module Tests.Cube
where
+import Debug.Trace (trace)
import Test.QuickCheck
import Comparisons
import Cube
-import FunctionValues (FunctionValues(FunctionValues))
-import Tests.FunctionValues
-import Tetrahedron (v0, volume)
+import FunctionValues (FunctionValues)
+import Tests.FunctionValues ()
+import Tetrahedron (b0, b1, b2, b3, c,
+ Tetrahedron(Tetrahedron),
+ v0, v1, v2, v3, volume)
instance Arbitrary Cube where
arbitrary = do
-- | In fact, since all of the tetrahedra are identical, we should
-- already know their volumes. There's 24 tetrahedra to a cube, so
-- we'd expect the volume of each one to be (1/24)*h^3.
-prop_all_volumes_exact :: Cube -> Bool
-prop_all_volumes_exact c =
- volume t ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron0_volumes_exact :: Cube -> Bool
+prop_tetrahedron0_volumes_exact c =
+ volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron1_volumes_exact :: Cube -> Bool
+prop_tetrahedron1_volumes_exact c =
+ volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron2_volumes_exact :: Cube -> Bool
+prop_tetrahedron2_volumes_exact c =
+ volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron3_volumes_exact :: Cube -> Bool
+prop_tetrahedron3_volumes_exact c =
+ volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron4_volumes_exact :: Cube -> Bool
+prop_tetrahedron4_volumes_exact c =
+ volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron5_volumes_exact :: Cube -> Bool
+prop_tetrahedron5_volumes_exact c =
+ volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron6_volumes_exact :: Cube -> Bool
+prop_tetrahedron6_volumes_exact c =
+ volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
+ where
+ delta = h c
+
+-- | In fact, since all of the tetrahedra are identical, we should
+-- already know their volumes. There's 24 tetrahedra to a cube, so
+-- we'd expect the volume of each one to be (1/24)*h^3.
+prop_tetrahedron7_volumes_exact :: Cube -> Bool
+prop_tetrahedron7_volumes_exact c =
+ volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
where
- t = head $ tetrahedrons c
delta = h c
-- | All tetrahedron should have their v0 located at the center of the cube.
prop_tetrahedron7_volumes_positive :: Cube -> Bool
prop_tetrahedron7_volumes_positive c =
volume (tetrahedron7 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron8_volumes_positive :: Cube -> Bool
+prop_tetrahedron8_volumes_positive c =
+ volume (tetrahedron8 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron9_volumes_positive :: Cube -> Bool
+prop_tetrahedron9_volumes_positive c =
+ volume (tetrahedron9 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron10_volumes_positive :: Cube -> Bool
+prop_tetrahedron10_volumes_positive c =
+ volume (tetrahedron10 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron11_volumes_positive :: Cube -> Bool
+prop_tetrahedron11_volumes_positive c =
+ volume (tetrahedron11 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron12_volumes_positive :: Cube -> Bool
+prop_tetrahedron12_volumes_positive c =
+ volume (tetrahedron12 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron13_volumes_positive :: Cube -> Bool
+prop_tetrahedron13_volumes_positive c =
+ volume (tetrahedron13 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron14_volumes_positive :: Cube -> Bool
+prop_tetrahedron14_volumes_positive c =
+ volume (tetrahedron14 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron15_volumes_positive :: Cube -> Bool
+prop_tetrahedron15_volumes_positive c =
+ volume (tetrahedron15 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron16_volumes_positive :: Cube -> Bool
+prop_tetrahedron16_volumes_positive c =
+ volume (tetrahedron16 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron17_volumes_positive :: Cube -> Bool
+prop_tetrahedron17_volumes_positive c =
+ volume (tetrahedron17 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron18_volumes_positive :: Cube -> Bool
+prop_tetrahedron18_volumes_positive c =
+ volume (tetrahedron18 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron19_volumes_positive :: Cube -> Bool
+prop_tetrahedron19_volumes_positive c =
+ volume (tetrahedron19 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron20_volumes_positive :: Cube -> Bool
+prop_tetrahedron20_volumes_positive c =
+ volume (tetrahedron20 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron21_volumes_positive :: Cube -> Bool
+prop_tetrahedron21_volumes_positive c =
+ volume (tetrahedron21 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron22_volumes_positive :: Cube -> Bool
+prop_tetrahedron22_volumes_positive c =
+ volume (tetrahedron22 c) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+-- but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron23_volumes_positive :: Cube -> Bool
+prop_tetrahedron23_volumes_positive c =
+ volume (tetrahedron23 c) > 0
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+--prop_c0120_identity1 :: Cube -> Bool
+--prop_c0120_identity1 cube =
+-- c0 ~= (c1 + c2) / 2
+-- where
+-- c0 = trace ("c0 :" ++ (show (c t0 0 1 2 0))) (c t0 0 1 2 0)
+-- c1 = trace ("c1 :" ++ (show (c t0 0 0 2 1))) (c t0 0 0 2 1)
+-- c2 = trace ("c2 :" ++ (show (c t1 0 0 2 1))) (c t1 0 0 2 1)
+-- t0 = tetrahedron0 cube
+-- t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+-- prop_cijk1_identity :: Cube -> Bool
+-- prop_cijk1_identity cube =
+-- and [ c t0 i j k 1 ~=
+-- (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
+-- (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
+-- (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
+-- (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
+-- j <- [0..2],
+-- k <- [0..2],
+-- i + j + k == 2]
+-- where
+-- t0 = tetrahedron0 cube
+-- t1 = tetrahedron1 cube
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