-instance Arbitrary Grid where
- arbitrary = do
- (Positive h') <- arbitrary :: Gen (Positive Double)
- fvs <- arbitrary :: Gen [[[Double]]]
- return (make_grid h' fvs)
-
-
--- | 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_t0 :: Assertion
-test_trilinear_reproduced_t0 =
- 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],
- 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
- t0 = tetrahedron0 c0
- p = polynomial t0
-
-test_trilinear_reproduced_t1 :: Assertion
-test_trilinear_reproduced_t1 =
- 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],
- 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
- t1 = tetrahedron1 c0
- p = polynomial t1
-
-test_trilinear_reproduced_t2 :: Assertion
-test_trilinear_reproduced_t2 =
- 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],
- 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
- t2 = tetrahedron2 c0
- p = polynomial t2
-
-test_trilinear_reproduced_t3 :: Assertion
-test_trilinear_reproduced_t3 =
- 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],
- 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
- t3 = tetrahedron3 c0
- p = polynomial t3
-
-test_trilinear_reproduced_t4 :: Assertion
-test_trilinear_reproduced_t4 =
- 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],
- 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
- t4 = tetrahedron4 c0
- p = polynomial t4
-
-test_trilinear_reproduced_t5 :: Assertion
-test_trilinear_reproduced_t5 =
- 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],
- 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
- t5 = tetrahedron5 c0
- p = polynomial t5
-
-test_trilinear_reproduced_t6 :: Assertion
-test_trilinear_reproduced_t6 =
- 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],
- 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
- t6 = tetrahedron6 c0
- p = polynomial t6
-
-test_trilinear_reproduced_t7 :: Assertion
-test_trilinear_reproduced_t7 =
- 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],
- 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
- t7 = tetrahedron7 c0
- p = polynomial t7
-
-test_trilinear_reproduced_t8 :: Assertion
-test_trilinear_reproduced_t8 =
- 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],
- 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
- t8 = tetrahedron8 c0
- p = polynomial t8
-
-test_trilinear_reproduced_t9 :: Assertion
-test_trilinear_reproduced_t9 =
- 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],
- 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
- t9 = tetrahedron9 c0
- p = polynomial t9
-
-test_trilinear_reproduced_t10 :: Assertion
-test_trilinear_reproduced_t10 =