module Tests.Cube
where

import Prelude hiding (LT)

import Cardinal
import Comparisons
import Cube hiding (i, j, k)
import FunctionValues
import Misc (all_equal, disjoint)
import Tetrahedron (b0, b1, b2, b3, c, fv,
                    v0, v1, v2, v3, volume)


-- Quickcheck tests.

-- | The 'front_half_tetrahedra' and 'back_half_tetrahedra' should
--   have no tetrahedra in common.
prop_front_back_tetrahedra_disjoint :: Cube -> Bool
prop_front_back_tetrahedra_disjoint c =
    disjoint (front_half_tetrahedra c) (back_half_tetrahedra c)


-- | The 'top_half_tetrahedra' and 'down_half_tetrahedra' should
--   have no tetrahedra in common.
prop_top_down_tetrahedra_disjoint :: Cube -> Bool
prop_top_down_tetrahedra_disjoint c =
    disjoint (top_half_tetrahedra c) (down_half_tetrahedra c)


-- | The 'left_half_tetrahedra' and 'right_half_tetrahedra' should
--   have no tetrahedra in common.
prop_left_right_tetrahedra_disjoint :: Cube -> Bool
prop_left_right_tetrahedra_disjoint c =
    disjoint (left_half_tetrahedra c) (right_half_tetrahedra c)


-- | Since the grid size is necessarily positive, all tetrahedra
--   (which comprise cubes of positive volume) must have positive volume
--   as well.
prop_all_volumes_positive :: Cube -> Bool
prop_all_volumes_positive cube =
    null nonpositive_volumes
    where
      ts = tetrahedra cube
      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_all_volumes_exact :: Cube -> Bool
prop_all_volumes_exact cube =
    and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
    where
      delta = h cube

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


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
--   third and fourth indices of c-t1 have been switched. This is
--   because we store the triangles oriented such that their volume is
--   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
--   in opposite directions, one of them has to have negative volume!
prop_c0120_identity1 :: Cube -> Bool
prop_c0120_identity1 cube =
   c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
     where
       t0 = tetrahedron cube 0
       t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--   'prop_c0120_identity1' with tetrahedrons 1 and 2.
prop_c0120_identity2 :: Cube -> Bool
prop_c0120_identity2 cube =
   c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
     where
       t0 = tetrahedron cube 0
       t1 = tetrahedron cube 1
            
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--   'prop_c0120_identity1' with tetrahedrons 1 and 2.
prop_c0120_identity3 :: Cube -> Bool
prop_c0120_identity3 cube =
   c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
     where
       t1 = tetrahedron cube 1
       t2 = tetrahedron cube 2

-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--   'prop_c0120_identity1' with tetrahedrons 2 and 3.
prop_c0120_identity4 :: Cube -> Bool
prop_c0120_identity4 cube =
   c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
     where
       t2 = tetrahedron cube 2
       t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--   'prop_c0120_identity1' with tetrahedrons 4 and 5.
prop_c0120_identity5 :: Cube -> Bool
prop_c0120_identity5 cube =
    c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
    where
      t4 = tetrahedron cube 4
      t5 = tetrahedron cube 5

-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- --   'prop_c0120_identity1' with tetrahedrons 5 and 6.
prop_c0120_identity6 :: Cube -> Bool
prop_c0120_identity6 cube =
   c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
     where
       t5 = tetrahedron cube 5
       t6 = tetrahedron cube 6


-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- --   'prop_c0120_identity1' with tetrahedrons 6 and 7.
prop_c0120_identity7 :: Cube -> Bool
prop_c0120_identity7 cube =
   c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
     where
       t6 = tetrahedron cube 6
       t7 = tetrahedron cube 7


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--   'prop_c0120_identity1'.
prop_c0210_identity1 :: Cube -> Bool
prop_c0210_identity1 cube =
    c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--   'prop_c0120_identity1'.
prop_c0300_identity1 :: Cube -> Bool
prop_c0300_identity1 cube =
    c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--   'prop_c0120_identity1'.
prop_c1110_identity :: Cube -> Bool
prop_c1110_identity cube =
    c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--   'prop_c0120_identity1'.
prop_c1200_identity1 :: Cube -> Bool
prop_c1200_identity1 cube =
    c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3


-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--   'prop_c0120_identity1'.
prop_c2100_identity1 :: Cube -> Bool
prop_c2100_identity1 cube =
    c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3



-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
--   third and fourth indices of c-t3 have been switched. This is
--   because we store the triangles oriented such that their volume is
--   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
--   point in opposite directions, one of them has to have negative
--   volume!
prop_c0102_identity1 :: Cube -> Bool
prop_c0102_identity1 cube =
    c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--   'prop_c0102_identity1'.
prop_c0201_identity1 :: Cube -> Bool
prop_c0201_identity1 cube =
    c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--   'prop_c0102_identity1'.
prop_c0300_identity2 :: Cube -> Bool
prop_c0300_identity2 cube =
    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--   'prop_c0102_identity1'.
prop_c1101_identity :: Cube -> Bool
prop_c1101_identity cube =
    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--   'prop_c0102_identity1'.
prop_c1200_identity2 :: Cube -> Bool
prop_c1200_identity2 cube =
    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--   'prop_c0102_identity1'.
prop_c2100_identity2 :: Cube -> Bool
prop_c2100_identity2 cube =
    c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
--   fourth indices of c-t6 have been switched. This is because we
--   store the triangles oriented such that their volume is
--   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
--   point in opposite directions, one of them has to have negative
--   volume!
prop_c3000_identity :: Cube -> Bool
prop_c3000_identity cube =
    c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0
                    - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--   'prop_c3000_identity'.
prop_c2010_identity :: Cube -> Bool
prop_c2010_identity cube =
    c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 0 1
                    - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--   'prop_c3000_identity'.
prop_c2001_identity :: Cube -> Bool
prop_c2001_identity cube =
    c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 1 0
                    - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--   'prop_c3000_identity'.
prop_c1020_identity :: Cube -> Bool
prop_c1020_identity cube =
    c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 0 2
                    - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--   'prop_c3000_identity'.
prop_c1002_identity :: Cube -> Bool
prop_c1002_identity cube =
    c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 2 0
                    - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6


-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--   'prop_c3000_identity'.
prop_c1011_identity :: Cube -> Bool
prop_c1011_identity cube =
    c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 -
                    ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6



-- | 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 = tetrahedron cube 0
        t1 = tetrahedron cube 1


-- | The function values at the interior should be the same for all
--   tetrahedra.
prop_interior_values_all_identical :: Cube -> Bool
prop_interior_values_all_identical cube =
    all_equal [ eval (Tetrahedron.fv tet) I | tet <- tetrahedra cube ]


-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
--   This test checks the rotation works as expected.
prop_c_tilde_2100_rotation_correct :: Cube -> Bool
prop_c_tilde_2100_rotation_correct cube =
    expr1 == expr2
    where
      t0 = tetrahedron cube 0
      t6 = tetrahedron cube 6

      -- What gets computed for c2100 of t6.
      expr1 = eval (Tetrahedron.fv t6) $
          (3/8)*I +
          (1/12)*(T + R + L + D) +
          (1/64)*(FT + FR + FL + FD) +
          (7/48)*F +
          (1/48)*B +
          (1/96)*(RT + LD + LT + RD) +
          (1/192)*(BT + BR + BL + BD)

      -- What should be computed for c2100 of t6.
      expr2 = eval (Tetrahedron.fv t0) $
              (3/8)*I +
              (1/12)*(F + R + L + B) +
              (1/64)*(FT + RT + LT + BT) +
              (7/48)*T +
              (1/48)*D +
              (1/96)*(FR + FL + BR + BL) +
              (1/192)*(FD + RD + LD + BD)


-- | We know what (c t6 2 1 0 0) should be from Sorokina and
--   Zeilfelder, p. 87.  This test checks the actual value based on
--   the FunctionValues of the cube.
--
--   If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
--   even meaningful!
prop_c_tilde_2100_correct :: Cube -> Bool
prop_c_tilde_2100_correct cube =
    c t6 2 1 0 0 == expected
    where
      t0 = tetrahedron cube 0
      t6 = tetrahedron cube 6
      fvs = Tetrahedron.fv t0
      expected = eval fvs $
                  (3/8)*I +
                  (1/12)*(F + R + L + B) +
                  (1/64)*(FT + RT + LT + BT) +
                  (7/48)*T +
                  (1/48)*D +
                  (1/96)*(FR + FL + BR + BL) +
                  (1/192)*(FD + RD + LD + BD)


-- Tests to check that the correct edges are incidental.
prop_t0_shares_edge_with_t1 :: Cube -> Bool
prop_t0_shares_edge_with_t1 cube =
    (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
      where
        t0 = tetrahedron cube 0
        t1 = tetrahedron cube 1

prop_t0_shares_edge_with_t3 :: Cube -> Bool
prop_t0_shares_edge_with_t3 cube =
    (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
      where
        t0 = tetrahedron cube 0
        t3 = tetrahedron cube 3

prop_t0_shares_edge_with_t6 :: Cube -> Bool
prop_t0_shares_edge_with_t6 cube =
    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
      where
        t0 = tetrahedron cube 0
        t6 = tetrahedron cube 6

prop_t1_shares_edge_with_t2 :: Cube -> Bool
prop_t1_shares_edge_with_t2 cube =
    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
      where
        t1 = tetrahedron cube 1
        t2 = tetrahedron cube 2

prop_t1_shares_edge_with_t19 :: Cube -> Bool
prop_t1_shares_edge_with_t19 cube =
    (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
      where
        t1 = tetrahedron cube 1
        t19 = tetrahedron cube 19

prop_t2_shares_edge_with_t3 :: Cube -> Bool
prop_t2_shares_edge_with_t3 cube =
    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
      where
        t1 = tetrahedron cube 1
        t2 = tetrahedron cube 2

prop_t2_shares_edge_with_t12 :: Cube -> Bool
prop_t2_shares_edge_with_t12 cube =
    (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
      where
        t2 = tetrahedron cube 2
        t12 = tetrahedron cube 12

prop_t3_shares_edge_with_t21 :: Cube -> Bool
prop_t3_shares_edge_with_t21 cube =
    (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
      where
        t3 = tetrahedron cube 3
        t21 = tetrahedron cube 21

prop_t4_shares_edge_with_t5 :: Cube -> Bool
prop_t4_shares_edge_with_t5 cube =
    (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
      where
        t4 = tetrahedron cube 4
        t5 = tetrahedron cube 5

prop_t4_shares_edge_with_t7 :: Cube -> Bool
prop_t4_shares_edge_with_t7 cube =
    (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
      where
        t4 = tetrahedron cube 4
        t7 = tetrahedron cube 7

prop_t4_shares_edge_with_t10 :: Cube -> Bool
prop_t4_shares_edge_with_t10 cube =
    (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
      where
        t4 = tetrahedron cube 4
        t10 = tetrahedron cube 10

prop_t5_shares_edge_with_t6 :: Cube -> Bool
prop_t5_shares_edge_with_t6 cube =
    (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
      where
        t5 = tetrahedron cube 5
        t6 = tetrahedron cube 6

prop_t5_shares_edge_with_t16 :: Cube -> Bool
prop_t5_shares_edge_with_t16 cube =
    (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
      where
        t5 = tetrahedron cube 5
        t16 = tetrahedron cube 16

prop_t6_shares_edge_with_t7 :: Cube -> Bool
prop_t6_shares_edge_with_t7 cube =
    (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
      where
        t6 = tetrahedron cube 6
        t7 = tetrahedron cube 7

prop_t7_shares_edge_with_t20 :: Cube -> Bool
prop_t7_shares_edge_with_t20 cube =
    (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
      where
        t7 = tetrahedron cube 7
        t20 = tetrahedron cube 20