#!/usr/bin/perl -W ## rubikrotation.pl (version2.0) ##============================= # Copyright 20 January 2014 RWD Nickalls and A Syropoulos # # This file is part of the LaTeX rubikrotation package, and # requires rubikcube.sty and rubikrotation.sty # # rubikrotation.pl is a Perl-5 program and free software: # you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # any later version. # # rubikrotation.pl is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. ##============================= ##--------------------------------------------------------------------- ## OVERVIEW ## This program is part of the rubikrotation package, and is complementary to ## the LaTeX rubikcube package. It processes Rubik rotation sequences on-the-fly. ## The program reads a datafile (rubikstate.dat) output by the rubikcube package ## and writes the new state to the file rubikstateNEW.dat, which is then input ## by the TeX file. Further documentation accompanies the rubikrotation package. ## Note that all posible state changing rotations of a 3x3x3 cube are ## either conbinations of, or the inverse of, just 9 different rotations, ## three associated with each XYZ axis. ##-------------------------------------------------- ##=============main=================================================== ## This main module opens three files, and ## sets up an array for collecting all errors (%error), and sets an error flag to "", ## reads in the rubik state data file =rubikstate.dat (output by TeXfile), ## and calls subs to write the TeX_OUT_FILE, ## and finally closes all files. ## Each line of the input file consists of a comma separated list of arguments. ## The first argument in each line of the file rubikstate.dat is the rubikkeyword. ## Program is documented in the rubikrotation.pdf (see section ``Overview'') ### start by opening the three working files (last one ``for append'') open (IN_FILE, "rubikstateNEW.dat")||die "ERROR: can't open file rubikstateNEW.dat\n"; open (ERROR_OUT_FILE, ">>rubikstateERRORS.dat")||die "ERROR: can't open file rubikstateERRORS,dat\n"; ## use dots for Perl messages (I have used dashes for LaTeX messages in the .sty) ## gprint sub prints its argument (message) to both the screen and to the TeX_OUT_FILE gprint ("...PERL process..................................."); ## setup global error parameters, so we can write all the errors to a file as an array %error = (); # setup an array for error messages (was %) $erroralert = ""; # error flag $errornumber = 0; #set number of errors to zero gprint ("...reading the current rubik state (rubikstate.dat)"); LINE: while (){ next LINE if /^#/; #skip comments next LINE if /^%/; #skip comments next LINE if /^$/; #skip blank lines $dataline = $_; # grab the whole line as a string chomp $dataline; # remove the line-ending characters #$n++; # count the number of lines @data=split (/,/, $dataline); # create an array called data ## we have 10 fields (0--9) ## check for rubikkeyword= up,down,left,right,front,back,rotation, checkstate: gprint ("...$dataline"); $rubikkeyword=$data[0]; if ($rubikkeyword eq 'up') { $Ult[0]=$data[1], $Umt[0]=$data[2],$Urt[0]=$data[3], $Ulm[0]=$data[4], $Umm[0]=$data[5],$Urm[0]=$data[6], $Ulb[0]=$data[7], $Umb[0]=$data[8],$Urb[0]=$data[9] } if ($rubikkeyword eq 'down') { $Dlt[0]=$data[1], $Dmt[0]=$data[2],$Drt[0]=$data[3], $Dlm[0]=$data[4], $Dmm[0]=$data[5],$Drm[0]=$data[6], $Dlb[0]=$data[7], $Dmb[0]=$data[8],$Drb[0]=$data[9] } if ($rubikkeyword eq 'left') { $Llt[0]=$data[1], $Lmt[0]=$data[2],$Lrt[0]=$data[3], $Llm[0]=$data[4], $Lmm[0]=$data[5],$Lrm[0]=$data[6], $Llb[0]=$data[7], $Lmb[0]=$data[8],$Lrb[0]=$data[9] } if ($rubikkeyword eq 'right') { $Rlt[0]=$data[1], $Rmt[0]=$data[2],$Rrt[0]=$data[3], $Rlm[0]=$data[4], $Rmm[0]=$data[5],$Rrm[0]=$data[6], $Rlb[0]=$data[7], $Rmb[0]=$data[8],$Rrb[0]=$data[9] } if ($rubikkeyword eq 'front') { $Flt[0]=$data[1], $Fmt[0]=$data[2],$Frt[0]=$data[3], $Flm[0]=$data[4], $Fmm[0]=$data[5],$Frm[0]=$data[6], $Flb[0]=$data[7], $Fmb[0]=$data[8],$Frb[0]=$data[9] } if ($rubikkeyword eq 'back') { $Blt[0]=$data[1], $Bmt[0]=$data[2],$Brt[0]=$data[3], $Blm[0]=$data[4], $Bmm[0]=$data[5],$Brm[0]=$data[6], $Blb[0]=$data[7], $Bmb[0]=$data[8],$Brb[0]=$data[9] } ## if the rubikkeyword is `checkstate' we just check the ## state and write the output data to a file. if ($rubikkeyword eq 'checkstate') { gprint ("..."); $rotationcommand=$dataline; ## used in output message gprint ("...command=$rotationcommand"); checkstate(); }; ## if the rubikkeyword is `rotation' we first check to see if the second argument=random. ## if so, then we check that the third argument is an integer, if so --> random sub ## else --> exit line and get next line. ## finally we write the output data to a file. if ($rubikkeyword eq 'rotation') { gprint ("..."); $rotationcommand=$dataline; ## used in output message gprint ("...command=$rotationcommand"); ## if second argument = random, ## then we also need to check if third argument is an integer; ## if so -->random sub. ## if the 3rd argument is NOT an integer then reject line & get next input line if ($data[1] eq 'random') { if ($data[2] =~/\D/) { errormessage("[$data[2]] not an integer"); ## we reject the whole line and look at next line in the file next } else{ ## data[2] must be an integer (n), so we just do n random rotations random($data[2]) }; } else { # the line must be an ordinary rotation sequence line, so send the sequence # to the rotation sub, BUT, need to first remove the # rubikkeyword `rotation' from the begining of line (array) # as we need to send ONLY the sequence string to the rotation sub. shift (@data); rotation(@data); } } }; ## we have finished reading in all the lines from the rubikstate.dat file, ## and doing all the rotations etc, so we now just write the new cube state ## to the output file = TeX_OUT_FILE (so LaTeX can read it) writestate(); close; ##close all files exit; ##==============end of main========================== ##=============================subs==================== sub errormessage{ ## writes the argument as a standard error message to out file my $errormess = $_[0]; $erroralert = "YES"; ## set error alert flag (for use in out message) $error[$errornumber] = "** ERROR: $errormess"; $errornumber++; ## increment number }; ##====================================== ## prints argument (comments) to screen and also to TeX_OUT_FILE (= rubikstateNEW.dat). ## The typeout commands will find its way into the log file when read by latex ## Important to include trailing % for messages written to the TeX_OUT_FILE ## to stop extra being seen by TeX. sub gprint{ my $gmess=$_[0]; print "$gmess\n"; print (TeX_OUT_FILE "\\typeout{$gmess}\%\n"); }; ##======================================== sub checkstate{ ### simple check to see if wrong no of colours being used etc ### uses the cubie colours as used by rubikcube package= ROYGBWX gprint ("...checking state of cube"); my @cubies=($Ult[0],$Umt[0],$Urt[0], $Ulm[0],$Umm[0],$Urm[0], $Ulb[0],$Umb[0],$Urb[0], $Dlt[0],$Dmt[0],$Drt[0], $Dlm[0],$Dmm[0],$Drm[0], $Dlb[0],$Dmb[0],$Drb[0], $Llt[0],$Lmt[0],$Lrt[0], $Llm[0],$Lmm[0],$Lrm[0], $Llb[0],$Lmb[0],$Lrb[0], $Rlt[0],$Rmt[0],$Rrt[0], $Rlm[0],$Rmm[0],$Rrm[0], $Rlb[0],$Rmb[0],$Rrb[0], $Flt[0],$Fmt[0],$Frt[0], $Flm[0],$Fmm[0],$Frm[0], $Flb[0],$Fmb[0],$Frb[0], $Blt[0],$Bmt[0],$Brt[0], $Blm[0],$Bmm[0],$Brm[0], $Blb[0],$Bmb[0],$Brb[0]); my $R=0,my $O=0,my $Y=0,my $G=0,my $B=0,my $W=0,my $X=0; foreach $cubiecolour (@cubies) { if ($cubiecolour eq R) {$R = $R+1} elsif ($cubiecolour eq O) {$O = $O+1} elsif ($cubiecolour eq Y) {$Y = $Y+1} elsif ($cubiecolour eq G) {$G = $G+1} elsif ($cubiecolour eq B) {$B = $B+1} elsif ($cubiecolour eq W) {$W = $W+1} elsif ($cubiecolour eq X) {$X = $X+1} else {print " cubiecolour counting ERROR \n";} }; my $cubiesum=0; $cubiesum = $R+$O+$Y+$G+$B+$W+$X; gprint ("...cubiesum = $cubiesum (Red=$R, Or=$O, Ye=$Y, Gr=$G, Bl=$B, Wh=$W, X=$X)"); if ($cubiesum != 54) { errormessage("cubiesum not = 54")}; if ($R >9){ errormessage("No of Red cubies > 9 (=$R)")}; if ($O >9){ errormessage("No of Orange cubies > 9 (=$O)")}; if ($Y >9){ errormessage("No of Yellow cubies > 9 (=$Y)")}; if ($G >9){ errormessage("No of Green cubies > 9 (=$G)")}; if ($B >9){ errormessage("No of Blue cubies > 9 (=$B)")}; if ($W >9){ errormessage("No of White cubies > 9 (=$W)")}; }; ##==================================================== # no of arguments passed to the sub = $#_ (black book p 156) sub rotation { ## here we process an array (from main) consisting of all ## the rotation commands associated with ## a single RubikRotation command. my $m; #multiple associated with the char, eg D2 etc my $n = ($#_ +1); ##total no of arguments passed my $originalchar=""; my $j; my $numberofchars; ## length of a string gprint ("...arguments passed to `rotation' sub = @_ (n= $n)"); foreach $char (@_) { $char =~s/^\s+//, $char=~s/\s+$//; ## clean leading and trailing white space ## grab a copy of the original char for use if m Mod4=0 $originalchar=$char; ## if argument has a leading * then it is a label (not a rotation) so jump to next one if (substr ($char,0,1) eq "*"){ gprint ("...$char is a label OK"); next; }; ## Need to detect any trailing integer associated with a command (eg rotation multiple, eg:U3, L2 etc) ## NOTES: since we are using mod4, we are only interested in trailing digit ## if trailing character is a digit, then ## split char string into front chars (= $char) + trailing digit (= $m) $m = 1; # initialise m ## if terminal char is a digit (d) then d --> m and let frontstring --> char ## (Black book p 130 & 136) ## if the frontstring contains any digits then it will be rejected in the filter below anyway. if ( substr ($char,-1) =~ /(\d)/) { $m = $1; ## grab the trailing digit (only traps a single digit) $numberofchars = 0; #initialise it $numberofchars = length $originalchar; $nfrontchars = $numberofchars-1; ## reassign the string except the terminal digit $char = substr($char,0,$nfrontchars); ## use MOD 4 since we are dealing with Rubik rotations $m = $m % 4; ## (if MOD 4 = 0 then nothing will happen as j starts at 1) ## but should generate an errormessage if ( $m == 0 ){ gprint ("...rotation $originalchar equiv 0 MOD 4 (NOT IMPLEMENTED)"); errormessage ("[$originalchar] in RubikRotation (= 0 MOD 4)"); next; }; }; ## if single trailing digit present, then we implement the rotation command m times. ## if more than one trailing digit ## then the error is trapped at the end (as frontstring will not be recognised ## ie will not be in the following list, and hence will be trapped as an error, eg R3) ## if ($char eq "R") {for($j=1;$j<=$m;$j++) { gprint ("...rotation R OK"); &rrR}} elsif ($char eq "Rp") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rp OK (= rrR3)"); &rrRp}} elsif ($char eq "Rw") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rw OK (= rrR + rrSr)"); &rrRw}} elsif ($char eq "Rwp") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rwp OK (= rrRp + rrSrp)"); &rrRwp}} elsif ($char eq "Rs") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rs OK (= rrR + rrLp)"); &rrRs}} elsif ($char eq "Rsp") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rsp OK (= rrRp + rrL)"); &rrRsp}} elsif ($char eq "Ra") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Ra OK (= rrR + rrL)"); &rrRa}} elsif ($char eq "Rap") {for($j=1;$j<=$m;$j++) { gprint ("...rotation Rap OK (= rrRp + rrLp)"); &rrRap}} #### elsif ($char eq "L") {for($j=1;$j<=$m;$j++) {gprint ("...rotation L OK (= rrLp3)"); &rrL}} elsif ($char eq "Lp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Lp OK"); &rrLp}} elsif ($char eq "Lw") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Lw OK (= rrLp3 + rrSrp)"); &rrLw}} elsif ($char eq "Lwp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Lwp OK (= rrLp + rrSr)"); &rrLwp}} elsif ($char eq "Ls") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Ls OK (= rrL + rrRp)"); &rrLs}} elsif ($char eq "Lsp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Lsp OK (= rrLp + rrR)"); &rrLsp}} elsif ($char eq "La") {for($j=1;$j<=$m;$j++) {gprint ("...rotation La OK (= rrL + rrR)"); &rrLa}} elsif ($char eq "Lap") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Lap OK (= rrLp + rrRp)"); &rrLap}} #### elsif ($char eq "U") {for($j=1;$j<=$m;$j++) {gprint ("...rotation U OK"); &rrU}} elsif ($char eq "Up") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Up OK (= rrU3)"); &rrUp}} elsif ($char eq "Uw") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Uw OK (= rrU + rrSu)"); &rrUw}} elsif ($char eq "Uwp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Uwp OK (= rrUp + rrSup)"); &rrUwp}} elsif ($char eq "Us") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Us OK (= rrU + rrDp)"); &rrUs}} elsif ($char eq "Usp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Usp OK (= rrUp + rrD)"); &rrUsp}} elsif ($char eq "Ua") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Ua OK (= rrU + rrD)"); &rrUa}} elsif ($char eq "Uap") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Uap OK (= rrUp + rrDp)"); &rrUap}} #### elsif ($char eq "D") {for($j=1;$j<=$m;$j++) {gprint ("...rotation D OK (= rrDp3)"); &rrD}} elsif ($char eq "Dp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Dp OK "); &rrDp}} elsif ($char eq "Dw") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Dw OK (= rrDp3 + rrSup)"); &rrDw}} elsif ($char eq "Dwp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Dwp OK (= rrDp + rrSu)"); &rrDwp}} elsif ($char eq "Ds") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Ds OK (= rrD + rrUp)"); &rrDs}} elsif ($char eq "Dsp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Dsp OK (= rrDp + rrU)"); &rrDsp}} elsif ($char eq "Da") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Da OK (= rrD + rrU)"); &rrDa}} elsif ($char eq "Dap") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Dap OK (= rrDp + rrUp)"); &rrDap}} #### elsif ($char eq "F") {for($j=1;$j<=$m;$j++) {gprint ("...rotation F OK"); &rrF}} elsif ($char eq "Fp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fp OK (= rrF3)"); &rrFp}} elsif ($char eq "Fw") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fw OK (= rrF + rrSf)"); &rrFw}} elsif ($char eq "Fwp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fwp OK (= rrFp + rrSfp)"); &rrFwp}} elsif ($char eq "Fs") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fs OK (= rrF + rrBp)"); &rrFs}} elsif ($char eq "Fsp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fsp OK (= rrFp + rrB)"); &rrFsp}} elsif ($char eq "Fa") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fa OK (= rrF + rrB)"); &rrFa}} elsif ($char eq "Fap") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Fap OK (= rrFp + rrBp)"); &rrFap}} #### elsif ($char eq "B") {for($j=1;$j<=$m;$j++) {gprint ("...rotation B OK (= rrFp3)"); &rrB}} elsif ($char eq "Bp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bp OK"); &rrBp}} elsif ($char eq "Bw") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bw OK (= rrFp3 + rrSfp)"); &rrBw}} elsif ($char eq "Bwp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bwp OK (= rrFp + rrSf)"); &rrBwp}} elsif ($char eq "Bs") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bs OK (= rrB + rrFp)"); &rrBs}} elsif ($char eq "Bsp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bsp OK (= rrBp + rrF)"); &rrBsp}} elsif ($char eq "Ba") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Ba OK (= rrB + rrF)"); &rrBa}} elsif ($char eq "Bap") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Bap OK (= rrBp + rrFp)"); &rrBap}} #### elsif ($char eq "Su") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Su OK "); &rrSu}} elsif ($char eq "Sup") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sup OK (= rrSu3)"); &rrSup}} elsif ($char eq "Sd") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sd OK (= rrSup)"); &rrSd}} elsif ($char eq "Sdp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sdp OK (= rrSu)"); &rrSdp}} elsif ($char eq "Sl") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sl OK (= rrSrp)"); &rrSl}} elsif ($char eq "Slp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Slp OK (= rrSr)"); &rrSlp}} elsif ($char eq "Sr") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sr OK"); &rrSr}} elsif ($char eq "Srp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Srp OK (= rrSr3)"); &rrSrp}} elsif ($char eq "Sf") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sf OK"); &rrSf}} elsif ($char eq "Sfp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sfp OK (= rrSf3)"); &rrSfp}} elsif ($char eq "Sb") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sb OK (= rrSfp)"); &rrSb}} elsif ($char eq "Sbp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sbp OK (= rrSf)"); &rrSbp}} ## XYZ stuff ## need to include lowercase x,y,x, and also u,d,l,r,f,b equivalents elsif ($char eq "X" or $char eq "x" or $char eq "r") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrR + rrSr + rrLp)"); &rrR;&rrSr;&rrLp}} elsif ($char eq "Xp" or $char eq "xp" or $char eq "l") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrRp + rrSrp + rrL)");&rrRp;&rrSrp;&rrL}} elsif ($char eq "Y" or $char eq "y" or $char eq "u") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrU + rrSu + rrDp)"); &rrU;&rrSu;&rrDp}} elsif ($char eq "Yp" or $char eq "yp" or $char eq "d") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrUp + rrSup + rrD)");&rrUp;&rrSup;&rrD}} elsif ($char eq "Z" or $char eq "z" or $char eq "f") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrF + rrSf + rrBp)"); &rrF;&rrSf;&rrBp}} elsif ($char eq "Zp" or $char eq "zp" or $char eq "b") {for($j=1;$j<=$m;$j++) {gprint ("...rotation $char OK (= rrFp + rrSfp + rrB)");&rrFp;&rrSfp;&rrB}} ## extras elsif ($char eq "M") {for($j=1;$j<=$m;$j++) {gprint ("...rotation M OK (= Sl) "); &rrSl}} elsif ($char eq "Mp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Mp OK (= Sr) "); &rrSr}} elsif ($char eq "E") {for($j=1;$j<=$m;$j++) {gprint ("...rotation E OK (= Sd) "); &rrSd}} elsif ($char eq "Ep") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Ep OK (= Su) "); &rrSu}} elsif ($char eq "S") {for($j=1;$j<=$m;$j++) {gprint ("...rotation S OK (= Sf) "); &rrSf}} elsif ($char eq "Sp") {for($j=1;$j<=$m;$j++) {gprint ("...rotation Sp OK (= Sb) "); &rrSb}} #### else { gprint ("...rotation $originalchar NOT KNOWN"); errormessage("[$originalchar] in RubikRotation"); }; } }; ## aNOTE we only defined and determined 9 primary rotation transforms, ## rrR, rrSr, rrLp ## rrU, rrSu, rrDp ## rrF, rrSf, rrBp ## and since all the remaining ones are simply combinations of these 9 ## we now define all the other rotation subs in terms of these 9 primary moves. ## do NOT use multiples here: write each rotation separately ## ------------- ## derivative subs from R and Sr and Lp sub rrRp{&rrR;&rrR;&rrR}; # (=rrR3) sub rrRw{&rrR; &rrSr}; # (= rrR + rrSr) sub rrRwp{&rrR;&rrR;&rrR; &rrSr;&rrSr;&rrSr}; # (= rrRp + rrSrp) sub rrRs{&rrR;&rrLp}; sub rrRsp{&rrRp;&rrL}; sub rrRa{&rrR;&rrL}; sub rrRap{&rrRp;&rrLp}; #### sub rrL{&rrLp;&rrLp;&rrLp}; # (= rrLp3) sub rrLw{&rrLp;&rrLp;&rrLp;&rrSrp}; # (=rrLp3 + rrSrp) sub rrLwp{&rrLp;&rrSr}; sub rrLs{&rrL;&rrRp}; sub rrLsp{&rrLp;&rrR}; sub rrLa{&rrL;&rrR}; sub rrLap{&rrLp;&rrRp}; ##------------- ## derivative subs from U sub rrUp{&rrU;&rrU;&rrU}; # (=rrU3) sub rrUw{&rrU;&rrSu}; # sub rrUwp{&rrUp;&rrSup}; sub rrUs{&rrU;&rrDp}; sub rrUsp{&rrUp;&rrD}; sub rrUa{&rrU;&rrD}; sub rrUap{&rrUp;&rrDp}; #### sub rrD{&rrDp;&rrDp;&rrDp}; # (= rrDp3) sub rrDw{&rrDp;&rrDp;&rrDp;&rrSup}; # (=rrDp3 + rrSup) sub rrDwp{&rrDp;&rrSu}; sub rrDs{&rrD;&rrUp}; sub rrDsp{&rrDp;&rrU}; sub rrDa{&rrD;&rrU}; sub rrDap{&rrDp;&rrUp}; ##------------- ## derivative subs from F sub rrFw{&rrF; &rrSf}; # (= rrF + rrSf) sub rrFp{ &rrF;&rrF;&rrF}; # (=rrF3) sub rrFwp{&rrF;&rrF;&rrF; &rrSf;&rrSf;&rrSf}; # (= rrF3 + rrSf3) sub rrFs{&rrF;&rrBp}; sub rrFsp{&rrFp;&rrB}; sub rrFa{&rrF;&rrB}; sub rrFap{&rrFp;&rrBp}; #### sub rrB{&rrBp;&rrBp;&rrBp}; # (= rrBp3) sub rrBw{&rrBp;&rrBp;&rrBp; &rrSfp}; # (=rrBp3 + rrSfp) sub rrBwp{&rrBp;&rrSf}; sub rrBs{&rrB;&rrFp}; sub rrBsp{&rrBp;&rrF}; sub rrBa{&rrB;&rrF}; sub rrBap{&rrBp;&rrFp}; #### ## bring all the S versions together sub rrSup{&rrSu;&rrSu;&rrSu}; # (=rrSu3) sub rrSd{&rrSup}; # (=rrSup) sub rrSdp{&rrSu}; # (=rrSu) sub rrSl{&rrSrp}; # (=rrSrp) sub rrSlp{&rrSr}; # (=rrSr) sub rrSrp{&rrSr;&rrSr;&rrSr}; # (=rrSr3) sub rrSfp{&rrSf;&rrSf;&rrSf}; # (=rrSf3) sub rrSb{&rrSfp}; # (=rrSfp) sub rrSbp{&rrSf}; # (=rrSf) ##========================================================== # no of arguments passed to the sub = $#_ (black book p 156) # parameters passed = $_[0] sub random{ ## scramble randomly using n rotations ## example command = RubikRotation{random,74} ## if no n given (second argument = ""), then use default n=50 ## if second argument is some string (not integer) then --> ERROR ## ## asign numbers to the minimal set of rotations to be used using a hash array list ## (perl 5 book page 68) ## ? maybe we should only use the 18 rotations mentioned in Rokicki 2013 paper? ## but here I have included all the S ones too. @rrlist= ("U", "Up", "Su", "Sup", "D", "Dp", "Sd", "Sdp", "L", "Lp", "Sl", "Slp", "R", "Rp", "Sr", "Srp", "F", "Fp", "Sf", "Sfp", "B", "Bp", "Sb", "Sbp"); my $rrlistnumber=$#rrlist; print " rrlistnumber = $rrlistnumber\n"; # these are numbered 0--$rrlistnumber, ## let default no of random rotations for scrambling = 50 my $defaultn = 50; my $maxn = 200; ## grab the integer passed from the random() command in main $s = $_[0]; if ($s >= $maxn) {$s = $maxn; gprint ("...WARNING: maximum n = 200")} elsif ($s == 0) {$s = $defaultn; gprint ("...WARNING: integer = 0 or not given: using default value 50")}; my @rr; ## array to hold all the random rotations print " randomising the available rotations\n"; ## set the seed for the randomisation (BlackBook p 235) srand; ## now select s numbers at random (with replacement) from range 0--listnumber+1 ## Since we are using int(rand x), and using nos from 0--lastindex number, ## then max rand vaue = (lastindexnumber -1).99999, the integer of which ## = (lastindexnumber -1). Therefore we need to use the range 0--(lastindexnumber+1) ## in order to randomise all posibilities on our list. for ($j = 1; $j <=$s; $j=$j+1) { $p= int(rand ($rrlistnumber +1)); print "Rotation = $p, $rrlist[$p] \n"; ## push rotation code $rrlist[$p] on to END of array @rr push (@rr, $rrlist[$p]); }; ## we assume the user is starting from a solved cube (ie use the state given by user) gprint ("...scrambling Rubik cube using $s random rotations"); ## now send the array off to the rotation sub rotation(@rr); } ##===================subs================================== sub writestate{ ## this just writes the final state to the TeX_OUT_FILE (= rubikstateNEW) will be read by latex. print (TeX_OUT_FILE "\%\% file=rubikstateNEW.dat (Perl)\n"); print (TeX_OUT_FILE "\\RubikFaceUp\{$Ult[0]\}\{$Umt[0]\}\{$Urt[0]\}\{$Ulm[0]\}\{$Umm[0]\}\{$Urm[0]\}\{$Ulb[0]\}\{$Umb[0]\}\{$Urb[0]\}\%\n"); print (TeX_OUT_FILE "\\RubikFaceDown\{$Dlt[0]\}\{$Dmt[0]\}\{$Drt[0]\}\{$Dlm[0]\}\{$Dmm[0]\}\{$Drm[0]\}\{$Dlb[0]\}\{$Dmb[0]\}\{$Drb[0]\}\%\n"); print (TeX_OUT_FILE "\\RubikFaceLeft\{$Llt[0]\}\{$Lmt[0]\}\{$Lrt[0]\}\{$Llm[0]\}\{$Lmm[0]\}\{$Lrm[0]\}\{$Llb[0]\}\{$Lmb[0]\}\{$Lrb[0]\}\%\n"); print (TeX_OUT_FILE "\\RubikFaceRight\{$Rlt[0]\}\{$Rmt[0]\}\{$Rrt[0]\}\{$Rlm[0]\}\{$Rmm[0]\}\{$Rrm[0]\}\{$Rlb[0]\}\{$Rmb[0]\}\{$Rrb[0]\}\%\n"); print (TeX_OUT_FILE "\\RubikFaceFront\{$Flt[0]\}\{$Fmt[0]\}\{$Frt[0]\}\{$Flm[0]\}\{$Fmm[0]\}\{$Frm[0]\}\{$Flb[0]\}\{$Fmb[0]\}\{$Frb[0]\}\%\n"); print (TeX_OUT_FILE "\\RubikFaceBack\{$Blt[0]\}\{$Bmt[0]\}\{$Brt[0]\}\{$Blm[0]\}\{$Bmm[0]\}\{$Brm[0]\}\{$Blb[0]\}\{$Bmb[0]\}\{$Brb[0]\}\%\n"); print (TeX_OUT_FILE "\\typeout{...writing new Rubik state to file rubikstateNEW.dat}\%\n"); ## now include any error messages generated ## (these are all in an array waiting to be printed out) if ($erroralert eq "YES") { ## open a separate file just for errors (we append the errrors to end of file) ## this file (rubikstate.cfg) was opened by the TeX file my $ne; #number of errors $ne=$#error; ## number of errors= largest index num since we started at zero ### do not attach error to a command if ($rotationcommand eq "checkstate") {} else { print (TeX_OUT_FILE "\\typeout{** ERROR: command=$rotationcommand}\%\n"); print (ERROR_OUT_FILE "** ERROR: $rotationcommand\n"); }; ## last index number or array = $#arrayname (Black book p 62) my $k; for ($k=0; $k<=$ne; $k=$k+1) { print (TeX_OUT_FILE "\\typeout{$error[$k]}\%\n"); print (ERROR_OUT_FILE "$error[$k]\n"); }; }; print " Perl output file written OK\n"; } ##=========================================== ##================================================ ## The following 9 (90 degree) rotation transformations are used ## to generate all the rotations used in the `rotation sub' ## each of these is a permutation for both colours and numbers ## of the cubie facelets. ## The following 9 subroutines are named as follows: ## (about X-axis) rrR, rrSr, rrLp ## (about Y-axis) rrU, rrSu, rrDp ## (about Z-axis) rrF, rrSf, rrBp ## see the rubikcube package documentation for full details regarding ## rotation notation and commands. ## METHOD & NOTATION ## each sub (below) starts by making an array[0] for the cubie colour ## and an array[1] for the cubie number. ## Each of the face rotations (rrR, rrLp, rrU, rrDp, rrF, rrBp) is involved with ## two pairs of connected but different permutations/transformations as follows: ## (a) one pair for the 12 Side cubies (arrays = @Xs0 (for Side colours), @Xs1 (for Side numbers)), and ## (b) one pair for the 9 Face cubies (arrays = @Xf0 (for Face colours), @Xf1 (for Face numbers)). ## Each of the center slice rotations (rrSr, rrSu, rrSf) is involved with just one pair of ## permutations for the 12 Side cubies (arrays = @Xs0 (for Side colours), @Xs1 (for Side numbers)). ## We document only the side and face of the first sub (rrR) in detail, since the other subs are of similar form. ##================================================ sub rrR{ ## the R (slice + face) transform ## R = RIGHT, s = side; 0=colour, 1= number ## make the clockwise rotation permutation ## In this permutation the Front-right-bottom (Frb) (side)facelet rotates to ## the new position of Up-right-bottom (Urb) (side)facelet. ##-----------SIDE------- ## 12 side cubie facelets in arrays @Rs0 (colours) and @Rs1 (numbers) ## these are the initial positions @Rs0=($Frb[0],$Frm[0],$Frt[0], $Urb[0],$Urm[0],$Urt[0], $Blt[0],$Blm[0],$Blb[0], $Drb[0],$Drm[0],$Drt[0]); @Rs1=($Frb[1],$Frm[1],$Frt[1], $Urb[1],$Urm[1],$Urt[1], $Blt[1],$Blm[1],$Blb[1], $Drb[1],$Drm[1],$Drt[1]); ## now we reallocate the initial array elements to the new ## post (90 degree clockwise) rotation position. ## Cube is viewed from FRONT. ## positions of side facelets of Right slice are numbered 0-11 in clockwise direction, ## (as seen from Right face) starting with Up-right-bottom facelet. ## first line example: ## variable $Urb[0] (Upface-right-bottom colour) <-- colour of first element in @Rs0 (=Frb[0]) ## variable $Urb[1] (Upface-right-bottom number) <-- number of first element in @Rs1 (=Frb[1]) $Urb[0]=$Rs0[0]; $Urb[1]=$Rs1[0]; $Urm[0]=$Rs0[1]; $Urm[1]=$Rs1[1]; $Urt[0]=$Rs0[2]; $Urt[1]=$Rs1[2]; $Blt[0]=$Rs0[3]; $Blt[1]=$Rs1[3]; $Blm[0]=$Rs0[4]; $Blm[1]=$Rs1[4]; $Blb[0]=$Rs0[5]; $Blb[1]=$Rs1[5]; $Drb[0]=$Rs0[6]; $Drb[1]=$Rs1[6]; $Drm[0]=$Rs0[7]; $Drm[1]=$Rs1[7]; $Drt[0]=$Rs0[8]; $Drt[1]=$Rs1[8]; $Frb[0]=$Rs0[9]; $Frb[1]=$Rs1[9]; $Frm[0]=$Rs0[10]; $Frm[1]=$Rs1[10]; $Frt[0]=$Rs0[11]; $Frt[1]=$Rs1[11]; ##-------------Right FACE--------------------- ## R FACE (9 cubies in each array) ## (numbered in rows: 1,2,3/4,5,6/7,8,9 from top left(1) to bottom right(9)) ## R=Right, f = face; 0=colour, 1= number ## do the Rface (90 degree) rotation transform ## here the Right-left-bottom (Rlb) facelet rotates to the possn of Right-left-top (Rlt) ## we start with two arrays (one for colours @Rf0, one for numbers @Rf1) with 9 elements each. @Rf0=($Rlb[0], $Rlm[0], $Rlt[0], $Rmb[0], $Rmm[0], $Rmt[0], $Rrb[0], $Rrm[0], $Rrt[0]); @Rf1=($Rlb[1], $Rlm[1], $Rlt[1], $Rmb[1], $Rmm[1], $Rmt[1], $Rrb[1], $Rrm[1], $Rrt[1]); ## now we reallocate the array elements to the new ## post (90 degree clockwise) rotation facelet position. ## Right face is viewed from RIGHT. ## First line example: ## variable $Rlt[0] (=Right-left-top colour) <-- colour of first element in @Rf0 (=Rlb[0]) ## variable $Rlt[1] (=Right-left-top number) <-- number of first element in @Rf1 (=Rlb[1]) $Rlt[0]=$Rf0[0]; $Rlt[1]=$Rf1[0]; $Rmt[0]=$Rf0[1]; $Rmt[1]=$Rf1[1]; $Rrt[0]=$Rf0[2]; $Rrt[1]=$Rf1[2]; $Rlm[0]=$Rf0[3]; $Rlm[1]=$Rf1[3]; $Rmm[0]=$Rf0[4]; $Rmm[1]=$Rf1[4]; $Rrm[0]=$Rf0[5]; $Rrm[1]=$Rf1[5]; $Rlb[0]=$Rf0[6]; $Rlb[1]=$Rf1[6]; $Rmb[0]=$Rf0[7]; $Rmb[1]=$Rf1[7]; $Rrb[0]=$Rf0[8]; $Rrb[1]=$Rf1[8]; } #============================ sub rrSr { ## Sr = Right middle SLICE rotation (only 12 side facelets) ## modified from rrR (change the U,D,F, r --> m and Back Bl-->Bm; Rs--> ?Srs) ## change only the slice ## s = side; 0=colour, 1= number ## make the post rotation permutation @SRs0=($Fmb[0],$Fmm[0],$Fmt[0], $Umb[0],$Umm[0],$Umt[0], $Bmt[0],$Bmm[0],$Bmb[0], $Dmb[0],$Dmm[0],$Dmt[0]); @SRs1=($Fmb[1],$Fmm[1],$Fmt[1], $Umb[1],$Umm[1],$Umt[1], $Bmt[1],$Bmm[1],$Bmb[1], $Dmb[1],$Dmm[1],$Dmt[1]); $Umb[0]=$SRs0[0]; $Umb[1]=$SRs1[0]; $Umm[0]=$SRs0[1]; $Umm[1]=$SRs1[1]; $Umt[0]=$SRs0[2]; $Umt[1]=$SRs1[2]; $Bmt[0]=$SRs0[3]; $Bmt[1]=$SRs1[3]; $Bmm[0]=$SRs0[4]; $Bmm[1]=$SRs1[4]; $Bmb[0]=$SRs0[5]; $Bmb[1]=$SRs1[5]; $Dmb[0]=$SRs0[6]; $Dmb[1]=$SRs1[6]; $Dmm[0]=$SRs0[7]; $Dmm[1]=$SRs1[7]; $Dmt[0]=$SRs0[8]; $Dmt[1]=$SRs1[8]; $Fmb[0]=$SRs0[9]; $Fmb[1]=$SRs1[9]; $Fmm[0]=$SRs0[10]; $Fmm[1]=$SRs1[10]; $Fmt[0]=$SRs0[11]; $Fmt[1]=$SRs1[11]; } ##=================== sub rrLp{ ## Left slice (side + face) anticlockwise rotation ## s = side; 0=colour, 1= number ##-------------side----------- @LPs0=($Flb[0],$Flm[0],$Flt[0], $Ulb[0],$Ulm[0],$Ult[0], $Brt[0],$Brm[0],$Brb[0], $Dlb[0],$Dlm[0],$Dlt[0]); @LPs1=($Flb[1],$Flm[1],$Flt[1], $Ulb[1],$Ulm[1],$Ult[1], $Brt[1],$Brm[1],$Brb[1], $Dlb[1],$Dlm[1],$Dlt[1]); $Ulb[0]=$LPs0[0]; $Ulb[1]=$LPs1[0]; $Ulm[0]=$LPs0[1]; $Ulm[1]=$LPs1[1]; $Ult[0]=$LPs0[2]; $Ult[1]=$LPs1[2]; $Brt[0]=$LPs0[3]; $Brt[1]=$LPs1[3]; $Brm[0]=$LPs0[4]; $Brm[1]=$LPs1[4]; $Brb[0]=$LPs0[5]; $Brb[1]=$LPs1[5]; $Dlb[0]=$LPs0[6]; $Dlb[1]=$LPs1[6]; $Dlm[0]=$LPs0[7]; $Dlm[1]=$LPs1[7]; $Dlt[0]=$LPs0[8]; $Dlt[1]=$LPs1[8]; $Flb[0]=$LPs0[9]; $Flb[1]=$LPs1[9]; $Flm[0]=$LPs0[10]; $Flm[1]=$LPs1[10]; $Flt[0]=$LPs0[11]; $Flt[1]=$LPs1[11]; ##---------------Left FACE------------- ## do the Lface transform (in rows: 1,2,3//4,5,6//7,8,9) ## f = face; 0=colour, 1= number ## NOTES: not same as for R @LPf0=($Lrt[0], $Lrm[0], $Lrb[0], $Lmt[0], $Lmm[0], $Lmb[0], $Llt[0], $Llm[0], $Llb[0]); @LPf1=($Lrt[1], $Lrm[1], $Lrb[1], $Lmt[1], $Lmm[1], $Lmb[1], $Llt[1], $Llm[1], $Llb[1]); $Llt[0]=$LPf0[0]; $Llt[1]=$LPf1[0]; $Lmt[0]=$LPf0[1]; $Lmt[1]=$LPf1[1]; $Lrt[0]=$LPf0[2]; $Lrt[1]=$LPf1[2]; $Llm[0]=$LPf0[3]; $Llm[1]=$LPf1[3]; $Lmm[0]=$LPf0[4]; $Lmm[1]=$LPf1[4]; $Lrm[0]=$LPf0[5]; $Lrm[1]=$LPf1[5]; $Llb[0]=$LPf0[6]; $Llb[1]=$LPf1[6]; $Lmb[0]=$LPf0[7]; $Lmb[1]=$LPf1[7]; $Lrb[0]=$LPf0[8]; $Lrb[1]=$LPf1[8]; } ##================================== ##============================== sub rrU{ ## Up slice (side + face) ## do the Uside transform ## s = side; 0=colour, 1= number ## ----------SIDE-------------- @Us0=($Lrt[0],$Lmt[0],$Llt[0], $Brt[0],$Bmt[0],$Blt[0], $Rrt[0],$Rmt[0],$Rlt[0], $Frt[0],$Fmt[0],$Flt[0]); @Us1=($Lrt[1],$Lmt[1],$Llt[1], $Brt[1],$Bmt[1],$Blt[1], $Rrt[1],$Rmt[1],$Rlt[1], $Frt[1],$Fmt[1],$Flt[1]); $Brt[0]=$Us0[0]; $Brt[1]=$Us1[0]; $Bmt[0]=$Us0[1]; $Bmt[1]=$Us1[1]; $Blt[0]=$Us0[2]; $Blt[1]=$Us1[2]; $Rrt[0]=$Us0[3]; $Rrt[1]=$Us1[3]; $Rmt[0]=$Us0[4]; $Rmt[1]=$Us1[4]; $Rlt[0]=$Us0[5]; $Rlt[1]=$Us1[5]; $Frt[0]=$Us0[6]; $Frt[1]=$Us1[6]; $Fmt[0]=$Us0[7]; $Fmt[1]=$Us1[7]; $Flt[0]=$Us0[8]; $Flt[1]=$Us1[8]; $Lrt[0]=$Us0[9]; $Lrt[1]=$Us1[9]; $Lmt[0]=$Us0[10]; $Lmt[1]=$Us1[10]; $Llt[0]=$Us0[11]; $Llt[1]=$Us1[11]; ##-------------Up FACE------------------- ## do the Rface transform (in rows: 1,2,3//4,5,6//7,8,9) ## f = face; 0=colour, 1= number @Uf0=($Ulb[0], $Ulm[0], $Ult[0], $Umb[0], $Umm[0], $Umt[0], $Urb[0], $Urm[0], $Urt[0]); @Uf1=($Ulb[1], $Ulm[1], $Ult[1], $Umb[1], $Umm[1], $Umt[1], $Urb[1], $Urm[1], $Urt[1]); $Ult[0]=$Uf0[0]; $Ult[1]=$Uf1[0]; $Umt[0]=$Uf0[1]; $Umt[1]=$Uf1[1]; $Urt[0]=$Uf0[2]; $Urt[1]=$Uf1[2]; $Ulm[0]=$Uf0[3]; $Ulm[1]=$Uf1[3]; $Umm[0]=$Uf0[4]; $Umm[1]=$Uf1[4]; $Urm[0]=$Uf0[5]; $Urm[1]=$Uf1[5]; $Ulb[0]=$Uf0[6]; $Ulb[1]=$Uf1[6]; $Umb[0]=$Uf0[7]; $Umb[1]=$Uf1[7]; $Urb[0]=$Uf0[8]; $Urb[1]=$Uf1[8]; } ##============================== sub rrSu{ ## middle slice rotation (side only 12 facelets) ## s = side; 0=colour, 1= number ## make the post rotation permutation ##-----------SIDE------------------- @SUs0=($Lrm[0],$Lmm[0],$Llm[0], $Brm[0],$Bmm[0],$Blm[0], $Rrm[0],$Rmm[0],$Rlm[0], $Frm[0],$Fmm[0],$Flm[0]); @SUs1=($Lrm[1],$Lmm[1],$Llm[1], $Brm[1],$Bmm[1],$Blm[1], $Rrm[1],$Rmm[1],$Rlm[1], $Frm[1],$Fmm[1],$Flm[1]); $Brm[0]=$SUs0[0]; $Brm[1]=$SUs1[0]; $Bmm[0]=$SUs0[1]; $Bmm[1]=$SUs1[1]; $Blm[0]=$SUs0[2]; $Blm[1]=$SUs1[2]; $Rrm[0]=$SUs0[3]; $Rrm[1]=$SUs1[3]; $Rmm[0]=$SUs0[4]; $Rmm[1]=$SUs1[4]; $Rlm[0]=$SUs0[5]; $Rlm[1]=$SUs1[5]; $Frm[0]=$SUs0[6]; $Frm[1]=$SUs1[6]; $Fmm[0]=$SUs0[7]; $Fmm[1]=$SUs1[7]; $Flm[0]=$SUs0[8]; $Flm[1]=$SUs1[8]; $Lrm[0]=$SUs0[9]; $Lrm[1]=$SUs1[9]; $Lmm[0]=$SUs0[10]; $Lmm[1]=$SUs1[10]; $Llm[0]=$SUs0[11]; $Llm[1]=$SUs1[11]; } ##============================== sub rrDp{ ## Dpwn Face anticlockwise rotation (side and face) ## s = side; 0=colour, 1= number ## make the post rotation permutation ##--------------SIDE---------------- @DPs0=($Lrb[0],$Lmb[0],$Llb[0], $Brb[0],$Bmb[0],$Blb[0], $Rrb[0],$Rmb[0],$Rlb[0], $Frb[0],$Fmb[0],$Flb[0]); @DPs1=($Lrb[1],$Lmb[1],$Llb[1], $Brb[1],$Bmb[1],$Blb[1], $Rrb[1],$Rmb[1],$Rlb[1], $Frb[1],$Fmb[1],$Flb[1]); $Brb[0]=$DPs0[0]; $Brb[1]=$DPs1[0]; $Bmb[0]=$DPs0[1]; $Bmb[1]=$DPs1[1]; $Blb[0]=$DPs0[2]; $Blb[1]=$DPs1[2]; $Rrb[0]=$DPs0[3]; $Rrb[1]=$DPs1[3]; $Rmb[0]=$DPs0[4]; $Rmb[1]=$DPs1[4]; $Rlb[0]=$DPs0[5]; $Rlb[1]=$DPs1[5]; $Frb[0]=$DPs0[6]; $Frb[1]=$DPs1[6]; $Fmb[0]=$DPs0[7]; $Fmb[1]=$DPs1[7]; $Flb[0]=$DPs0[8]; $Flb[1]=$DPs1[8]; $Lrb[0]=$DPs0[9]; $Lrb[1]=$DPs1[9]; $Lmb[0]=$DPs0[10]; $Lmb[1]=$DPs1[10]; $Llb[0]=$DPs0[11]; $Llb[1]=$DPs1[11]; ##---------------Down FACE------------------- ## f = face; 0=colour, 1= number @DPf0=($Dlt[0], $Dlm[0], $Dlb[0], $Dmt[0], $Dmm[0], $Dmb[0], $Drt[0], $Drm[0], $Drb[0]); @DPf1=($Dlt[1], $Dlm[1], $Dlb[1], $Dmt[1], $Dmm[1], $Dmb[1], $Drt[1], $Drm[1], $Drb[1]); $Dlb[0]=$DPf0[0]; $Dlb[1]=$DPf1[0]; $Dmb[0]=$DPf0[1]; $Dmb[1]=$DPf1[1]; $Drb[0]=$DPf0[2]; $Drb[1]=$DPf1[2]; $Dlm[0]=$DPf0[3]; $Dlm[1]=$DPf1[3]; $Dmm[0]=$DPf0[4]; $Dmm[1]=$DPf1[4]; $Drm[0]=$DPf0[5]; $Drm[1]=$DPf1[5]; $Dlt[0]=$DPf0[6]; $Dlt[1]=$DPf1[6]; $Dmt[0]=$DPf0[7]; $Dmt[1]=$DPf1[7]; $Drt[0]=$DPf0[8]; $Drt[1]=$DPf1[8]; } ##============================== sub rrF{ ## do the Fside transform (side and face) ## s = side; 0=colour, 1= number ## -----------SIDE----------------- @Fs0=($Lrb[0],$Lrm[0],$Lrt[0], $Ulb[0],$Umb[0],$Urb[0], $Rlt[0],$Rlm[0],$Rlb[0], $Drt[0],$Dmt[0],$Dlt[0]); @Fs1=($Lrb[1],$Lrm[1],$Lrt[1], $Ulb[1],$Umb[1],$Urb[1], $Rlt[1],$Rlm[1],$Rlb[1], $Drt[1],$Dmt[1],$Dlt[1]); $Ulb[0]=$Fs0[0]; $Ulb[1]=$Fs1[0]; $Umb[0]=$Fs0[1]; $Umb[1]=$Fs1[1]; $Urb[0]=$Fs0[2]; $Urb[1]=$Fs1[2]; $Rlt[0]=$Fs0[3]; $Rlt[1]=$Fs1[3]; $Rlm[0]=$Fs0[4]; $Rlm[1]=$Fs1[4]; $Rlb[0]=$Fs0[5]; $Rlb[1]=$Fs1[5]; $Drt[0]=$Fs0[6]; $Drt[1]=$Fs1[6]; $Dmt[0]=$Fs0[7]; $Dmt[1]=$Fs1[7]; $Dlt[0]=$Fs0[8]; $Dlt[1]=$Fs1[8]; $Lrb[0]=$Fs0[9]; $Lrb[1]=$Fs1[9]; $Lrm[0]=$Fs0[10]; $Lrm[1]=$Fs1[10]; $Lrt[0]=$Fs0[11]; $Lrt[1]=$Fs1[11]; ## -------Front FACE------------------- ## f = face; 0=colour, 1= number @Lf0=($Flb[0], $Flm[0], $Flt[0], $Fmb[0], $Fmm[0], $Fmt[0], $Frb[0], $Frm[0], $Frt[0]); @Lf1=($Flb[1], $Flm[1], $Flt[1], $Fmb[1], $Fmm[1], $Fmt[1], $Frb[1], $Frm[1], $Frt[1]); $Flt[0]=$Lf0[0]; $Flt[1]=$Lf1[0]; $Fmt[0]=$Lf0[1]; $Fmt[1]=$Lf1[1]; $Frt[0]=$Lf0[2]; $Frt[1]=$Lf1[2]; $Flm[0]=$Lf0[3]; $Flm[1]=$Lf1[3]; $Fmm[0]=$Lf0[4]; $Fmm[1]=$Lf1[4]; $Frm[0]=$Lf0[5]; $Frm[1]=$Lf1[5]; $Flb[0]=$Lf0[6]; $Flb[1]=$Lf1[6]; $Fmb[0]=$Lf0[7]; $Fmb[1]=$Lf1[7]; $Frb[0]=$Lf0[8]; $Frb[1]=$Lf1[8]; } ##============================== sub rrSf{ ## do the Fs transform (side only) ## s = side; 0=colour, 1= number ##----------SIDE--------------- @SFs0=($Lmb[0],$Lmm[0],$Lmt[0], $Ulm[0],$Umm[0],$Urm[0], $Rmt[0],$Rmm[0],$Rmb[0], $Drm[0],$Dmm[0],$Dlm[0]); @SFs1=($Lmb[1],$Lmm[1],$Lmt[1], $Ulm[1],$Umm[1],$Urm[1], $Rmt[1],$Rmm[1],$Rmb[1], $Drm[1],$Dmm[1],$Dlm[1]); $Ulm[0]=$SFs0[0]; $Ulm[1]=$SFs1[0]; $Umm[0]=$SFs0[1]; $Umm[1]=$SFs1[1]; $Urm[0]=$SFs0[2]; $Urm[1]=$SFs1[2]; $Rmt[0]=$SFs0[3]; $Rmt[1]=$SFs1[3]; $Rmm[0]=$SFs0[4]; $Rmm[1]=$SFs1[4]; $Rmb[0]=$SFs0[5]; $Rmb[1]=$SFs1[5]; $Drm[0]=$SFs0[6]; $Drm[1]=$SFs1[6]; $Dmm[0]=$SFs0[7]; $Dmm[1]=$SFs1[7]; $Dlm[0]=$SFs0[8]; $Dlm[1]=$SFs1[8]; $Lmb[0]=$SFs0[9]; $Lmb[1]=$SFs1[9]; $Lmm[0]=$SFs0[10]; $Lmm[1]=$SFs1[10]; $Lmt[0]=$SFs0[11]; $Lmt[1]=$SFs1[11]; } ##============================== sub rrBp{ ## Back rotation anticlockwise (side + face) ## do the Bp side transform ## s = side; 0=colour, 1= number ## --------------Side----------------- @BPs0=($Llb[0],$Llm[0],$Llt[0], $Ult[0],$Umt[0],$Urt[0], $Rrt[0],$Rrm[0],$Rrb[0], $Drb[0],$Dmb[0],$Dlb[0]); @BPs1=($Llb[1],$Llm[1],$Llt[1], $Ult[1],$Umt[1],$Urt[1], $Rrt[1],$Rrm[1],$Rrb[1], $Drb[1],$Dmb[1],$Dlb[1]); $Ult[0]=$BPs0[0]; $Ult[1]=$BPs1[0]; $Umt[0]=$BPs0[1]; $Umt[1]=$BPs1[1]; $Urt[0]=$BPs0[2]; $Urt[1]=$BPs1[2]; $Rrt[0]=$BPs0[3]; $Rrt[1]=$BPs1[3]; $Rrm[0]=$BPs0[4]; $Rrm[1]=$BPs1[4]; $Rrb[0]=$BPs0[5]; $Rrb[1]=$BPs1[5]; $Drb[0]=$BPs0[6]; $Drb[1]=$BPs1[6]; $Dmb[0]=$BPs0[7]; $Dmb[1]=$BPs1[7]; $Dlb[0]=$BPs0[8]; $Dlb[1]=$BPs1[8]; $Llb[0]=$BPs0[9]; $Llb[1]=$BPs1[9]; $Llm[0]=$BPs0[10]; $Llm[1]=$BPs1[10]; $Llt[0]=$BPs0[11]; $Llt[1]=$BPs1[11]; ##-----------------Back FACE------------- ## do the B face transform (in rows: 1,2,3/4,5,6/7,8,9) ## f = face; 0=colour, 1= number @BPf0=($Brb[0], $Brm[0], $Brt[0], $Bmb[0], $Bmm[0], $Bmt[0], $Blb[0], $Blm[0], $Blt[0]); @BPf1=($Brb[1], $Brm[1], $Brt[1], $Bmb[1], $Bmm[1], $Bmt[1], $Blb[1], $Blm[1], $Blt[1]); $Brt[0]=$BPf0[0]; $Brt[1]=$BPf1[0]; $Bmt[0]=$BPf0[1]; $Bmt[1]=$BPf1[1]; $Blt[0]=$BPf0[2]; $Blt[1]=$BPf1[2]; $Brm[0]=$BPf0[3]; $Brm[1]=$BPf1[3]; $Bmm[0]=$BPf0[4]; $Bmm[1]=$BPf1[4]; $Blm[0]=$BPf0[5]; $Blm[1]=$BPf1[5]; $Brb[0]=$BPf0[6]; $Brb[1]=$BPf1[6]; $Bmb[0]=$BPf0[7]; $Bmb[1]=$BPf1[7]; $Blb[0]=$BPf0[8]; $Blb[1]=$BPf1[8]; } ##=====================end===================================