module Tests.Cube
where
+import Prelude hiding (LT)
import Test.QuickCheck
+import Cardinal
import Comparisons
import Cube
import FunctionValues
+import Misc (all_equal)
import Tests.FunctionValues ()
import Tetrahedron (b0, b1, b2, b3, c, fv,
v0, v1, v2, v3, volume)
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron0_volumes_exact :: Cube -> Bool
prop_tetrahedron0_volumes_exact cube =
- volume (tetrahedron0 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron0 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
+
-- | 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 cube =
- volume (tetrahedron1 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron1 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron2_volumes_exact :: Cube -> Bool
prop_tetrahedron2_volumes_exact cube =
- volume (tetrahedron2 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron2 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron3_volumes_exact :: Cube -> Bool
prop_tetrahedron3_volumes_exact cube =
- volume (tetrahedron3 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron3 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron4_volumes_exact :: Cube -> Bool
prop_tetrahedron4_volumes_exact cube =
- volume (tetrahedron4 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron4 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron5_volumes_exact :: Cube -> Bool
prop_tetrahedron5_volumes_exact cube =
- volume (tetrahedron5 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron5 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron6_volumes_exact :: Cube -> Bool
prop_tetrahedron6_volumes_exact cube =
- volume (tetrahedron6 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron6 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
-- we'd expect the volume of each one to be (1/24)*h^3.
prop_tetrahedron7_volumes_exact :: Cube -> Bool
prop_tetrahedron7_volumes_exact cube =
- volume (tetrahedron7 cube) ~= (1/24)*(delta^(3::Int))
+ volume (tetrahedron7 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron8_volumes_exact :: Cube -> Bool
+prop_tetrahedron8_volumes_exact cube =
+ volume (tetrahedron8 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron9_volumes_exact :: Cube -> Bool
+prop_tetrahedron9_volumes_exact cube =
+ volume (tetrahedron9 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron10_volumes_exact :: Cube -> Bool
+prop_tetrahedron10_volumes_exact cube =
+ volume (tetrahedron10 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron11_volumes_exact :: Cube -> Bool
+prop_tetrahedron11_volumes_exact cube =
+ volume (tetrahedron11 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron12_volumes_exact :: Cube -> Bool
+prop_tetrahedron12_volumes_exact cube =
+ volume (tetrahedron12 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron13_volumes_exact :: Cube -> Bool
+prop_tetrahedron13_volumes_exact cube =
+ volume (tetrahedron13 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron14_volumes_exact :: Cube -> Bool
+prop_tetrahedron14_volumes_exact cube =
+ volume (tetrahedron14 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron15_volumes_exact :: Cube -> Bool
+prop_tetrahedron15_volumes_exact cube =
+ volume (tetrahedron15 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron16_volumes_exact :: Cube -> Bool
+prop_tetrahedron16_volumes_exact cube =
+ volume (tetrahedron16 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron17_volumes_exact :: Cube -> Bool
+prop_tetrahedron17_volumes_exact cube =
+ volume (tetrahedron17 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron18_volumes_exact :: Cube -> Bool
+prop_tetrahedron18_volumes_exact cube =
+ volume (tetrahedron18 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron19_volumes_exact :: Cube -> Bool
+prop_tetrahedron19_volumes_exact cube =
+ volume (tetrahedron19 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron20_volumes_exact :: Cube -> Bool
+prop_tetrahedron20_volumes_exact cube =
+ volume (tetrahedron20 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron21_volumes_exact :: Cube -> Bool
+prop_tetrahedron21_volumes_exact cube =
+ volume (tetrahedron21 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron22_volumes_exact :: Cube -> Bool
+prop_tetrahedron22_volumes_exact cube =
+ volume (tetrahedron22 cube) ~~= (1/24)*(delta^(3::Int))
+ where
+ delta = h cube
+
+-- | 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_tetrahedron23_volumes_exact :: Cube -> Bool
+prop_tetrahedron23_volumes_exact cube =
+ volume (tetrahedron23 cube) ~~= (1/24)*(delta^(3::Int))
where
delta = h cube
+-- | The function values at the interior should be the same for all tetrahedra.
+prop_interior_values_all_identical :: Cube -> Bool
+prop_interior_values_all_identical cube =
+ all_equal [i0, i1, i2, i3, i4, i5, i6, i7, i8,
+ i9, i10, i11, i12, i13, i14, i15, i16,
+ i17, i18, i19, i20, i21, i22, i23]
+ where
+ i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) $ I
+ i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) $ I
+ i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) $ I
+ i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) $ I
+ i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) $ I
+ i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) $ I
+ i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) $ I
+ i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) $ I
+ i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) $ I
+ i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) $ I
+ i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) $ I
+ i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) $ I
+ i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) $ I
+ i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) $ I
+ i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) $ I
+ i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) $ I
+ i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) $ I
+ i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) $ I
+ i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) $ I
+ i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) $ I
+ i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) $ I
+ i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) $ I
+ i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) $ I
+ i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) $ I
+
+
+-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
+-- This test checks the rotation works as expected.
+prop_c_tilde_2100_rotation_correct :: Cube -> Bool
+prop_c_tilde_2100_rotation_correct cube =
+ expr1 == expr2
+ where
+ t0 = tetrahedron0 cube
+ t6 = tetrahedron6 cube
+
+ -- What gets computed for c2100 of t6.
+ expr1 = eval (Tetrahedron.fv t6) $
+ (3/8)*I +
+ (1/12)*(T + R + L + D) +
+ (1/64)*(FT + FR + FL + FD) +
+ (7/48)*F +
+ (1/48)*B +
+ (1/96)*(RT + LD + LT + RD) +
+ (1/192)*(BT + BR + BL + BD)
+
+ -- What should be computed for c2100 of t6.
+ expr2 = eval (Tetrahedron.fv t0) $
+ (3/8)*I +
+ (1/12)*(F + R + L + B) +
+ (1/64)*(FT + RT + LT + BT) +
+ (7/48)*T +
+ (1/48)*D +
+ (1/96)*(FR + FL + BR + BL) +
+ (1/192)*(FD + RD + LD + BD)
+
+
-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
-- This test checks the actual value based on the FunctionValues of the cube.
prop_c_tilde_2100_correct :: Cube -> Bool
+ (7/48)*t + (1/48)*d + (1/96)*(fr + fl + br + bl)
+ (1/192)*(fd + rd + ld + bd)
where
+ t0 = tetrahedron0 cube
t6 = tetrahedron6 cube
- fvs = Tetrahedron.fv t6
+ fvs = Tetrahedron.fv t0
int = interior fvs
f = front fvs
r = right fvs
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