X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FGrid.hs;h=15bbc9826e11ca15a6d80c4ed646ca3a2d76a62a;hb=574a15e7ccfa3109f06fa05ed09e2282a03a7dad;hp=e22557b6e396f4951e208aa097f122c3463c5523;hpb=89b8b6e94fcc944a1f4611811265f3c6217af850;p=spline3.git

diff --git a/src/Tests/Grid.hs b/src/Tests/Grid.hs
index e22557b..15bbc98 100644
--- a/src/Tests/Grid.hs
+++ b/src/Tests/Grid.hs
@@ -1,11 +1,714 @@
 module Tests.Grid
 where
 
+import Data.Maybe (fromJust)
+import Test.HUnit
 import Test.QuickCheck
+
+import Assertions
+import Comparisons
+import Cube hiding (i, j, k)
+import Examples
+import FunctionValues (value_at)
 import Grid
+import Tetrahedron
+
 
 instance Arbitrary Grid where
     arbitrary = do
       (Positive h') <- arbitrary :: Gen (Positive Double)
-      fv <- arbitrary :: Gen [[[Double]]]
-      return (make_grid h' fv)
+      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 =
+    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
+      t10 = tetrahedron10 c0
+      p = polynomial t10
+
+test_trilinear_reproduced_t11 :: Assertion
+test_trilinear_reproduced_t11 =
+    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
+      t11 = tetrahedron11 c0
+      p = polynomial t11
+
+test_trilinear_reproduced_t12 :: Assertion
+test_trilinear_reproduced_t12 =
+    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
+      t12 = tetrahedron12 c0
+      p = polynomial t12
+
+test_trilinear_reproduced_t13 :: Assertion
+test_trilinear_reproduced_t13 =
+    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
+      t13 = tetrahedron13 c0
+      p = polynomial t13
+
+
+test_trilinear_reproduced_t14 :: Assertion
+test_trilinear_reproduced_t14 =
+    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
+      t14 = tetrahedron14 c0
+      p = polynomial t14
+
+test_trilinear_reproduced_t15 :: Assertion
+test_trilinear_reproduced_t15 =
+    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
+      t15 = tetrahedron15 c0
+      p = polynomial t15
+
+test_trilinear_reproduced_t16 :: Assertion
+test_trilinear_reproduced_t16 =
+    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
+      t16 = tetrahedron16 c0
+      p = polynomial t16
+
+test_trilinear_reproduced_t17 :: Assertion
+test_trilinear_reproduced_t17 =
+    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
+      t17 = tetrahedron17 c0
+      p = polynomial t17
+
+test_trilinear_reproduced_t18 :: Assertion
+test_trilinear_reproduced_t18 =
+    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
+      t18 = tetrahedron18 c0
+      p = polynomial t18
+
+test_trilinear_reproduced_t19 :: Assertion
+test_trilinear_reproduced_t19 =
+    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
+      t19 = tetrahedron19 c0
+      p = polynomial t19
+
+test_trilinear_reproduced_t20 :: Assertion
+test_trilinear_reproduced_t20 =
+    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
+      t20 = tetrahedron20 c0
+      p = polynomial t20
+
+
+test_trilinear_reproduced_t21 :: Assertion
+test_trilinear_reproduced_t21 =
+    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
+      t21 = tetrahedron21 c0
+      p = polynomial t21
+
+test_trilinear_reproduced_t22 :: Assertion
+test_trilinear_reproduced_t22 =
+    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
+      t22 = tetrahedron22 c0
+      p = polynomial t22
+
+
+test_trilinear_reproduced_t23 :: Assertion
+test_trilinear_reproduced_t23 =
+    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
+      t19 = tetrahedron19 c0
+      p = polynomial t19
+
+
+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