+ g = make_grid 1 trilinear
+ cube = cube_at g 1 1 1
+ t = tetrahedron cube 0
+
+ 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
+
+ test_trilinear_f0_t0_v0 :: Assertion
+ test_trilinear_f0_t0_v0 =
+ assertEqual "v0 is correct" (v0 t) (Point 1 1 1)
+
+ test_trilinear_f0_t0_v1 :: Assertion
+ test_trilinear_f0_t0_v1 =
+ assertEqual "v1 is correct" (v1 t) (Point 0.5 1 1)
+
+ test_trilinear_f0_t0_v2 :: Assertion
+ test_trilinear_f0_t0_v2 =
+ assertEqual "v2 is correct" (v2 t) (Point 0.5 0.5 1.5)
+
+ test_trilinear_f0_t0_v3 :: Assertion
+ test_trilinear_f0_t0_v3 =
+ assertEqual "v3 is correct" (v3 t) (Point 0.5 1.5 1.5)
+
+
+test_trilinear_reproduced :: Assertion
+test_trilinear_reproduced =
+ assertTrue "trilinears are reproduced correctly" $
+ and [p (Point i' j' k') ~= value_at trilinear i j k
+ | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ c0 <- cs,
+ 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
+ cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
+
+
+test_zeros_reproduced :: Assertion
+test_zeros_reproduced =
+ assertTrue "the zero function is reproduced correctly" $
+ and [p (Point 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,
+ c0 <- cs,
+ t0 <- tetrahedra c0,
+ let p = polynomial t0 ]
+ where
+ g = make_grid 1 zeros
+ cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
+