module Tests.Grid
where

import Test.Framework (Test, testGroup)
import Test.Framework.Providers.HUnit (testCase)
import Test.HUnit

import Assertions
import Comparisons
import Cube hiding (i, j, k)
import Examples
import FunctionValues (value_at)
import Grid
import Point (Point)
import Tetrahedron
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.
--
--   We also verify that the four vertices on face0 of the cube are
--   in the correct location.
--
trilinear_c0_t0_tests :: Test.Framework.Test
trilinear_c0_t0_tests =
  testGroup "trilinear c0 t0"
    [testGroup "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],

    testGroup "face0 vertices"
      [testCase "v0 is correct" test_trilinear_f0_t0_v0,
       testCase "v1 is correct" test_trilinear_f0_t0_v1,
       testCase "v2 is correct" test_trilinear_f0_t0_v2,
       testCase "v3 is correct" test_trilinear_f0_t0_v3]
    ]
  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

    test_trilinear_f0_t0_v0 :: Assertion
    test_trilinear_f0_t0_v0 =
      assertEqual "v0 is correct" (v0 t) (1, 1, 1)

    test_trilinear_f0_t0_v1 :: Assertion
    test_trilinear_f0_t0_v1 =
      assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)

    test_trilinear_f0_t0_v2 :: Assertion
    test_trilinear_f0_t0_v2 =
      assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)

    test_trilinear_f0_t0_v3 :: Assertion
    test_trilinear_f0_t0_v3 =
      assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)


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 = cube_at g 1 1 1


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 = cube_at g 1 1 1
      t0 = tetrahedron0 c0
      p = polynomial t0


-- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
--   Use (t <- tetrahedra c0) for a much slower but comprehensive
--   test.
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 <- [head $ 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