X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCardinal.hs;h=6017fa1f78721597ddd3cffffb5a939f0438cd19;hb=6cc5300fea6115c324a0f16d33d8717200076d26;hp=3bff38f206c5983cb29ac9f80ef99275f6a88e4c;hpb=ecb77f944fcba8c8cfe60ca782bc5d9c8ab68cf9;p=spline3.git diff --git a/src/Cardinal.hs b/src/Cardinal.hs index 3bff38f..6017fa1 100644 --- a/src/Cardinal.hs +++ b/src/Cardinal.hs @@ -1,14 +1,49 @@ +{-# LANGUAGE NoMonomorphismRestriction #-} + +-- +-- Disable the MR so that let tp = testProperty does what it should! +-- + -- | The Cardinal module contains the Cardinal data type, representing -- a cardinal direction (one of the 26 directions surrounding the -- center of a cube. In addition to those 26 directions, we also -- include the interior point and a number of composite types that -- allow us to perform arithmetic on directions. -module Cardinal +-- +module Cardinal ( + Cardinal(..), + cardinal_properties, + cardinal_tests, + ccwx, + ccwy, + ccwz, + cwx, + cwy, + cwz ) where import Control.Monad (liftM, liftM2) -import Prelude hiding (LT) -import Test.QuickCheck (Arbitrary(..), oneof) +import Prelude ( + (.), + Bool, + Double, + Eq( (==), (/=) ), + Fractional( (/), fromRational, recip ), + Num( (+), (-), (*), abs, negate, signum, fromInteger ), + Show, + elem, + fromIntegral, + length, + return ) +import Test.Tasty ( TestTree, testGroup ) +import Test.Tasty.HUnit ( Assertion, assertEqual, testCase ) +import Test.Tasty.QuickCheck ( + Arbitrary( arbitrary ), + Gen, + Property, (==>), + oneof, + testProperty ) + data Cardinal = F -- ^ Front | B -- ^ Back @@ -76,33 +111,33 @@ instance Arbitrary Cardinal where rd,rt,fld,flt,frd,frt,bld,blt,brd,brt,i, scalar,csum,cdiff,cprod,cquot] where - f = return F - b = return B - l = return L - r = return R - d = return D - t = return T - fl = return FL - fr = return FR - fd = return FD - ft = return FT - bl = return BL - br = return BR - bd = return BD - bt = return BT - ld = return LD - lt = return LT - rd = return RD - rt = return RT - fld = return FLD - flt = return FLT - frd = return FRD - frt = return FRT - bld = return BLD - blt = return BLT - brd = return BRD - brt = return BRT - i = return I + f = return F :: Gen Cardinal + b = return B :: Gen Cardinal + l = return L :: Gen Cardinal + r = return R :: Gen Cardinal + d = return D :: Gen Cardinal + t = return T :: Gen Cardinal + fl = return FL :: Gen Cardinal + fr = return FR :: Gen Cardinal + fd = return FD :: Gen Cardinal + ft = return FT :: Gen Cardinal + bl = return BL :: Gen Cardinal + br = return BR :: Gen Cardinal + bd = return BD :: Gen Cardinal + bt = return BT :: Gen Cardinal + ld = return LD :: Gen Cardinal + lt = return LT :: Gen Cardinal + rd = return RD :: Gen Cardinal + rt = return RT :: Gen Cardinal + fld = return FLD :: Gen Cardinal + flt = return FLT :: Gen Cardinal + frd = return FRD :: Gen Cardinal + frt = return FRT :: Gen Cardinal + bld = return BLD :: Gen Cardinal + blt = return BLT :: Gen Cardinal + brd = return BRD :: Gen Cardinal + brt = return BRT :: Gen Cardinal + i = return I :: Gen Cardinal scalar = liftM Scalar arbitrary csum = liftM2 Sum arbitrary arbitrary cdiff = liftM2 Difference arbitrary arbitrary @@ -228,3 +263,255 @@ ccwz (Quotient c0 c1) = Quotient (ccwz c0) (ccwz c1) -- | Rotate a cardinal direction clockwise about the z-axis. cwz :: Cardinal -> Cardinal cwz = ccwz . ccwz . ccwz + + + + +-- | 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 = + 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 + + +cardinal_tests :: TestTree +cardinal_tests = + testGroup "Cardinal tests" [ + testCase "c-tilde_2100 rotation correct"test_c_tilde_2100_rotation_correct ] + + +cardinal_properties :: TestTree +cardinal_properties = + testGroup "Cardinal properties" [ + testProperty + "ccwx rotation changes direction" + prop_ccwx_rotation_changes_direction, + testProperty + "cwx rotation changes direction" + prop_cwx_rotation_changes_direction, + testProperty + "ccwy rotation changes direction" + prop_ccwy_rotation_changes_direction, + testProperty + "cwy rotation changes direction" + prop_cwy_rotation_changes_direction, + testProperty + "ccwz rotation changes direction" + prop_ccwz_rotation_changes_direction, + testProperty + "cwz rotation changes direction" + prop_cwz_rotation_changes_direction, + testProperty + "ccwx rotation result unique" + prop_ccwx_rotation_result_unique, + testProperty + "cwx rotation result unique" + prop_cwx_rotation_result_unique, + testProperty + "ccwy rotation result unique" + prop_ccwy_rotation_result_unique, + testProperty + "cwy rotation result unique" + prop_cwy_rotation_result_unique, + testProperty + "ccwz rotation result unique" + prop_ccwz_rotation_result_unique, + testProperty + "cwz rotation result unique" + prop_cwz_rotation_result_unique, + testProperty + "four cwx is identity" + prop_four_cwx_is_identity, + testProperty + "four ccwx is identity" + prop_four_ccwx_is_identity, + testProperty + "four cwy is identity" + prop_four_cwy_is_identity, + testProperty + "four ccwy is identity" + prop_four_ccwy_is_identity, + testProperty + "four cwz is identity" + prop_four_cwz_is_identity, + testProperty + "four ccwz is identity" + prop_four_ccwz_is_identity ]