)
v2' = Face.v3 (left_face c)
v3' = Face.v0 (left_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) ccwy
+ 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,
tetrahedron21 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 = tetrahedra c