module Tests.Face
where

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

import Comparisons
import Cube (Cube(grid), cube_at, top)
import Face (face0,
             face2,
             face5,
             tetrahedron0,
             tetrahedron1,
             tetrahedron2,
             tetrahedron3,
             tetrahedrons)
import Grid (Grid(h), make_grid)
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


-- | 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.


face_tests :: [Test]
face_tests = [test_trilinear_c0030,
              test_trilinear_c0003,
              test_trilinear_c0021,
              test_trilinear_c0012,
              test_trilinear_c0120]


-- 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 -> Property
prop_all_volumes_positive c =
    (delta > 0) ==> (null nonpositive_volumes)
    where
      delta = h (grid c)
      ts = tetrahedrons c
      volumes = map volume ts
      nonpositive_volumes = filter (<= 0) volumes


-- | 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)