Move all of the Cube tests into the Cube module.
Re-enable that failing test.
-module Cube
+module Cube (
+ Cube(..),
+ cube_properties,
+ find_containing_tetrahedron,
+ tetrahedra,
+ tetrahedron
+ )
where
import Data.Maybe (fromJust)
snoc,
unsafeIndex
)
+import Prelude hiding (LT)
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.QuickCheck2 (testProperty)
import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
import Cardinal
+import Comparisons ((~=), (~~=))
import qualified Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
+import Misc (all_equal, disjoint)
import Point
-import Tetrahedron (Tetrahedron(Tetrahedron))
+import Tetrahedron (
+ Tetrahedron(..),
+ c,
+ b0,
+ b1,
+ b2,
+ b3,
+ volume
+ )
import ThreeDimensional
data Cube = Cube { h :: Double,
tetrahedron :: Cube -> Int -> Tetrahedron
tetrahedron c 0 =
- Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol
+ Tetrahedron (fv c) v0' v1' v2' v3' vol
where
v0' = center c
v1' = center (front_face c)
v1' = center (front_face c)
v2' = Face.v1 (front_face c)
v3' = Face.v2 (front_face c)
- fv' = rotate ccwx (Cube.fv c)
+ fv' = rotate ccwx (fv c)
vol = tetrahedra_volume c
tetrahedron c 2 =
v1' = center (front_face c)
v2' = Face.v2 (front_face c)
v3' = Face.v3 (front_face c)
- fv' = rotate ccwx $ rotate ccwx $ Cube.fv c
+ fv' = rotate ccwx $ rotate ccwx $ fv c
vol = tetrahedra_volume c
tetrahedron c 3 =
v1' = center (front_face c)
v2' = Face.v3 (front_face c)
v3' = Face.v0 (front_face c)
- fv' = rotate cwx (Cube.fv c)
+ fv' = rotate cwx (fv c)
vol = tetrahedra_volume c
tetrahedron c 4 =
v1' = center (top_face c)
v2' = Face.v0 (top_face c)
v3' = Face.v1 (top_face c)
- fv' = rotate cwy (Cube.fv c)
+ fv' = rotate cwy (fv c)
vol = tetrahedra_volume c
tetrahedron c 5 =
lucky_idx = V.findIndex
(\t -> (center t) `dot` p == shortest_distance)
candidates
+
+
+
+
+
+
+-- Tests
+
+-- Quickcheck tests.
+
+prop_opposite_octant_tetrahedra_disjoint1 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint1 c =
+ disjoint (front_left_top_tetrahedra c) (front_right_down_tetrahedra c)
+
+prop_opposite_octant_tetrahedra_disjoint2 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint2 c =
+ disjoint (back_left_top_tetrahedra c) (back_right_down_tetrahedra c)
+
+prop_opposite_octant_tetrahedra_disjoint3 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint3 c =
+ disjoint (front_left_top_tetrahedra c) (back_right_top_tetrahedra c)
+
+prop_opposite_octant_tetrahedra_disjoint4 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint4 c =
+ disjoint (front_left_down_tetrahedra c) (back_right_down_tetrahedra c)
+
+prop_opposite_octant_tetrahedra_disjoint5 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint5 c =
+ disjoint (front_left_top_tetrahedra c) (back_left_down_tetrahedra c)
+
+prop_opposite_octant_tetrahedra_disjoint6 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint6 c =
+ disjoint (front_right_top_tetrahedra c) (back_right_down_tetrahedra c)
+
+
+-- | Since the grid size is necessarily positive, all tetrahedra
+-- (which comprise cubes of positive volume) must have positive volume
+-- as well.
+prop_all_volumes_positive :: Cube -> Bool
+prop_all_volumes_positive cube =
+ null nonpositive_volumes
+ where
+ ts = tetrahedra cube
+ volumes = map volume ts
+ nonpositive_volumes = filter (<= 0) volumes
+
+-- | 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 cube =
+ and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
+ where
+ delta = h cube
+
+-- | All tetrahedron should have their v0 located at the center of the cube.
+prop_v0_all_equal :: Cube -> Bool
+prop_v0_all_equal cube = (v0 t0) == (v0 t1)
+ where
+ t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
+ t1 = head $ tail (tetrahedra cube)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
+-- third and fourth indices of c-t1 have been switched. This is
+-- because we store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+ c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
+prop_c0120_identity2 :: Cube -> Bool
+prop_c0120_identity2 cube =
+ c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
+prop_c0120_identity3 :: Cube -> Bool
+prop_c0120_identity3 cube =
+ c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
+ where
+ t1 = tetrahedron cube 1
+ t2 = tetrahedron cube 2
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- 'prop_c0120_identity1' with tetrahedrons 2 and 3.
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+ c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
+ where
+ t2 = tetrahedron cube 2
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- 'prop_c0120_identity1' with tetrahedrons 4 and 5.
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+ c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
+ where
+ t4 = tetrahedron cube 4
+ t5 = tetrahedron cube 5
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- -- 'prop_c0120_identity1' with tetrahedrons 5 and 6.
+prop_c0120_identity6 :: Cube -> Bool
+prop_c0120_identity6 cube =
+ c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
+ where
+ t5 = tetrahedron cube 5
+ t6 = tetrahedron cube 6
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- -- 'prop_c0120_identity1' with tetrahedrons 6 and 7.
+prop_c0120_identity7 :: Cube -> Bool
+prop_c0120_identity7 cube =
+ c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+ where
+ t6 = tetrahedron cube 6
+ t7 = tetrahedron cube 7
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
+-- 'prop_c0120_identity1'.
+prop_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+ c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
+-- 'prop_c0120_identity1'.
+prop_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
+-- 'prop_c0120_identity1'.
+prop_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+ c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
+-- 'prop_c0120_identity1'.
+prop_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
+-- 'prop_c0120_identity1'.
+prop_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
+ where
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
+-- third and fourth indices of c-t3 have been switched. This is
+-- because we store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
+-- point in opposite directions, one of them has to have negative
+-- volume!
+prop_c0102_identity1 :: Cube -> Bool
+prop_c0102_identity1 cube =
+ c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
+-- 'prop_c0102_identity1'.
+prop_c0201_identity1 :: Cube -> Bool
+prop_c0201_identity1 cube =
+ c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
+-- 'prop_c0102_identity1'.
+prop_c0300_identity2 :: Cube -> Bool
+prop_c0300_identity2 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
+-- 'prop_c0102_identity1'.
+prop_c1101_identity :: Cube -> Bool
+prop_c1101_identity cube =
+ c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
+-- 'prop_c0102_identity1'.
+prop_c1200_identity2 :: Cube -> Bool
+prop_c1200_identity2 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
+-- 'prop_c0102_identity1'.
+prop_c2100_identity2 :: Cube -> Bool
+prop_c2100_identity2 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
+ where
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
+-- fourth indices of c-t6 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
+-- point in opposite directions, one of them has to have negative
+-- volume!
+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 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
+-- 'prop_c3000_identity'.
+prop_c2010_identity :: Cube -> Bool
+prop_c2010_identity cube =
+ c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 0 1
+ - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
+-- 'prop_c3000_identity'.
+prop_c2001_identity :: Cube -> Bool
+prop_c2001_identity cube =
+ c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 1 0
+ - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
+-- 'prop_c3000_identity'.
+prop_c1020_identity :: Cube -> Bool
+prop_c1020_identity cube =
+ c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 0 2
+ - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
+-- 'prop_c3000_identity'.
+prop_c1002_identity :: Cube -> Bool
+prop_c1002_identity cube =
+ c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 2 0
+ - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
+-- 'prop_c3000_identity'.
+prop_c1011_identity :: Cube -> Bool
+prop_c1011_identity cube =
+ c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 -
+ ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+
+
+-- | 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 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+
+-- | 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 [ eval (function_values tet) I | tet <- tetrahedra cube ]
+
+
+-- | 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 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+ -- What gets computed for c2100 of t6.
+ expr1 = eval (function_values 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 (function_values 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.
+--
+-- If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
+-- even meaningful!
+prop_c_tilde_2100_correct :: Cube -> Bool
+prop_c_tilde_2100_correct cube =
+ c t6 2 1 0 0 == expected
+ where
+ t0 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+ fvs = function_values t0
+ expected = eval fvs $
+ (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)
+
+
+-- 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 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
+
+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 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
+
+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 = tetrahedron cube 0
+ t6 = tetrahedron cube 6
+
+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 = tetrahedron cube 1
+ t2 = tetrahedron cube 2
+
+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 = tetrahedron cube 1
+ t19 = tetrahedron cube 19
+
+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 = tetrahedron cube 1
+ t2 = tetrahedron cube 2
+
+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 = tetrahedron cube 2
+ t12 = tetrahedron cube 12
+
+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 = tetrahedron cube 3
+ t21 = tetrahedron cube 21
+
+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 = tetrahedron cube 4
+ t5 = tetrahedron cube 5
+
+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 = tetrahedron cube 4
+ t7 = tetrahedron cube 7
+
+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 = tetrahedron cube 4
+ t10 = tetrahedron cube 10
+
+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 = tetrahedron cube 5
+ t6 = tetrahedron cube 6
+
+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 = tetrahedron cube 5
+ t16 = tetrahedron cube 16
+
+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 = tetrahedron cube 6
+ t7 = tetrahedron cube 7
+
+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 = tetrahedron cube 7
+ t20 = tetrahedron cube 20
+
+
+
+
+
+p78_25_properties :: Test.Framework.Test
+p78_25_properties =
+ testGroup "p. 78, Section (2.5) Properties" [
+ testProperty "c_ijk1 identity" prop_cijk1_identity ]
+
+p79_26_properties :: Test.Framework.Test
+p79_26_properties =
+ testGroup "p. 79, Section (2.6) Properties" [
+ testProperty "c0120 identity1" prop_c0120_identity1,
+ testProperty "c0120 identity2" prop_c0120_identity2,
+ testProperty "c0120 identity3" prop_c0120_identity3,
+ testProperty "c0120 identity4" prop_c0120_identity4,
+ testProperty "c0120 identity5" prop_c0120_identity5,
+ testProperty "c0120 identity6" prop_c0120_identity6,
+ testProperty "c0120 identity7" prop_c0120_identity7,
+ testProperty "c0210 identity1" prop_c0210_identity1,
+ testProperty "c0300 identity1" prop_c0300_identity1,
+ testProperty "c1110 identity" prop_c1110_identity,
+ testProperty "c1200 identity1" prop_c1200_identity1,
+ testProperty "c2100 identity1" prop_c2100_identity1]
+
+p79_27_properties :: Test.Framework.Test
+p79_27_properties =
+ testGroup "p. 79, Section (2.7) Properties" [
+ testProperty "c0102 identity1" prop_c0102_identity1,
+ testProperty "c0201 identity1" prop_c0201_identity1,
+ testProperty "c0300 identity2" prop_c0300_identity2,
+ testProperty "c1101 identity" prop_c1101_identity,
+ testProperty "c1200 identity2" prop_c1200_identity2,
+ testProperty "c2100 identity2" prop_c2100_identity2 ]
+
+
+p79_28_properties :: Test.Framework.Test
+p79_28_properties =
+ testGroup "p. 79, Section (2.8) Properties" [
+ testProperty "c3000 identity" prop_c3000_identity,
+ testProperty "c2010 identity" prop_c2010_identity,
+ testProperty "c2001 identity" prop_c2001_identity,
+ testProperty "c1020 identity" prop_c1020_identity,
+ testProperty "c1002 identity" prop_c1002_identity,
+ testProperty "c1011 identity" prop_c1011_identity ]
+
+
+edge_incidence_tests :: Test.Framework.Test
+edge_incidence_tests =
+ testGroup "Edge Incidence Tests" [
+ testProperty "t0 shares edge with t6" prop_t0_shares_edge_with_t6,
+ testProperty "t0 shares edge with t1" prop_t0_shares_edge_with_t1,
+ testProperty "t0 shares edge with t3" prop_t0_shares_edge_with_t3,
+ testProperty "t1 shares edge with t2" prop_t1_shares_edge_with_t2,
+ testProperty "t1 shares edge with t19" prop_t1_shares_edge_with_t19,
+ testProperty "t2 shares edge with t3" prop_t2_shares_edge_with_t3,
+ testProperty "t2 shares edge with t12" prop_t2_shares_edge_with_t12,
+ testProperty "t3 shares edge with t21" prop_t3_shares_edge_with_t21,
+ testProperty "t4 shares edge with t5" prop_t4_shares_edge_with_t5,
+ testProperty "t4 shares edge with t7" prop_t4_shares_edge_with_t7,
+ testProperty "t4 shares edge with t10" prop_t4_shares_edge_with_t10,
+ testProperty "t5 shares edge with t6" prop_t5_shares_edge_with_t6,
+ testProperty "t5 shares edge with t16" prop_t5_shares_edge_with_t16,
+ testProperty "t6 shares edge with t7" prop_t6_shares_edge_with_t7,
+ testProperty "t7 shares edge with t20" prop_t7_shares_edge_with_t20 ]
+
+cube_properties :: Test.Framework.Test
+cube_properties =
+ testGroup "Cube Properties" [
+ p78_25_properties,
+ p79_26_properties,
+ p79_27_properties,
+ p79_28_properties,
+ edge_incidence_tests,
+ testProperty "opposite octant tetrahedra are disjoint (1)"
+ prop_opposite_octant_tetrahedra_disjoint1,
+ testProperty "opposite octant tetrahedra are disjoint (2)"
+ prop_opposite_octant_tetrahedra_disjoint2,
+ testProperty "opposite octant tetrahedra are disjoint (3)"
+ prop_opposite_octant_tetrahedra_disjoint3,
+ testProperty "opposite octant tetrahedra are disjoint (4)"
+ prop_opposite_octant_tetrahedra_disjoint4,
+ testProperty "opposite octant tetrahedra are disjoint (5)"
+ prop_opposite_octant_tetrahedra_disjoint5,
+ testProperty "opposite octant tetrahedra are disjoint (6)"
+ prop_opposite_octant_tetrahedra_disjoint6,
+ testProperty "all volumes positive" prop_all_volumes_positive,
+ testProperty "all volumes exact" prop_all_volumes_exact,
+ testProperty "v0 all equal" prop_v0_all_equal,
+ testProperty "interior values all identical"
+ prop_interior_values_all_identical,
+ testProperty "c-tilde_2100 rotation correct"
+ prop_c_tilde_2100_rotation_correct,
+ testProperty "c-tilde_2100 correct"
+ prop_c_tilde_2100_correct ]
import MRI as X
import Point as X
import RealFunction as X
-import Tetrahedron as X hiding (fv)
+import Tetrahedron as X
import Values as X
+++ /dev/null
-module Tests.Cube
-where
-
-import Prelude hiding (LT)
-
-import Cardinal
-import Comparisons
-import Cube hiding (i, j, k)
-import FunctionValues
-import Misc (all_equal, disjoint)
-import Tetrahedron (b0, b1, b2, b3, c, fv,
- v0, v1, v2, v3, volume)
-
-
--- Quickcheck tests.
-
-prop_opposite_octant_tetrahedra_disjoint1 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint1 c =
- disjoint (front_left_top_tetrahedra c) (front_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint2 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint2 c =
- disjoint (back_left_top_tetrahedra c) (back_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint3 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint3 c =
- disjoint (front_left_top_tetrahedra c) (back_right_top_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint4 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint4 c =
- disjoint (front_left_down_tetrahedra c) (back_right_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint5 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint5 c =
- disjoint (front_left_top_tetrahedra c) (back_left_down_tetrahedra c)
-
-prop_opposite_octant_tetrahedra_disjoint6 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint6 c =
- disjoint (front_right_top_tetrahedra c) (back_right_down_tetrahedra c)
-
-
--- | Since the grid size is necessarily positive, all tetrahedra
--- (which comprise cubes of positive volume) must have positive volume
--- as well.
-prop_all_volumes_positive :: Cube -> Bool
-prop_all_volumes_positive cube =
- null nonpositive_volumes
- where
- ts = tetrahedra cube
- volumes = map volume ts
- nonpositive_volumes = filter (<= 0) volumes
-
--- | 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 cube =
- and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
- where
- delta = h cube
-
--- | All tetrahedron should have their v0 located at the center of the cube.
-prop_v0_all_equal :: Cube -> Bool
-prop_v0_all_equal cube = (v0 t0) == (v0 t1)
- where
- t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
- t1 = head $ tail (tetrahedra cube)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
--- third and fourth indices of c-t1 have been switched. This is
--- because we store the triangles oriented such that their volume is
--- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
--- in opposite directions, one of them has to have negative volume!
-prop_c0120_identity1 :: Cube -> Bool
-prop_c0120_identity1 cube =
- c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
-prop_c0120_identity2 :: Cube -> Bool
-prop_c0120_identity2 cube =
- c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
-prop_c0120_identity3 :: Cube -> Bool
-prop_c0120_identity3 cube =
- c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
- where
- t1 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 2 and 3.
-prop_c0120_identity4 :: Cube -> Bool
-prop_c0120_identity4 cube =
- c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
- where
- t2 = tetrahedron cube 2
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- 'prop_c0120_identity1' with tetrahedrons 4 and 5.
-prop_c0120_identity5 :: Cube -> Bool
-prop_c0120_identity5 cube =
- c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
- where
- t4 = tetrahedron cube 4
- t5 = tetrahedron cube 5
-
--- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- -- 'prop_c0120_identity1' with tetrahedrons 5 and 6.
-prop_c0120_identity6 :: Cube -> Bool
-prop_c0120_identity6 cube =
- c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
- where
- t5 = tetrahedron cube 5
- t6 = tetrahedron cube 6
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
--- -- 'prop_c0120_identity1' with tetrahedrons 6 and 7.
-prop_c0120_identity7 :: Cube -> Bool
-prop_c0120_identity7 cube =
- c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
- where
- t6 = tetrahedron cube 6
- t7 = tetrahedron cube 7
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-prop_c0210_identity1 :: Cube -> Bool
-prop_c0210_identity1 cube =
- c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-prop_c0300_identity1 :: Cube -> Bool
-prop_c0300_identity1 cube =
- c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-prop_c1110_identity :: Cube -> Bool
-prop_c1110_identity cube =
- c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-prop_c1200_identity1 :: Cube -> Bool
-prop_c1200_identity1 cube =
- c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
--- 'prop_c0120_identity1'.
-prop_c2100_identity1 :: Cube -> Bool
-prop_c2100_identity1 cube =
- c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
- where
- t0 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
--- third and fourth indices of c-t3 have been switched. This is
--- because we store the triangles oriented such that their volume is
--- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
--- point in opposite directions, one of them has to have negative
--- volume!
-prop_c0102_identity1 :: Cube -> Bool
-prop_c0102_identity1 cube =
- c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-prop_c0201_identity1 :: Cube -> Bool
-prop_c0201_identity1 cube =
- c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-prop_c0300_identity2 :: Cube -> Bool
-prop_c0300_identity2 cube =
- c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-prop_c1101_identity :: Cube -> Bool
-prop_c1101_identity cube =
- c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-prop_c1200_identity2 :: Cube -> Bool
-prop_c1200_identity2 cube =
- c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
--- 'prop_c0102_identity1'.
-prop_c2100_identity2 :: Cube -> Bool
-prop_c2100_identity2 cube =
- c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
- where
- t0 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
--- fourth indices of c-t6 have been switched. This is because we
--- store the triangles oriented such that their volume is
--- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
--- point in opposite directions, one of them has to have negative
--- volume!
-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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-prop_c2010_identity :: Cube -> Bool
-prop_c2010_identity cube =
- c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 0 1
- - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-prop_c2001_identity :: Cube -> Bool
-prop_c2001_identity cube =
- c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 1 0
- - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-prop_c1020_identity :: Cube -> Bool
-prop_c1020_identity cube =
- c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 0 2
- - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-prop_c1002_identity :: Cube -> Bool
-prop_c1002_identity cube =
- c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 2 0
- - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
--- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
--- 'prop_c3000_identity'.
-prop_c1011_identity :: Cube -> Bool
-prop_c1011_identity cube =
- c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 -
- ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-
-
--- | 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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-
--- | 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 [ eval (Tetrahedron.fv tet) I | tet <- tetrahedra cube ]
-
-
--- | 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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
- -- 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.
---
--- If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
--- even meaningful!
-prop_c_tilde_2100_correct :: Cube -> Bool
-prop_c_tilde_2100_correct cube =
- c t6 2 1 0 0 == expected
- where
- t0 = tetrahedron cube 0
- t6 = tetrahedron cube 6
- fvs = Tetrahedron.fv t0
- expected = eval fvs $
- (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)
-
-
--- 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 = tetrahedron cube 0
- t1 = tetrahedron cube 1
-
-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 = tetrahedron cube 0
- t3 = tetrahedron cube 3
-
-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 = tetrahedron cube 0
- t6 = tetrahedron cube 6
-
-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 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
-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 = tetrahedron cube 1
- t19 = tetrahedron cube 19
-
-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 = tetrahedron cube 1
- t2 = tetrahedron cube 2
-
-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 = tetrahedron cube 2
- t12 = tetrahedron cube 12
-
-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 = tetrahedron cube 3
- t21 = tetrahedron cube 21
-
-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 = tetrahedron cube 4
- t5 = tetrahedron cube 5
-
-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 = tetrahedron cube 4
- t7 = tetrahedron cube 7
-
-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 = tetrahedron cube 4
- t10 = tetrahedron cube 10
-
-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 = tetrahedron cube 5
- t6 = tetrahedron cube 6
-
-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 = tetrahedron cube 5
- t16 = tetrahedron cube 16
-
-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 = tetrahedron cube 6
- t7 = tetrahedron cube 7
-
-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 = tetrahedron cube 7
- t20 = tetrahedron cube 20
import ThreeDimensional
data Tetrahedron =
- Tetrahedron { fv :: FunctionValues,
+ Tetrahedron { function_values :: FunctionValues,
v0 :: Point,
v1 :: Point,
v2 :: Point,
instance Show Tetrahedron where
show t = "Tetrahedron:\n" ++
- " fv: " ++ (show (fv t)) ++ "\n" ++
+ " function_values: " ++ (show (function_values t)) ++ "\n" ++
" v0: " ++ (show (v0 t)) ++ "\n" ++
" v1: " ++ (show (v1 t)) ++ "\n" ++
" v2: " ++ (show (v2 t)) ++ "\n" ++
-- Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
-- function will simply error.
c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-c t 0 0 3 0 = eval (fv t) $
+c t 0 0 3 0 = eval (function_values t) $
(1/8) * (I + F + L + T + LT + FL + FT + FLT)
-c t 0 0 0 3 = eval (fv t) $
+c t 0 0 0 3 = eval (function_values t) $
(1/8) * (I + F + R + T + RT + FR + FT + FRT)
-c t 0 0 2 1 = eval (fv t) $
+c t 0 0 2 1 = eval (function_values t) $
(5/24)*(I + F + T + FT) +
(1/24)*(L + FL + LT + FLT)
-c t 0 0 1 2 = eval (fv t) $
+c t 0 0 1 2 = eval (function_values t) $
(5/24)*(I + F + T + FT) +
(1/24)*(R + FR + RT + FRT)
-c t 0 1 2 0 = eval (fv t) $
+c t 0 1 2 0 = eval (function_values t) $
(5/24)*(I + F) +
(1/8)*(L + T + FL + FT) +
(1/24)*(LT + FLT)
-c t 0 1 0 2 = eval (fv t) $
+c t 0 1 0 2 = eval (function_values t) $
(5/24)*(I + F) +
(1/8)*(R + T + FR + FT) +
(1/24)*(RT + FRT)
-c t 0 1 1 1 = eval (fv t) $
+c t 0 1 1 1 = eval (function_values t) $
(13/48)*(I + F) +
(7/48)*(T + FT) +
(1/32)*(L + R + FL + FR) +
(1/96)*(LT + RT + FLT + FRT)
-c t 0 2 1 0 = eval (fv t) $
+c t 0 2 1 0 = eval (function_values t) $
(13/48)*(I + F) +
(17/192)*(L + T + FL + FT) +
(1/96)*(LT + FLT) +
(1/64)*(R + D + FR + FD) +
(1/192)*(RT + LD + FRT + FLD)
-c t 0 2 0 1 = eval (fv t) $
+c t 0 2 0 1 = eval (function_values t) $
(13/48)*(I + F) +
(17/192)*(R + T + FR + FT) +
(1/96)*(RT + FRT) +
(1/64)*(L + D + FL + FD) +
(1/192)*(RD + LT + FLT + FRD)
-c t 0 3 0 0 = eval (fv t) $
+c t 0 3 0 0 = eval (function_values t) $
(13/48)*(I + F) +
(5/96)*(L + R + T + D + FL + FR + FT + FD) +
(1/192)*(RT + RD + LT + LD + FRT + FRD + FLT + FLD)
-c t 1 0 2 0 = eval (fv t) $
+c t 1 0 2 0 = eval (function_values t) $
(1/4)*I +
(1/6)*(F + L + T) +
(1/12)*(LT + FL + FT)
-c t 1 0 0 2 = eval (fv t) $
+c t 1 0 0 2 = eval (function_values t) $
(1/4)*I +
(1/6)*(F + R + T) +
(1/12)*(RT + FR + FT)
-c t 1 0 1 1 = eval (fv t) $
+c t 1 0 1 1 = eval (function_values t) $
(1/3)*I +
(5/24)*(F + T) +
(1/12)*FT +
(1/24)*(L + R) +
(1/48)*(LT + RT + FL + FR)
-c t 1 1 1 0 = eval (fv t) $
+c t 1 1 1 0 = eval (function_values t) $
(1/3)*I +
(5/24)*F +
(1/8)*(L + T) +
(1/48)*(D + R + LT) +
(1/96)*(FD + LD + RT + FR)
-c t 1 1 0 1 = eval (fv t) $
+c t 1 1 0 1 = eval (function_values t) $
(1/3)*I +
(5/24)*F +
(1/8)*(R + T) +
(1/48)*(D + L + RT) +
(1/96)*(FD + LT + RD + FL)
-c t 1 2 0 0 = eval (fv t) $
+c t 1 2 0 0 = eval (function_values t) $
(1/3)*I +
(5/24)*F +
(7/96)*(L + R + T + D) +
(1/32)*(FL + FR + FT + FD) +
(1/96)*(RT + RD + LT + LD)
-c t 2 0 1 0 = eval (fv t) $
+c t 2 0 1 0 = eval (function_values t) $
(3/8)*I +
(7/48)*(F + T + L) +
(1/48)*(R + D + B + LT + FL + FT) +
(1/96)*(RT + BT + FR + FD + LD + BL)
-c t 2 0 0 1 = eval (fv t) $
+c t 2 0 0 1 = eval (function_values t) $
(3/8)*I +
(7/48)*(F + T + R) +
(1/48)*(L + D + B + RT + FR + FT) +
(1/96)*(LT + BT + FL + FD + RD + BR)
-c t 2 1 0 0 = eval (fv t) $
+c t 2 1 0 0 = eval (function_values t) $
(3/8)*I +
(1/12)*(T + R + L + D) +
(1/64)*(FT + FR + FL + FD) +
(1/96)*(RT + LD + LT + RD) +
(1/192)*(BT + BR + BL + BD)
-c t 3 0 0 0 = eval (fv t) $
+c t 3 0 0 0 = eval (function_values t) $
(3/8)*I +
(1/12)*(T + F + L + R + D + B) +
(1/96)*(LT + FL + FT + RT + BT + FR) +
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
volume1 :: Assertion
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
volume1 :: Assertion
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
contained = contains_point t exterior_point
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
contained = contains_point t exterior_point
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
contained = contains_point t exterior_point
v1 = p1,
v2 = p2,
v3 = p3,
- fv = empty_values,
+ function_values = empty_values,
precomputed_volume = 0 }
contained = contains_point t exterior_point
import Test.QuickCheck (Testable ())
import Cardinal (cardinal_tests, cardinal_properties)
+import Cube (cube_properties)
import FunctionValues (function_values_tests, function_values_properties)
import Grid (grid_tests, slow_tests)
import Misc (misc_tests, misc_properties)
-import Tests.Cube as TC
import Tetrahedron (tetrahedron_tests, tetrahedron_properties)
main :: IO ()
tp = testProperty
-
-p78_25_properties :: Test.Framework.Test
-p78_25_properties =
- testGroup "p. 78, Section (2.5) Properties" [
- tp "c_ijk1 identity" prop_cijk1_identity ]
-
-edge_incidence_tests :: Test.Framework.Test
-edge_incidence_tests =
- testGroup "Edge Incidence Tests" [
- tp "t0 shares edge with t6" prop_t0_shares_edge_with_t6,
- tp "t0 shares edge with t1" prop_t0_shares_edge_with_t1,
- tp "t0 shares edge with t3" prop_t0_shares_edge_with_t3,
- tp "t1 shares edge with t2" prop_t1_shares_edge_with_t2,
- tp "t1 shares edge with t19" prop_t1_shares_edge_with_t19,
- tp "t2 shares edge with t3" prop_t2_shares_edge_with_t3,
- tp "t2 shares edge with t12" prop_t2_shares_edge_with_t12,
- tp "t3 shares edge with t21" prop_t3_shares_edge_with_t21,
- tp "t4 shares edge with t5" prop_t4_shares_edge_with_t5,
- tp "t4 shares edge with t7" prop_t4_shares_edge_with_t7,
- tp "t4 shares edge with t10" prop_t4_shares_edge_with_t10,
- tp "t5 shares edge with t6" prop_t5_shares_edge_with_t6,
- tp "t5 shares edge with t16" prop_t5_shares_edge_with_t16,
- tp "t6 shares edge with t7" prop_t6_shares_edge_with_t7,
- tp "t7 shares edge with t20" prop_t7_shares_edge_with_t20 ]
-
-
-p79_26_properties :: Test.Framework.Test
-p79_26_properties =
- testGroup "p. 79, Section (2.6) Properties" [
- tp "c0120 identity1" TC.prop_c0120_identity1,
- tp "c0120 identity2" TC.prop_c0120_identity2,
- tp "c0120 identity3" TC.prop_c0120_identity3,
- tp "c0120 identity4" TC.prop_c0120_identity4,
- tp "c0120 identity5" TC.prop_c0120_identity5,
- tp "c0120 identity6" TC.prop_c0120_identity6,
- tp "c0120 identity7" TC.prop_c0120_identity7,
- tp "c0210 identity1" TC.prop_c0210_identity1,
- tp "c0300 identity1" TC.prop_c0300_identity1,
- tp "c1110 identity" TC.prop_c1110_identity,
- tp "c1200 identity1" TC.prop_c1200_identity1,
- tp "c2100 identity1" TC.prop_c2100_identity1]
-
-p79_27_properties :: Test.Framework.Test
-p79_27_properties =
- testGroup "p. 79, Section (2.7) Properties" [
- tp "c0102 identity1" TC.prop_c0102_identity1,
- tp "c0201 identity1" TC.prop_c0201_identity1,
- tp "c0300 identity2" TC.prop_c0300_identity2,
- tp "c1101 identity" TC.prop_c1101_identity,
- tp "c1200 identity2" TC.prop_c1200_identity2,
- tp "c2100 identity2" TC.prop_c2100_identity2 ]
-
-
-p79_28_properties :: Test.Framework.Test
-p79_28_properties =
- testGroup "p. 79, Section (2.8) Properties" [
- tp "c3000 identity" TC.prop_c3000_identity,
- tp "c2010 identity" TC.prop_c2010_identity,
- tp "c2001 identity" TC.prop_c2001_identity,
- tp "c1020 identity" TC.prop_c1020_identity,
- tp "c1002 identity" TC.prop_c1002_identity,
- tp "c1011 identity" TC.prop_c1011_identity ]
-
-
-cube_properties :: Test.Framework.Test
-cube_properties =
- testGroup "Cube Properties" [
- tp "opposite octant tetrahedra are disjoint (1)"
- prop_opposite_octant_tetrahedra_disjoint1,
- tp "opposite octant tetrahedra are disjoint (2)"
- prop_opposite_octant_tetrahedra_disjoint2,
- tp "opposite octant tetrahedra are disjoint (3)"
- prop_opposite_octant_tetrahedra_disjoint3,
- tp "opposite octant tetrahedra are disjoint (4)"
- prop_opposite_octant_tetrahedra_disjoint4,
- tp "opposite octant tetrahedra are disjoint (5)"
- prop_opposite_octant_tetrahedra_disjoint5,
- tp "opposite octant tetrahedra are disjoint (6)"
- prop_opposite_octant_tetrahedra_disjoint6,
- tp "all volumes positive" prop_all_volumes_positive,
- tp "all volumes exact" prop_all_volumes_exact,
- tp "v0 all equal" prop_v0_all_equal,
- tp "interior values all identical" prop_interior_values_all_identical,
- tp "c-tilde_2100 rotation correct" prop_c_tilde_2100_rotation_correct,
- tp "c-tilde_2100 correct" prop_c_tilde_2100_correct ]
-
-
tests :: [Test.Framework.Test]
tests = [ cardinal_tests,
function_values_tests,
tetrahedron_properties,
misc_properties,
cardinal_properties,
- edge_incidence_tests,
--- p78_25_properties,
- p79_26_properties,
- p79_27_properties,
- p79_28_properties,
slow_tests ]
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