X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FGrid.hs;h=f72d31235264a6987bff9ebdde0b985357485106;hb=b70a46d402df62ea02a4b111ab59666d2405462a;hp=15bbc9826e11ca15a6d80c4ed646ca3a2d76a62a;hpb=a97defacc74e0b34c7f12f8a436da39e5124ac10;p=spline3.git

diff --git a/src/Tests/Grid.hs b/src/Tests/Grid.hs
index 15bbc98..f72d312 100644
--- a/src/Tests/Grid.hs
+++ b/src/Tests/Grid.hs
@@ -1,9 +1,9 @@
 module Tests.Grid
 where
 
-import Data.Maybe (fromJust)
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.HUnit (testCase)
 import Test.HUnit
-import Test.QuickCheck
 
 import Assertions
 import Comparisons
@@ -11,254 +11,121 @@ import Cube hiding (i, j, k)
 import Examples
 import FunctionValues (value_at)
 import Grid
+import Point (Point)
 import Tetrahedron
-
-
-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
+import ThreeDimensional
+
+
+-- | Check all coefficients of tetrahedron0 belonging to the cube
+--   centered on (1,1,1) with a grid constructed from the trilinear
+--   values. See example one in the paper.
+trilinear_c0_t0_coefficient_tests :: Test.Framework.Test
+trilinear_c0_t0_coefficient_tests =
+  testGroup "trilinear c0 t0 coefficients" $
+    [testCase "c0030 is correct" test_trilinear_c0030,
+     testCase "c0003 is correct" test_trilinear_c0003,
+     testCase "c0021 is correct" test_trilinear_c0021,
+     testCase "c0012 is correct" test_trilinear_c0012,
+     testCase "c0120 is correct" test_trilinear_c0120,
+     testCase "c0102 is correct" test_trilinear_c0102,
+     testCase "c0111 is correct" test_trilinear_c0111,
+     testCase "c0210 is correct" test_trilinear_c0210,
+     testCase "c0201 is correct" test_trilinear_c0201,
+     testCase "c0300 is correct" test_trilinear_c0300,
+     testCase "c1020 is correct" test_trilinear_c1020,
+     testCase "c1002 is correct" test_trilinear_c1002,
+     testCase "c1011 is correct" test_trilinear_c1011,
+     testCase "c1110 is correct" test_trilinear_c1110,
+     testCase "c1101 is correct" test_trilinear_c1101,
+     testCase "c1200 is correct" test_trilinear_c1200,
+     testCase "c2010 is correct" test_trilinear_c2010,
+     testCase "c2001 is correct" test_trilinear_c2001,
+     testCase "c2100 is correct" test_trilinear_c2100,
+     testCase "c3000 is correct" test_trilinear_c3000]
+  where
+    g = make_grid 1 trilinear
+    cube = cube_at g 1 1 1
+    t = tetrahedron0 cube
+
+    test_trilinear_c0030 :: Assertion
+    test_trilinear_c0030 =
+      assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+
+    test_trilinear_c0003 :: Assertion
+    test_trilinear_c0003 =
+      assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+
+    test_trilinear_c0021 :: Assertion
+    test_trilinear_c0021 =
+      assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+
+    test_trilinear_c0012 :: Assertion
+    test_trilinear_c0012 =
+      assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+
+    test_trilinear_c0120 :: Assertion
+    test_trilinear_c0120 =
+      assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+
+    test_trilinear_c0102 :: Assertion
+    test_trilinear_c0102 =
+      assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+
+    test_trilinear_c0111 :: Assertion
+    test_trilinear_c0111 =
+      assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+
+    test_trilinear_c0210 :: Assertion
+    test_trilinear_c0210 =
+      assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+
+    test_trilinear_c0201 :: Assertion
+    test_trilinear_c0201 =
+      assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+
+    test_trilinear_c0300 :: Assertion
+    test_trilinear_c0300 =
+      assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+
+    test_trilinear_c1020 :: Assertion
+    test_trilinear_c1020 =
+      assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+
+    test_trilinear_c1002 :: Assertion
+    test_trilinear_c1002 =
+      assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+
+    test_trilinear_c1011 :: Assertion
+    test_trilinear_c1011 =
+      assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+
+    test_trilinear_c1110 :: Assertion
+    test_trilinear_c1110 =
+      assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+
+    test_trilinear_c1101 :: Assertion
+    test_trilinear_c1101 =
+      assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+
+    test_trilinear_c1200 :: Assertion
+    test_trilinear_c1200 =
+      assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+
+    test_trilinear_c2010 :: Assertion
+    test_trilinear_c2010 =
+      assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+
+    test_trilinear_c2001 :: Assertion
+    test_trilinear_c2001 =
+      assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+
+    test_trilinear_c2100 :: Assertion
+    test_trilinear_c2100 =
+      assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+
+    test_trilinear_c3000 :: Assertion
+    test_trilinear_c3000 =
+      assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 
 
 -- | Make sure that v0 of tetrahedron0 belonging to the cube centered
@@ -269,7 +136,7 @@ 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
+        cube = cube_at g 1 1 1
         t = tetrahedron0 cube
 
 
@@ -281,7 +148,7 @@ 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
+        cube = cube_at g 1 1 1
         t = tetrahedron0 cube
 
 
@@ -293,7 +160,7 @@ 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
+        cube = cube_at g 1 1 1
         t = tetrahedron0 cube
 
 
@@ -305,396 +172,25 @@ 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
+        cube = 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 =
+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
-      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
+      c0 = cube_at g 1 1 1
 
 
 test_zeros_reproduced :: Assertion
@@ -709,6 +205,44 @@ test_zeros_reproduced =
                       let k' = fromIntegral k]
     where
       g = make_grid 1 zeros
-      c0 = fromJust $ cube_at g 1 1 1
+      c0 = cube_at g 1 1 1
       t0 = tetrahedron0 c0
       p = polynomial t0
+
+
+-- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
+test_trilinear9x9x9_reproduced :: Assertion
+test_trilinear9x9x9_reproduced =
+    assertTrue "trilinear 9x9x9 is reproduced correctly" $
+      and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
+            | i <- [0..8],
+              j <- [0..8],
+              k <- [0..8],
+              t <- tetrahedra c0,
+              let p = polynomial t,
+              let i' = (fromIntegral i) * 0.5,
+              let j' = (fromIntegral j) * 0.5,
+              let k' = (fromIntegral k) * 0.5]
+    where
+      g = make_grid 1 trilinear
+      c0 = cube_at g 1 1 1
+
+
+-- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
+--   However, the 'contains_point' test fails due to some numerical innacuracy.
+--   This bug should have been fixed by setting a positive tolerance level.
+--
+--   Example from before the fix:
+--
+--   > b0 (tetrahedron15 c) p
+--   -3.4694469519536365e-18
+--
+test_tetrahedra_collision_sensitivity :: Assertion
+test_tetrahedra_collision_sensitivity =
+  assertTrue "tetrahedron collision tests isn't too sensitive" $
+             contains_point t15 p
+  where
+    g = make_grid 1 naturals_1d
+    c = cube_at g 0 17 1
+    p = (0, 16.75, 0.5) :: Point
+    t15 = tetrahedron15 c