module Tests.Tetrahedron
where

import Test.HUnit
import Test.QuickCheck

import Comparisons
import Point
import FunctionValues
import Tests.FunctionValues()
import Tetrahedron
import ThreeDimensional

instance Arbitrary Tetrahedron where
    arbitrary = do
      rnd_v0 <- arbitrary :: Gen Point
      rnd_v1 <- arbitrary :: Gen Point
      rnd_v2 <- arbitrary :: Gen Point
      rnd_v3 <- arbitrary :: Gen Point
      rnd_fv <- arbitrary :: Gen FunctionValues
      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)

-- HUnit Tests

-- Since p0, p1, p2 are in clockwise order, we expect the volume here
-- to be negative.
test_volume1 :: Test
test_volume1 =
    TestCase $ assertEqual "volume is correct" True (vol ~= (-1/3))
    where
      p0 = (0, -0.5, 0)
      p1 = (0, 0.5, 0)
      p2 = (2, 0, 0)
      p3 = (1, 0, 1)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }
      vol = volume t


-- Now, p0, p1, and p2 are in counter-clockwise order. The volume
-- should therefore be positive.
test_volume2 :: Test
test_volume2 =
    TestCase $ assertEqual "volume is correct" True (vol ~= (1/3))
    where
      p0 = (0, -0.5, 0)
      p1 = (2, 0, 0)
      p2 = (0, 0.5, 0)
      p3 = (1, 0, 1)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }
      vol = volume t

test_contains_point1 :: Test
test_contains_point1 =
    TestCase $ assertEqual "contains an inner point" True (contains_point t inner_point)
    where
      p0 = (0, -0.5, 0)
      p1 = (0, 0.5, 0)
      p2 = (2, 0, 0)
      p3 = (1, 0, 1)
      inner_point = (1, 0, 0.5)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }


test_doesnt_contain_point1 :: Test
test_doesnt_contain_point1 =
    TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
    where
      p0 = (0, -0.5, 0)
      p1 = (0, 0.5, 0)
      p2 = (2, 0, 0)
      p3 = (1, 0, 1)
      exterior_point = (5, 2, -9.0212)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }


test_doesnt_contain_point2 :: Test
test_doesnt_contain_point2 =
    TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
    where
      p0 = (0, 1, 1)
      p1 = (1, 1, 1)
      p2 = (0.5, 0.5, 1)
      p3 = (0.5, 0.5, 0.5)
      exterior_point = (0, 0, 0)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }

test_doesnt_contain_point3 :: Test
test_doesnt_contain_point3 =
    TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
    where
      p0 = (1, 1, 1)
      p1 = (1, 0, 1)
      p2 = (0.5, 0.5, 1)
      p3 = (0.5, 0.5, 0.5)
      exterior_point = (0, 0, 0)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }

test_doesnt_contain_point4 :: Test
test_doesnt_contain_point4 =
    TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
    where
      p0 = (1, 0, 1)
      p1 = (0, 0, 1)
      p2 = (0.5, 0.5, 1)
      p3 = (0.5, 0.5, 0.5)
      exterior_point = (0, 0, 0)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }

test_doesnt_contain_point5 :: Test
test_doesnt_contain_point5 =
    TestCase $ assertEqual "doesn't contain an exterior point" False (contains_point t exterior_point)
    where
      p0 = (0, 0, 1)
      p1 = (0, 1, 1)
      p2 = (0.5, 0.5, 1)
      p3 = (0.5, 0.5, 0.5)
      exterior_point = (0, 0, 0)
      t = Tetrahedron { v0 = p0,
                        v1 = p1,
                        v2 = p2,
                        v3 = p3,
                        fv = empty_values }

tetrahedron_tests :: [Test]
tetrahedron_tests = [test_volume1,
                     test_volume2,
                     test_contains_point1,
                     test_doesnt_contain_point1,
                     test_doesnt_contain_point2,
                     test_doesnt_contain_point3,
                     test_doesnt_contain_point4,
                     test_doesnt_contain_point5 ]

prop_b0_v0_always_unity :: Tetrahedron -> Property
prop_b0_v0_always_unity t =
    (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0

prop_b0_v1_always_zero :: Tetrahedron -> Property
prop_b0_v1_always_zero t =
    (volume t) > 0 ==> (b0 t) (v1 t) ~= 0

prop_b0_v2_always_zero :: Tetrahedron -> Property
prop_b0_v2_always_zero t =
    (volume t) > 0 ==> (b0 t) (v2 t) ~= 0

prop_b0_v3_always_zero :: Tetrahedron -> Property
prop_b0_v3_always_zero t =
    (volume t) > 0 ==> (b0 t) (v3 t) ~= 0

prop_b1_v1_always_unity :: Tetrahedron -> Property
prop_b1_v1_always_unity t =
    (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0

prop_b1_v0_always_zero :: Tetrahedron -> Property
prop_b1_v0_always_zero t =
    (volume t) > 0 ==> (b1 t) (v0 t) ~= 0

prop_b1_v2_always_zero :: Tetrahedron -> Property
prop_b1_v2_always_zero t =
    (volume t) > 0 ==> (b1 t) (v2 t) ~= 0

prop_b1_v3_always_zero :: Tetrahedron -> Property
prop_b1_v3_always_zero t =
    (volume t) > 0 ==> (b1 t) (v3 t) ~= 0

prop_b2_v2_always_unity :: Tetrahedron -> Property
prop_b2_v2_always_unity t =
    (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0

prop_b2_v0_always_zero :: Tetrahedron -> Property
prop_b2_v0_always_zero t =
    (volume t) > 0 ==> (b2 t) (v0 t) ~= 0

prop_b2_v1_always_zero :: Tetrahedron -> Property
prop_b2_v1_always_zero t =
    (volume t) > 0 ==> (b2 t) (v1 t) ~= 0

prop_b2_v3_always_zero :: Tetrahedron -> Property
prop_b2_v3_always_zero t =
    (volume t) > 0 ==> (b2 t) (v3 t) ~= 0

prop_b3_v3_always_unity :: Tetrahedron -> Property
prop_b3_v3_always_unity t =
    (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0

prop_b3_v0_always_zero :: Tetrahedron -> Property
prop_b3_v0_always_zero t =
    (volume t) > 0 ==> (b3 t) (v0 t) ~= 0

prop_b3_v1_always_zero :: Tetrahedron -> Property
prop_b3_v1_always_zero t =
    (volume t) > 0 ==> (b3 t) (v1 t) ~= 0

prop_b3_v2_always_zero :: Tetrahedron -> Property
prop_b3_v2_always_zero t =
    (volume t) > 0 ==> (b3 t) (v2 t) ~= 0


-- Used for convenience in the next few tests.
p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
p t i j k l = (polynomial t) (xi t i j k l)

-- | Given in Sorokina and Zeilfelder, p. 78.
prop_c3000_identity :: Tetrahedron -> Property
prop_c3000_identity t =
    (volume t) > 0 ==>
               c t 3 0 0 0 ~= p t 3 0 0 0

-- | Given in Sorokina and Zeilfelder, p. 78.
prop_c2100_identity :: Tetrahedron -> Property
prop_c2100_identity t =
    (volume t) > 0 ==>
      c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
        where
          term1 = (1/3)*(p t 0 3 0 0)
          term2 = (5/6)*(p t 3 0 0 0)
          term3 = 3*(p t 2 1 0 0)
          term4 = (3/2)*(p t 1 2 0 0)

-- | Given in Sorokina and Zeilfelder, p. 78.
prop_c1110_identity :: Tetrahedron -> Property
prop_c1110_identity t =
    (volume t) > 0 ==>
       c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
        where
          term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
          term2 = (9/2)*(p t 1 1 1 0)
          term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
          term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))