module Tests.Grid
where

import Data.Maybe (fromJust)
import Test.HUnit

import Assertions
import Comparisons
import Cube hiding (i, j, k)
import Examples
import FunctionValues (value_at)
import Grid
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_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


-- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
test_trilinearx2_reproduced_t0 :: Assertion
test_trilinearx2_reproduced_t0 =
    assertTrue "trilinearx2 is reproduced correctly" $
      and [p (i', j', k') ~= value_at trilinearx2 i j k
            | i <- [0..8],
              j <- [0..8],
              k <- [0..8],
              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 = fromJust $ cube_at g 1 1 1
      t0 = tetrahedron0 c0
      p = polynomial t0