module Tests.Cube
where

import Debug.Trace (trace)
import Test.QuickCheck

import Comparisons
import Cube
import FunctionValues (FunctionValues)
import Tests.FunctionValues ()
import Tetrahedron (b0, b1, b2, b3, c,
                    Tetrahedron(Tetrahedron),
                    v0, v1, v2, v3, volume)

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)


-- Quickcheck tests.

-- | Since the grid size is necessarily positive, all tetrahedrons
--   (which comprise cubes of positive volume) must have positive volume
--   as well.
prop_all_volumes_positive :: Cube -> Bool
prop_all_volumes_positive c =
    null nonpositive_volumes
    where
      ts = tetrahedrons c
      volumes = map volume ts
      nonpositive_volumes = filter (<= 0) volumes

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron0_volumes_exact :: Cube -> Bool
prop_tetrahedron0_volumes_exact c =
    volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron1_volumes_exact :: Cube -> Bool
prop_tetrahedron1_volumes_exact c =
    volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron2_volumes_exact :: Cube -> Bool
prop_tetrahedron2_volumes_exact c =
    volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron3_volumes_exact :: Cube -> Bool
prop_tetrahedron3_volumes_exact c =
    volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron4_volumes_exact :: Cube -> Bool
prop_tetrahedron4_volumes_exact c =
    volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron5_volumes_exact :: Cube -> Bool
prop_tetrahedron5_volumes_exact c =
    volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron6_volumes_exact :: Cube -> Bool
prop_tetrahedron6_volumes_exact c =
    volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | In fact, since all of the tetrahedra are identical, we should
--   already know their volumes. There's 24 tetrahedra to a cube, so
--   we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron7_volumes_exact :: Cube -> Bool
prop_tetrahedron7_volumes_exact c =
    volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
    where
      delta = h c

-- | All tetrahedron should have their v0 located at the center of the cube.
prop_v0_all_equal :: Cube -> Bool
prop_v0_all_equal c = (v0 t0) == (v0 t1)
    where
      t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
      t1 = head $ tail (tetrahedrons c)


-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron0_volumes_positive :: Cube -> Bool
prop_tetrahedron0_volumes_positive c =
    volume (tetrahedron0 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron1_volumes_positive :: Cube -> Bool
prop_tetrahedron1_volumes_positive c =
    volume (tetrahedron1 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron2_volumes_positive :: Cube -> Bool
prop_tetrahedron2_volumes_positive c =
    volume (tetrahedron2 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron3_volumes_positive :: Cube -> Bool
prop_tetrahedron3_volumes_positive c =
    volume (tetrahedron3 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron4_volumes_positive :: Cube -> Bool
prop_tetrahedron4_volumes_positive c =
    volume (tetrahedron4 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron5_volumes_positive :: Cube -> Bool
prop_tetrahedron5_volumes_positive c =
    volume (tetrahedron5 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron6_volumes_positive :: Cube -> Bool
prop_tetrahedron6_volumes_positive c =
    volume (tetrahedron6 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron7_volumes_positive :: Cube -> Bool
prop_tetrahedron7_volumes_positive c =
    volume (tetrahedron7 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron8_volumes_positive :: Cube -> Bool
prop_tetrahedron8_volumes_positive c =
    volume (tetrahedron8 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron9_volumes_positive :: Cube -> Bool
prop_tetrahedron9_volumes_positive c =
    volume (tetrahedron9 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron10_volumes_positive :: Cube -> Bool
prop_tetrahedron10_volumes_positive c =
    volume (tetrahedron10 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron11_volumes_positive :: Cube -> Bool
prop_tetrahedron11_volumes_positive c =
    volume (tetrahedron11 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron12_volumes_positive :: Cube -> Bool
prop_tetrahedron12_volumes_positive c =
    volume (tetrahedron12 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron13_volumes_positive :: Cube -> Bool
prop_tetrahedron13_volumes_positive c =
    volume (tetrahedron13 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron14_volumes_positive :: Cube -> Bool
prop_tetrahedron14_volumes_positive c =
    volume (tetrahedron14 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron15_volumes_positive :: Cube -> Bool
prop_tetrahedron15_volumes_positive c =
    volume (tetrahedron15 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron16_volumes_positive :: Cube -> Bool
prop_tetrahedron16_volumes_positive c =
    volume (tetrahedron16 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron17_volumes_positive :: Cube -> Bool
prop_tetrahedron17_volumes_positive c =
    volume (tetrahedron17 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron18_volumes_positive :: Cube -> Bool
prop_tetrahedron18_volumes_positive c =
    volume (tetrahedron18 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron19_volumes_positive :: Cube -> Bool
prop_tetrahedron19_volumes_positive c =
    volume (tetrahedron19 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron20_volumes_positive :: Cube -> Bool
prop_tetrahedron20_volumes_positive c =
    volume (tetrahedron20 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron21_volumes_positive :: Cube -> Bool
prop_tetrahedron21_volumes_positive c =
    volume (tetrahedron21 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron22_volumes_positive :: Cube -> Bool
prop_tetrahedron22_volumes_positive c =
    volume (tetrahedron22 c) > 0

-- | This pretty much repeats the prop_all_volumes_positive property,
--   but will let me know which tetrahedrons's vertices are disoriented.
prop_tetrahedron23_volumes_positive :: Cube -> Bool
prop_tetrahedron23_volumes_positive c =
    volume (tetrahedron23 c) > 0


-- | Given in Sorokina and Zeilfelder, p. 79.
--prop_c0120_identity1 :: Cube -> Bool
--prop_c0120_identity1 cube =
--   c0 ~= (c1 + c2) / 2
--     where
--       c0 = trace ("c0 :" ++ (show (c t0 0 1 2 0))) (c t0 0 1 2 0)
--       c1 = trace ("c1 :" ++ (show (c t0 0 0 2 1))) (c t0 0 0 2 1)
--       c2 = trace ("c2 :" ++ (show (c t1 0 0 2 1))) (c t1 0 0 2 1)
--       t0 = tetrahedron0 cube
--       t1 = tetrahedron1 cube


-- | Given in Sorokina and Zeilfelder, p. 78.
-- prop_cijk1_identity :: Cube -> Bool
-- prop_cijk1_identity cube =
--      and [ c t0 i j k 1 ~=
--                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
--                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
--                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
--                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
--                                                       j <- [0..2],
--                                                       k <- [0..2],
--                                                       i + j + k == 2]
--       where
--         t0 = tetrahedron0 cube
--         t1 = tetrahedron1 cube