X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCardinal.hs;h=7d4cfde00df4a1df66c621739d920a688aae3bb7;hb=f6d0c289ad3397cf392976c24f3afdb17da5d377;hp=cf1be4effc8fabb2a613b3f177e462050e133526;hpb=25d751371c1e01905abc25f1031a2bb6ef847a39;p=spline3.git diff --git a/src/Tests/Cardinal.hs b/src/Tests/Cardinal.hs index cf1be4e..7d4cfde 100644 --- a/src/Tests/Cardinal.hs +++ b/src/Tests/Cardinal.hs @@ -1,63 +1,192 @@ module Tests.Cardinal where -import Control.Monad (liftM, liftM2) import Prelude hiding (LT) -import Test.QuickCheck +import Test.HUnit +import Test.QuickCheck (Property, (==>)) import Cardinal +-- | 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) -instance Arbitrary Cardinal where - arbitrary = oneof [f,b,l,r,d,t,fl,fr,fd,ft,bl,br,bd,bt,ld,lt, - 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 - scalar = liftM Scalar arbitrary - csum = liftM2 Sum arbitrary arbitrary - cdiff = liftM2 Difference arbitrary arbitrary - cprod = liftM2 Product arbitrary arbitrary - cquot = liftM2 Quotient arbitrary arbitrary +-- | 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