module Tests.Cube
where

import Test.QuickCheck

import Comparisons
import Cube
import FunctionValues (FunctionValues)
import Tests.FunctionValues ()
import Tetrahedron (v0, 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