X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=11df961836d709565cb8f68e3f3b319a09376e4a;hb=a032d4426427de084931d194248f4086b12c11ce;hp=295eaa680f867cc0c453f807bb6d99dc58174a52;hpb=b3e24f3c735626ec203e0e8406b8333100a8375e;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 295eaa6..11df961 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -1,13 +1,16 @@
 module Tests.Cube
 where
 
+import Prelude hiding (LT)
 import Test.QuickCheck
 
+import Cardinal
 import Comparisons
 import Cube
-import FunctionValues (FunctionValues)
+import FunctionValues
+import Misc (all_equal)
 import Tests.FunctionValues ()
-import Tetrahedron (b0, b1, b2, b3, c,
+import Tetrahedron (b0, b1, b2, b3, c, fv,
                     v0, v1, v2, v3, volume)
 
 instance Arbitrary Cube where
@@ -41,16 +44,17 @@ prop_all_volumes_positive cube =
 --   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
 
@@ -59,7 +63,7 @@ prop_tetrahedron1_volumes_exact 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
 
@@ -68,7 +72,7 @@ prop_tetrahedron2_volumes_exact 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
 
@@ -77,7 +81,7 @@ prop_tetrahedron3_volumes_exact 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
 
@@ -86,7 +90,7 @@ prop_tetrahedron4_volumes_exact 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
 
@@ -95,7 +99,7 @@ prop_tetrahedron5_volumes_exact 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
 
@@ -104,7 +108,151 @@ prop_tetrahedron6_volumes_exact 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
 
@@ -467,21 +615,13 @@ prop_c2100_identity2 cube =
         t1 = tetrahedron1 cube
 
 
-prop_t0_shares_edge_with_t6 :: Cube -> Bool
-prop_t0_shares_edge_with_t6 cube =
-    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
-      where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
-
-
 -- | Given in Sorokina and Zeilfelder, p. 79.
 prop_c3000_identity :: Cube -> Bool
 prop_c3000_identity cube =
     c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0 - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
       where
         t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79.
@@ -543,3 +683,205 @@ prop_c1011_identity cube =
 --       where
 --         t0 = tetrahedron0 cube
 --         t1 = tetrahedron1 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
+prop_c_tilde_2100_correct cube =
+    c t6 2 1 0 0 == (3/8)*int + (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)
+    where
+      t0 = tetrahedron0 cube
+      t6 = tetrahedron6 cube
+      fvs = Tetrahedron.fv t0
+      int = interior fvs
+      f = front fvs
+      r = right fvs
+      l = left fvs
+      b = back fvs
+      ft = front_top fvs
+      rt = right_top fvs
+      lt = left_top fvs
+      bt = back_top fvs
+      t = top fvs
+      d = down fvs
+      fr = front_right fvs
+      fl = front_left fvs
+      br = back_right fvs
+      bl = back_left fvs
+      fd = front_down fvs
+      rd = right_down fvs
+      ld = left_down fvs
+      bd = back_down fvs
+
+-- Tests to check that the correct edges are incidental.
+prop_t0_shares_edge_with_t1 :: Cube -> Bool
+prop_t0_shares_edge_with_t1 cube =
+    (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+prop_t0_shares_edge_with_t3 :: Cube -> Bool
+prop_t0_shares_edge_with_t3 cube =
+    (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+prop_t0_shares_edge_with_t6 :: Cube -> Bool
+prop_t0_shares_edge_with_t6 cube =
+    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+prop_t1_shares_edge_with_t2 :: Cube -> Bool
+prop_t1_shares_edge_with_t2 cube =
+    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+      where
+        t1 = tetrahedron1 cube
+        t2 = tetrahedron2 cube
+
+prop_t1_shares_edge_with_t19 :: Cube -> Bool
+prop_t1_shares_edge_with_t19 cube =
+    (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
+      where
+        t1 = tetrahedron1 cube
+        t19 = tetrahedron19 cube
+
+prop_t2_shares_edge_with_t3 :: Cube -> Bool
+prop_t2_shares_edge_with_t3 cube =
+    (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+      where
+        t1 = tetrahedron1 cube
+        t2 = tetrahedron2 cube
+
+prop_t2_shares_edge_with_t12 :: Cube -> Bool
+prop_t2_shares_edge_with_t12 cube =
+    (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
+      where
+        t2 = tetrahedron2 cube
+        t12 = tetrahedron12 cube
+
+prop_t3_shares_edge_with_t21 :: Cube -> Bool
+prop_t3_shares_edge_with_t21 cube =
+    (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
+      where
+        t3 = tetrahedron3 cube
+        t21 = tetrahedron21 cube
+
+prop_t4_shares_edge_with_t5 :: Cube -> Bool
+prop_t4_shares_edge_with_t5 cube =
+    (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
+      where
+        t4 = tetrahedron4 cube
+        t5 = tetrahedron5 cube
+
+prop_t4_shares_edge_with_t7 :: Cube -> Bool
+prop_t4_shares_edge_with_t7 cube =
+    (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
+      where
+        t4 = tetrahedron4 cube
+        t7 = tetrahedron7 cube
+
+prop_t4_shares_edge_with_t10 :: Cube -> Bool
+prop_t4_shares_edge_with_t10 cube =
+    (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
+      where
+        t4 = tetrahedron4 cube
+        t10 = tetrahedron10 cube
+
+prop_t5_shares_edge_with_t6 :: Cube -> Bool
+prop_t5_shares_edge_with_t6 cube =
+    (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
+      where
+        t5 = tetrahedron5 cube
+        t6 = tetrahedron6 cube
+
+prop_t5_shares_edge_with_t16 :: Cube -> Bool
+prop_t5_shares_edge_with_t16 cube =
+    (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
+      where
+        t5 = tetrahedron5 cube
+        t16 = tetrahedron16 cube
+
+prop_t6_shares_edge_with_t7 :: Cube -> Bool
+prop_t6_shares_edge_with_t7 cube =
+    (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
+      where
+        t6 = tetrahedron6 cube
+        t7 = tetrahedron7 cube
+
+prop_t7_shares_edge_with_t20 :: Cube -> Bool
+prop_t7_shares_edge_with_t20 cube =
+    (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
+      where
+        t7 = tetrahedron7 cube
+        t20 = tetrahedron20 cube