+import Tetrahedron
+
+
+-- | Check the value of c0030 for tetrahedron0 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 :: Assertion
+test_trilinear_c0030 =
+ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0003 for tetrahedron0 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 :: Assertion
+test_trilinear_c0003 =
+ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0021 for tetrahedron0 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 :: Assertion
+test_trilinear_c0021 =
+ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0012 for tetrahedron0 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 :: Assertion
+test_trilinear_c0012 =
+ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0120 for tetrahedron0 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 :: Assertion
+test_trilinear_c0120 =
+ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0102 for tetrahedron0 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 :: Assertion
+test_trilinear_c0102 =
+ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0111 for tetrahedron0 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 :: Assertion
+test_trilinear_c0111 =
+ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0210 for tetrahedron0 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 :: Assertion
+test_trilinear_c0210 =
+ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0201 for tetrahedron0 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 :: Assertion
+test_trilinear_c0201 =
+ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c0300 for tetrahedron0 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 :: Assertion
+test_trilinear_c0300 =
+ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1020 for tetrahedron0 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 :: Assertion
+test_trilinear_c1020 =
+ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1002 for tetrahedron0 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 :: Assertion
+test_trilinear_c1002 =
+ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1011 for tetrahedron0 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 :: Assertion
+test_trilinear_c1011 =
+ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1110 for tetrahedron0 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 :: Assertion
+test_trilinear_c1110 =
+ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1101 for tetrahedron0 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 :: Assertion
+test_trilinear_c1101 =
+ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c1200 for tetrahedron0 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 :: Assertion
+test_trilinear_c1200 =
+ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c2010 for tetrahedron0 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 :: Assertion
+test_trilinear_c2010 =
+ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c2001 for tetrahedron0 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 :: Assertion
+test_trilinear_c2001 =
+ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c2100 for tetrahedron0 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 :: Assertion
+test_trilinear_c2100 =
+ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Check the value of c3000 for tetrahedron0 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 :: Assertion
+test_trilinear_c3000 =
+ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Make sure that v0 of tetrahedron0 belonging to the cube centered
+-- on (1,1,1) with a grid constructed from the trilinear values
+-- winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v0 :: Assertion
+test_trilinear_f0_t0_v0 =
+ assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Make sure that v1 of tetrahedron0 belonging to the cube centered
+-- on (1,1,1) with a grid constructed from the trilinear values
+-- winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v1 :: Assertion
+test_trilinear_f0_t0_v1 =
+ assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Make sure that v2 of tetrahedron0 belonging to the cube centered
+-- on (1,1,1) with a grid constructed from the trilinear values
+-- winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v2 :: Assertion
+test_trilinear_f0_t0_v2 =
+ assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+-- | Make sure that v3 of tetrahedron0 belonging to the cube centered
+-- on (1,1,1) with a grid constructed from the trilinear values
+-- winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v3 :: Assertion
+test_trilinear_f0_t0_v3 =
+ assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+ where
+ g = make_grid 1 trilinear
+ cube = fromJust $ cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+
+test_trilinear_reproduced :: Assertion
+test_trilinear_reproduced =
+ assertTrue "trilinears are reproduced correctly" $
+ and [p (i', j', k') ~= value_at trilinear i j k
+ | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ t <- tetrahedra c0,
+ let p = polynomial t,
+ let i' = fromIntegral i,
+ let j' = fromIntegral j,
+ let k' = fromIntegral k]
+ where
+ g = make_grid 1 trilinear
+ c0 = fromJust $ cube_at g 1 1 1
+
+
+test_zeros_reproduced :: Assertion
+test_zeros_reproduced =
+ assertTrue "the zero function is reproduced correctly" $
+ and [p (i', j', k') ~= value_at zeros i j k
+ | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ let i' = fromIntegral i,
+ let j' = fromIntegral j,
+ let k' = fromIntegral k]
+ where
+ g = make_grid 1 zeros
+ c0 = fromJust $ cube_at g 1 1 1
+ t0 = tetrahedron0 c0
+ p = polynomial t0
+