module Tests.Face
where

import Control.Monad (unless)
import Test.HUnit
import Test.QuickCheck

import Comparisons
import Face
import Grid (Grid(h), make_grid)
import Point
import Tetrahedron


-- HUnit tests.

-- | An HUnit assertion that wraps the almost_equals function. Stolen
--   from the definition of assertEqual in Test/HUnit/Base.hs.
assertAlmostEqual :: String -> Double -> Double -> Assertion
assertAlmostEqual preface expected actual =
  unless (actual ~= expected) (assertFailure msg)
 where msg = (if null preface then "" else preface ++ "\n") ++
             "expected: " ++ show expected ++ "\n but got: " ++ show actual


-- | An HUnit assertion that wraps the is_close function. Stolen
--   from the definition of assertEqual in Test/HUnit/Base.hs.
assertClose :: String -> Point -> Point -> Assertion
assertClose preface expected actual =
  unless (actual `is_close` expected) (assertFailure msg)
 where msg = (if null preface then "" else preface ++ "\n") ++
             "expected: " ++ show expected ++ "\n but got: " ++ show actual


-- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine
--   points (hi, hj, jk) with h = 1. From example one in the paper.
--   Used in the next bunch of tests.
trilinear :: [[[Double]]]
trilinear = [ [ [ 1, 2, 3 ],
                [ 1, 3, 5 ],
                [ 1, 4, 7 ] ],
              [ [ 1, 2, 3 ],
                [ 1, 4, 7 ],
                [ 1, 6, 11 ] ],
              [ [ 1, 2, 3 ],
                [ 1, 5, 9 ],
                [ 1, 8, 15 ]]]

-- | Check the value of c0030 for any tetrahedron belonging to the
--   cube centered on (1,1,1) with a grid constructed from the
--   trilinear values. See example one in the paper.
-- test_trilinear_c0030 :: Test
-- test_trilinear_c0030 =
--     TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0003 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0003 :: Test
-- test_trilinear_c0003 =
--     TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0021 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0021 :: Test
-- test_trilinear_c0021 =
--     TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0012 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0012 :: Test
-- test_trilinear_c0012 =
--     TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0120 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0120 :: Test
-- test_trilinear_c0120 =
--     TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0102 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0102 :: Test
-- test_trilinear_c0102 =
--     TestCase $ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0111 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0111 :: Test
-- test_trilinear_c0111 =
--     TestCase $ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0210 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0210 :: Test
-- test_trilinear_c0210 =
--     TestCase $ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0201 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0201 :: Test
-- test_trilinear_c0201 =
--     TestCase $ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c0300 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c0300 :: Test
-- test_trilinear_c0300 =
--     TestCase $ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1020 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1020 :: Test
-- test_trilinear_c1020 =
--     TestCase $ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1002 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1002 :: Test
-- test_trilinear_c1002 =
--     TestCase $ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1011 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1011 :: Test
-- test_trilinear_c1011 =
--     TestCase $ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1110 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1110 :: Test
-- test_trilinear_c1110 =
--     TestCase $ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1101 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1101 :: Test
-- test_trilinear_c1101 =
--     TestCase $ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c1200 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c1200 :: Test
-- test_trilinear_c1200 =
--     TestCase $ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c2010 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c2010 :: Test
-- test_trilinear_c2010 =
--     TestCase $ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c2001 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c2001 :: Test
-- test_trilinear_c2001 =
--     TestCase $ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c2100 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- test_trilinear_c2100 :: Test
-- test_trilinear_c2100 =
--     TestCase $ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
--       where
--         g = make_grid 1 trilinear
--         cube = cube_at g 1 1 1
--         t = head (tetrahedrons cube) -- Any one will do.


-- -- | Check the value of c3000 for any tetrahedron belonging to the
-- --   cube centered on (1,1,1) with a grid constructed from the
-- --   trilinear values. See example one in the paper.
-- -- test_trilinear_c3000 :: Test
-- -- test_trilinear_c3000 =
-- --     TestCase $ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
-- --       where
-- --         g = make_grid 1 trilinear
-- --         cube = cube_at g 1 1 1
-- --         t = head (tetrahedrons cube) -- Any one will do.



-- -- test_trilinear_f0_t0_v0 :: Test
-- -- test_trilinear_f0_t0_v0 =
-- --     TestCase $ assertClose "v0 is correct" (v0 t) (0.5, 1.5, 1.5)
-- --       where
-- --         g = make_grid 1 trilinear
-- --         cube = cube_at g 1 1 1
-- --         t = tetrahedron0 (face0 cube) -- Any one will do.


-- -- test_trilinear_f0_t0_v1 :: Test
-- -- test_trilinear_f0_t0_v1 =
-- --     TestCase $ assertClose "v1 is correct" (v1 t) (1.5, 1.5, 1.5)
-- --       where
-- --         g = make_grid 1 trilinear
-- --         cube = cube_at g 1 1 1
-- --         t = tetrahedron0 (face0 cube) -- Any one will do.


-- -- test_trilinear_f0_t0_v2 :: Test
-- -- test_trilinear_f0_t0_v2 =
-- --     TestCase $ assertClose "v2 is correct" (v2 t) (1, 1, 1.5)
-- --       where
-- --         g = make_grid 1 trilinear
-- --         cube = cube_at g 1 1 1
-- --         t = tetrahedron0 (face0 cube) -- Any one will do.



-- -- test_trilinear_f0_t0_v3 :: Test
-- -- test_trilinear_f0_t0_v3 =
-- --     TestCase $ assertClose "v3 is correct" (v3 t) (1, 1, 1)
-- --       where
-- --         g = make_grid 1 trilinear
-- --         cube = cube_at g 1 1 1
-- --         t = tetrahedron0 (face0 cube) -- Any one will do.



-- face_tests :: [Test]
face_tests = []
-- face_tests = [test_trilinear_c0030,
--               test_trilinear_c0003,
--               test_trilinear_c0021,
--               test_trilinear_c0012,
--               test_trilinear_c0120,
--               test_trilinear_c0102,
--               test_trilinear_c0111,
--               test_trilinear_c0210,
--               test_trilinear_c0201,
--               test_trilinear_c0300,
--               test_trilinear_c1020,
--               test_trilinear_c1002,
--               test_trilinear_c1011,
--               test_trilinear_c1110,
--               test_trilinear_c1101,
--               test_trilinear_c1200,
--               test_trilinear_c2010,
--               test_trilinear_c2001,
--               test_trilinear_c2100,
--               test_trilinear_c3000,
--               test_trilinear_f0_t0_v0,
--               test_trilinear_f0_t0_v1,
--               test_trilinear_f0_t0_v2,
--               test_trilinear_f0_t0_v3]


-- -- QuickCheck Tests.


-- -- | 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 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)

-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0120_identity1 :: Cube -> Bool
-- prop_c0120_identity1 cube =
--     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0210_identity1 :: Cube -> Bool
-- prop_c0210_identity1 cube =
--     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0300_identity1 :: Cube -> Bool
-- prop_c0300_identity1 cube =
--     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)

-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1110_identity :: Cube -> Bool
-- prop_c1110_identity cube =
--     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1200_identity1 :: Cube -> Bool
-- prop_c1200_identity1 cube =
--     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c2100_identity1 :: Cube -> Bool
-- prop_c2100_identity1 cube =
--     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron1 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0102_identity1 :: Cube -> Bool
-- prop_c0102_identity1 cube =
--     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0201_identity1 :: Cube -> Bool
-- prop_c0201_identity1 cube =
--     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c0300_identity2 :: Cube -> Bool
-- prop_c0300_identity2 cube =
--     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)

-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1101_identity :: Cube -> Bool
-- prop_c1101_identity cube =
--     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1200_identity2 :: Cube -> Bool
-- prop_c1200_identity2 cube =
--     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c2100_identity2 :: Cube -> Bool
-- prop_c2100_identity2 cube =
--     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t3 = tetrahedron3 (face0 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c3000_identity :: Cube -> Bool
-- prop_c3000_identity cube =
--     c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c2010_identity :: Cube -> Bool
-- prop_c2010_identity cube =
--     c t0' 2 0 1 0 ~= c t0' 1 1 1 0 + c t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c2001_identity :: Cube -> Bool
-- prop_c2001_identity cube =
--     c t0' 2 0 0 1 ~= c t0' 1 1 0 1 + c t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)

-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1020_identity :: Cube -> Bool
-- prop_c1020_identity cube =
--     c t0' 1 0 2 0 ~= c t0' 0 1 2 0 + c t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1002_identity :: Cube -> Bool
-- prop_c1002_identity cube =
--     c t0' 1 0 0 2 ~= c t0' 0 1 0 2 + c t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)


-- -- | Given in Sorokina and Zeilfelder, p. 79.
-- prop_c1011_identity :: Cube -> Bool
-- prop_c1011_identity cube =
--     c t0' 1 0 1 1 ~= c t0' 0 1 1 1 + c t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t2 = tetrahedron2 (face5 cube)
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0120_identity2 :: Cube -> Bool
-- prop_c0120_identity2 cube =
--         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0102_identity2 :: Cube -> Bool
-- prop_c0102_identity2 cube =
--     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0111_identity :: Cube -> Bool
-- prop_c0111_identity cube =
--     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0210_identity2 :: Cube -> Bool
-- prop_c0210_identity2 cube =
--     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0201_identity2 :: Cube -> Bool
-- prop_c0201_identity2 cube =
--     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)


-- -- | Given in Sorokina and Zeilfelder, p. 80.
-- prop_c0300_identity3 :: Cube -> Bool
-- prop_c0300_identity3 cube =
--     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
--       where
--         t0 = tetrahedron0 (face0 cube)
--         t1 = tetrahedron0 (face2 (top cube))
--         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)