import Control.Monad (liftM, liftM2)
import Prelude hiding (LT)
+import Test.HUnit
import Test.QuickCheck
import Cardinal
cquot = liftM2 Quotient arbitrary arbitrary
+-- | We know what (c t6 2 1 0 0) should be from Sorokina and
+-- Zeilfelder, p. 87. This test checks that the directions are
+-- rotated properly. The order of the letters has to be just right
+-- since I haven't defined a proper Eq instance for Cardinals.
+test_c_tilde_2100_rotation_correct :: Assertion
+test_c_tilde_2100_rotation_correct =
+ assertEqual "auto-rotate equals manual rotate" ((ccwz . ccwz . cwy) expr1) expr2
+ where
+ expr1 =
+ (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)
+
+ expr2 =
+ (3/8)*I +
+ (1/12)*(F + L + R + B) +
+ (1/64)*(FT + LT + RT + BT) +
+ (7/48)*T +
+ (1/48)*D +
+ (1/96)*(FL + BR + FR + BL) +
+ (1/192)*(FD + LD + RD + BD)
+
+-- | A list of all directions, sans the interior and composite types.
+all_directions :: [Cardinal]
+all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
+ BL, BR, BD, BT, LD, LT, RD, RT, FLD,
+ FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+
+
+-- | If we rotate a direction (other than front or back)
+-- counter-clockwise with respect to the x-axis, we should get a new
+-- direction.
prop_ccwx_rotation_changes_direction :: Cardinal -> Property
prop_ccwx_rotation_changes_direction c =
- -- The front and back faces are unchanged by x-rotation.
c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
==> ccwx c /= c
+-- | If we rotate a direction (other than front or back) clockwise
+-- with respect to the x-axis, we should get a new direction.
prop_cwx_rotation_changes_direction :: Cardinal -> Property
prop_cwx_rotation_changes_direction c =
-- The front and back faces are unchanged by x-rotation.
c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
==> cwx c /= c
+
+-- | If we rotate a direction (other than left or right)
+-- counter-clockwise with respect to the y-axis, we should get a new
+-- direction.
+prop_ccwy_rotation_changes_direction :: Cardinal -> Property
+prop_ccwy_rotation_changes_direction c =
+ c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+ RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+ ==> ccwy c /= c
+
+
+-- | If we rotate a direction (other than left or right) clockwise
+-- with respect to the y-axis, we should get a new direction.
+prop_cwy_rotation_changes_direction :: Cardinal -> Property
+prop_cwy_rotation_changes_direction c =
+ c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+ RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+ ==> cwy c /= c
+
+
+-- | If we rotate a direction (other than top or down)
+-- counter-clockwise with respect to the z-axis, we should get a new
+-- direction.
+prop_ccwz_rotation_changes_direction :: Cardinal -> Property
+prop_ccwz_rotation_changes_direction c =
+ c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+ RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+ ==> ccwz c /= c
+
+
+-- | If we rotate a direction (other than top or down) clockwise with
+-- respect to the z-axis, we should get a new direction.
+prop_cwz_rotation_changes_direction :: Cardinal -> Property
+prop_cwz_rotation_changes_direction c =
+ c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+ RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+ ==> cwz c /= c
+
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated counter-clockwise with respect to the
+-- x-axis, produces c.
+prop_ccwx_rotation_result_unique :: Cardinal -> Property
+prop_ccwx_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, ccwx d == c ]) == 1
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated clockwise with respect to the x-axis,
+-- produces c.
+prop_cwx_rotation_result_unique :: Cardinal -> Property
+prop_cwx_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, cwx d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated counter-clockwise with respect to the
+-- y-axis, produces c.
+prop_ccwy_rotation_result_unique :: Cardinal -> Property
+prop_ccwy_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, ccwy d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated clockwise with respect to the y-axis,
+-- produces c.
+prop_cwy_rotation_result_unique :: Cardinal -> Property
+prop_cwy_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, cwy d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated counter-clockwise with respect to the
+-- z-axis, produces c.
+prop_ccwz_rotation_result_unique :: Cardinal -> Property
+prop_ccwz_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, ccwz d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+-- d which, when rotated clockwise with respect to the z-axis,
+-- produces c.
+prop_cwz_rotation_result_unique :: Cardinal -> Property
+prop_cwz_rotation_result_unique c =
+ c `elem` all_directions ==>
+ (length [ d | d <- all_directions, cwz d == c ]) == 1
+
+
+-- | If you rotate a cardinal direction four times in the clockwise
+-- (with respect to x) direction, you should wind up with the same
+-- direction.
+prop_four_cwx_is_identity :: Cardinal -> Bool
+prop_four_cwx_is_identity c =
+ (cwx . cwx . cwx . cwx) c == c
+
+-- | If you rotate a cardinal direction four times in the
+-- counter-clockwise (with respect to x) direction, you should wind up
+-- with the same direction.
+prop_four_ccwx_is_identity :: Cardinal -> Bool
+prop_four_ccwx_is_identity c =
+ (ccwx . ccwx . ccwx . ccwx) c == c
+
+-- | If you rotate a cardinal direction four times in the clockwise
+-- (with respect to y) direction, you should wind up with the same
+-- direction.
+prop_four_cwy_is_identity :: Cardinal -> Bool
+prop_four_cwy_is_identity c =
+ (cwy . cwy . cwy . cwy) c == c
+
+-- | If you rotate a cardinal direction four times in the counter-clockwise
+-- (with respect to y) direction, you should wind up with the same
+-- direction.
+prop_four_ccwy_is_identity :: Cardinal -> Bool
+prop_four_ccwy_is_identity c =
+ (ccwy . ccwy . ccwy . ccwy) c == c
+
+-- | If you rotate a cardinal direction four times in the clockwise
+-- (with respect to z) direction, you should wind up with the same
+-- direction.
+prop_four_cwz_is_identity :: Cardinal -> Bool
+prop_four_cwz_is_identity c =
+ (cwz . cwz . cwz . cwz) c == c
+
+-- | If you rotate a cardinal direction four times in the
+-- counter-clockwise (with respect to z) direction, you should wind up
+-- with the same direction.
+prop_four_ccwz_is_identity :: Cardinal -> Bool
+prop_four_ccwz_is_identity c =
+ (ccwz . ccwz . ccwz . ccwz) c == c
projects / spline3.git / blobdiff