function Qube_mzip
%   MATLAB zip file, a self-extracting MATLAB archive.
%   Usage: Run this file to recreate the original directory.

    fname = mfilename;
    fin = fopen([fname '.m'],'r');
    dname = fname(1:find(fname=='_',1,'last')-1);
    mkdir(dname);
    mkdir([dname filesep 'lib'])
    addpath(dname)
    addpath([dname filesep 'lib'])    
    
    L = fgetl(fin);
    while length(L) < 2 || ~isequal(L(1:2),'%%')
        L = fgetl(fin);
    end
    while ~isequal(L,'%% EOF')
        F = [dname filesep L(4:end)];
        disp(F)
        fout = fopen(F,'w');
        L = fgetl(fin);
        while length(L) < 2 || ~isequal(L(1:2),'%%')
            fprintf(fout,'%s\n',L);
            L = fgetl(fin);
        end
        fclose(fout);
    end
    fclose(fin);
end
%% Q0.m
function Q = Q0(arg,~)
    % Q0(n), initial n^3 solved cube, default n qstate('nstr').

    q0 = 0.85*qzero;

    if nargin == 1
        n = str2double(arg);
    else
        n = str2double(qstate('nstr'));
    end
    m = n-1;
    mn = m + (n==1);

    p = 0;
    Q.V = cell(n,n,n);  % Vertices
    Q.C = cell(n,n,n);  % Colors for color mode.
    for z = -m:2:m%^
        for y = -m:2:m
            for x = -m:2:m
                p = p+1;
                Q.V{p} = q0 + [x y z];
                Q.C{p} = (mn-[-z y x])/(2*mn);
            end
        end 
    end
    if n == 1
        Q.C{1} = .5*[1 .95 .9];
    end

    if nargin == 2
        Qshow(Q)
        qstate('Q',Q)
    end

end
%% Q2026.m
function Q2026(arg,~)
    if isequal(arg.String,'Q20')
        S = "R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U";
    else
        S = "U U F U U R' L F F U F' B' R L U U R U D' R L' D R' L' D D";
    end
    Qpush(S)
end
%% Qfigure.m
function Qfigure
    % Initialize figure window for Qube
    clf
    shg
    fclose('all');
    sze = get(0,'screensize');
    set(gcf,'name','Qube', ...
        'position',sze, ...
        'numbertitle','off', ...
        'toolbar','none', ...
        'menubar','none', ...
        'color',0.65*[1 1 1], ...
        'inverthardcopy','off', ...
        'paperpositionmode','auto', ...
        'userdata',{})
    gps = get(gcf,'pos');
    font = floor(gps(4)/40);
    qstate('font',font)
    set(gca,'position',[3/8 7/24 1/2 1/2], ...
         'vis','on', ...
         'clipping','off', ...
         'userdata',eye(4,4))
    initaxis(3)
end
%% Qinit.m
function Qinit
    u = 60;
    alfa = 'LRUDFBXYZ';  % Singmaster alphabet
    for j = 1:9
        x = 4*j+2*(j>6)+8;
        pushbut([alfa(j)  ' '],[x 6 3 3]/u, @key)
        pushbut([alfa(j) ''''],[x 2 3 3]/u, @key)
    end

    pushbut(      "<=", [ 2  2 6 3]/u, @bs)
    toggbut(     "<==", [ 2  6 6 3]/u, @unscramble)
    toggbut(   "rubik", [ 2 30 6 3]/u, @modecb)
    pushbut(       "n", [ 2 26 6 3]/u, @nstrcb)
    pushbut(   "types", [ 2 22 6 3]/u, @typescb)
    pushbut(   "speed", [ 2 18 6 3]/u, @speedcb)
    toggbut(  "metric", [ 2 14 6 3]/u, @Qmetric)
    
    pushbut(      "=>", [53  2 6 3]/u, @randdo)
    toggbut(     "==>", [53  6 6 3]/u, @scramble)
    pushbut(   "scram", [53 10 6 3]/u, @scramcb)

    pushbut(    "info", [ 2 50 6 3]/u, @infocb)
    pushbut(   "apply", [53 22 6 3]/u, @apply)
    toggbut(     "viz", [53 18 6 3]/u, @Qviz)
    pushbut(     "Q26", [53 26 6 3]/u, @Q2026)
    pushbut(      "Q0", [53 30 6 3]/u, @Q0)
    pushbut(   "start", [53 42 6 3]/u, @Start_here)
    toggbut(   "solve", [53 38 6 3]/u, @Qsolve)
    toggbut(   "order", [53 34 6 3]/u, @Qorder)
    
    pushbut(    "ops2", [53 54 6 3]/u, @ops2)
    pushbut(    "ops1", [ 2 54 6 3]/u, @ops1)
    textbut(   "score", [53 50 6 3]/u, "score")
    pushbut(      " ", [ 9 54 43 3]/u, @stacker)
    framed_mat(        [ 2 36 18 11]/u)

    tooltips
    % rng('shuffle')
    rng(0)
end
%% Qinv.m
function x = Qinv(x)
    x = split(strip(x))';
    x =  x + "_";  
    x = erase(x,"'_");
    x = replace(x,"_","'");
    x = replace(x,"2'","2");
    x = flip(x);
    x = join(x);
end
%% Qmetric.m
function Qmetric(arg,~)
    arg.String = ['1/' num2str(4-2*arg.Value)];
    if arg.Value == 1
        set(findobj('string','Q26'),'string','Q20')
    else
        set(findobj('string','Q20'),'string','Q26')
    end
end
%% Qmove.m
    function Q = Qmove(op,Qin)
    [ax,f,sig] = axfsig(op);
    speed = qstate('speed');
    % Fractional steps.
    if speed > 0
        for j = 1:90/speed
            R = Rk(ax,sig*j*speed);
            Q = Qrot(Qin,ax,f,R);
            Qshow(Q)
            drawnow
            if qstate('gif') == 1
                gif_frame
            elseif ~isempty(qstate('video'))
                video_frame
            end
        end
    end
    
    % Full quarter turn, +/- 90 degrees.
    qstate('Q',Qin)
    Q = quarter(ax,f,sig,Qin);    
    Qshow(Q)
    if length(f) < 3
        Qscore(Q)
    end
    
end
%% Qnorm.m
function nrm = Qnorm(X,Y)
    % Qnorm(X,Y) = sum of singular values of X-Y. 
    % Also known as nuclear norm.
    ncube = str2double(qstate('nstr'))^3;
    nrm = 0;
    for p = 1:ncube
        nrm = nrm + sum(svd(X.V{p}-Y.V{p}));
    end
end
%% Qorder.m
function norms = Qorder(arg,~)
    % Qorder  Number of repetitions to return to Q0
    if nargin == 0
        arg = findobj('string','order');
        arg.Value = 1;
    end
    v = arg.Value;
    arg.BackgroundColor = 1-v*[.70 .25 .07];
    ops1 = findobj('callback',@ops1);
    ops2 = findobj('callback',@ops2);
    ops1.String = '0';
    ocount = 0; 
    ops2.String = int2str(ocount);
    Qshow(Q0)
    qstate('Q',Q0)
    nrm = inf;
    norms = nrm;
    while nrm > 0 && arg.Value > 0 
        apply
        nrm = Qnorm(qstate('Q'),Q0);
        norms(end+1,1) = nrm;
        ocount = ocount+1;
        ops2.String = int2str(ocount);
        drawnow
    end
    arg.Value = 0;
    arg.BackgroundColor = 'w';
end
%% Qpush.m
 function Qpush(ops)
    % Push ops onto stack.
    ops = split(string(ops));
    for k = 1:length(ops)
        push([char(ops(k)) ' '])
    end
end
%% Qrot.m
function Q = Qrot(Q,ax,f,R)
    % Q = Qrot(Q,ax,f,R)
    % Apply rotation R, face f, axis ax
    % to all the cubelets in Q.
    n = size(Q.V,1);
    switch ax
        case 'x'
            for j = 1:n
                for k = 1:n
                    for i = f
                        Q.V{i,j,k} = Q.V{i,j,k}*R;
                    end
                end
            end
        case 'y'
            for j = 1:n
                for k = 1:n
                    for i = f
                        Q.V{k,i,j} = Q.V{k,i,j}*R;
                    end
                end
            end
        case 'z'
            for j = 1:n
                for k = 1:n
                    for i = f
                        Q.V{k,j,i} = Q.V{k,j,i}*R;
                    end
               end
            end
    end
end
%% Qscore.m
function Qscore(Q)
    counter = findobj('tag','ops1');
    scorer = findobj('tag','score');
    nrm = Qnorm(Q,Q0);
    if ~isempty(counter)
        counter.Value = counter.Value + 1;
        counter.String = num2str(counter.Value);
    end
    if ~isempty(scorer)
        scorer.String = sprintf('%7.2f',round(nrm,2));
        scorer.FontName = 'Lucisa Sans Typewriter';
        scorer.FontWeight = 'bold';
    end
end
%% Qshow.m
function Qshow(Q)
% Qshow(Q)  Display Q.  Default qstate('Q')

    if nargin == 0
        Q = qstate('Q');
        n = size(Q.V,1);
        initaxis(n)
    end

    F = [1 5 7 3
         3 7 8 4
         1 3 4 2
         2 4 8 6
         1 2 6 5
         5 6 8 7];

    C = [1  3/5  0     % orange
         0  3/4  0     % green
        3/4  0   0     % red
         1   1   1     % white
         0   0  3/4    % blue
         1   1   0];   % yellow
    
    gps = get(gcf,'pos');
    lw = 0.5 + (gps(4) > 400);
    set(gca,'userdata',Q)
    rubik = isequal(qstate('mode'),'rubik');

    cla
    n = size(Q.V,1);
    m = n-1;
    p = 0;
    for z = -m:2:m
        for y = -m:2:m
            for x = -m:2:m
                p = p+1;
                type = norm([x y z],1)/2;
                alfa = 1.;
                if types(type) && p <= numel(Q.V)
                    if rubik
                        for k = 1:6
                            patch( ...
                                Vertices = Q.V{p}, ...
                                Faces = F(k,:), ...
                                FaceColor = C(k,:), ...
                                FaceAlpha = alfa, ...
                                LineWidth = lw); 
                        end
                    else
                        patch( ...
                            Vertices = Q.V{p}, ...
                            Faces = F, ...
                            FaceColor = Q.C{p}, ...
                            FaceAlpha = alfa, ...
                            LineWidth = lw); 
                    end
                end
                if qstate('gif') == 2
                    drawnow
                    gif_frame
                end
           end
        end
    end
end
%% Qsolve.m
function x = Qsolve(~,~)
    % Breadcrumbs algorithhm.
    x = Qinv(qstate('stack'));
    unscramble
    Qpush(x)
end
%% Qube.asv
    function Qube(~)
%  Linear algebra and computer science power Rubik/Color Qube. 
%  Most recent edit: '21-Apr-2023 15{2
%
%  L R U D F B X Y Z: Rotate clockwise,
%           Left, Right, Up, Down, Front, Back, x, y, z axes.
%   '  :    Rotate counter-clockwise.
%
%  <=  :    Apply inverse of most recent rotation. 
%  <== :    Unscramble with repeated <= 's.
%  =>  :    One random rotation.
%  ==> :    Scramble with scram =>'s. 
%
%  mode:    Rubik, Color Cube.
%  n:       nxnxn cube.
%  speed:   Fractional rotation degrees.
%  types:   Center=0, face=1, edge=2, corner=3.
%  metric:  Quarter- or half-turn metric.
%  scram:   Scramble count.
%
%  order:   Number of rotations to return to Q0.
%  solve:   Breadcrumbs algorithm.
%  restart: Complete restart. 
%  viz:     Visibility of gui controls.
%  apply:   Apply stack.
%  op:      One of the keys, followed by a blank, a prime or a 2.
%  ops1:    Total number of ops.
%  ops2:    Order or solve op count.
%  stack:   String of ops displayed in a window above the cube.
%
%  Q:       Cube, 3x3x3 array of 8x3 vertices of cubelets.
%  Q0:      Initial cube showing a single color on each face.
%  Q20:     Superflip, half-turn max scramble.
%  Q26:     Superflip * fourspot, quarter-turn max scramble.
%  score:   Nuclear norm = sum of svd(Q{j}-Q0{j}).
%
%  info:    https://blogs.mathworks.com/cleve/2022/ ...
%               02/13/rubiks-cube       
%               04/04/digital-simulation-of-rubiks-cube
%               04/12/digital-simulation-of-rubiks-cube-with-Qube
%               05/04/qube-the-movie
%               05/18/rotation-matrices
%               12/09/color-cube-meets-rubiks-cube

%    Copyright 2021-2022 Cleve Moler

    Qfigure
    Qinit
    Qshow(Q0)
end
%% Qube.m
    function Qube(~)
%  Linear algebra and computer science power Rubik/Color Qube. 
%  Most recent edit: '21-Apr-2023 15:26:00'
%
%  L R U D F B X Y Z: Rotate clockwise,
%           Left, Right, Up, Down, Front, Back, x, y, z axes.
%   '  :    Rotate counter-clockwise.
%
%  <=  :    Apply inverse of most recent rotation. 
%  <== :    Unscramble with repeated <= 's.
%  =>  :    One random rotation.
%  ==> :    Scramble with scram =>'s. 
%
%  mode:    Rubik, Color Cube.
%  n:       nxnxn cube.
%  speed:   Fractional rotation degrees.
%  types:   Center=0, face=1, edge=2, corner=3.
%  metric:  Quarter- or half-turn metric.
%  scram:   Scramble count.
%
%  order:   Number of rotations to return to Q0.
%  solve:   Breadcrumbs algorithm.
%  restart: Complete restart. 
%  viz:     Visibility of gui controls.
%  apply:   Apply stack.
%  op:      One of the keys, followed by a blank, a prime or a 2.
%  ops1:    Total number of ops.
%  ops2:    Order or solve op count.
%  stack:   String of ops displayed in a window above the cube.
%
%  Q:       Cube, 3x3x3 array of 8x3 vertices of cubelets.
%  Q0:      Initial cube showing a single color on each face.
%  Q20:     Superflip, half-turn max scramble.
%  Q26:     Superflip * fourspot, quarter-turn max scramble.
%  score:   Nuclear norm = sum of svd(Q{j}-Q0{j}).
%
%  info:    https://blogs.mathworks.com/cleve/2022/ ...
%               02/13/rubiks-cube       
%               04/04/digital-simulation-of-rubiks-cube
%               04/12/digital-simulation-of-rubiks-cube-with-Qube
%               05/04/qube-the-movie
%               05/18/rotation-matrices
%               12/09/color-cube-meets-rubiks-cube

%    Copyright 2021-2022 Cleve Moler

    Qfigure
    Qinit
    Qshow(Q0)
end
%% Qviz.m
function Qviz(arg,~)
    if nargin == 2
        av = arg.Value;
    else
        av = arg;
        arg = findobj('callback',@Qviz);
        arg.Value = av;
    end
    uic = findobj('type','uicontrol');
    if av == 1
        set(uic(2:end),'vis','off')
        set(uic(3),'pos',[0.15 0.90 0.8333 0.05])
        set(arg,'vis','on', ...
            'pos',[.96 .02 .02 .03], ...
            'style', 'toggle', ...
            'background',.65*[1,1,1], ...
            'string','')
        set(uic(8),'vis','on', ...  
            'pos',[.02 .02 .02 .03], ...
            'background',.65*[1,1,1])
        qstate('rpm',10)
    else
        set(uic,'vis','on')
        set(uic(3),'pos',[0.15 0.90 0.7167 0.05])
        set(arg,'vis','on', ...
            'pos',[.8833 .30 .10 .05], ...
            'style','toggle', ...
            'background',[1,1,1], ...
            'string','viz')
        set(uic(8),'vis','on', ...
            'pos',[.8833 .6333 .10 .05], ...
            'background','w')
    end
end
%% Rk.m
function R = Rk(ax,d)
    % Rk(ax,d), Rotation by d degrees about the x-, y- or z-axis.
    c = cosd(d);
    s = sind(d);
    switch ax
        case 'x', R = [ 1  0  0  
                        0  c  s
                        0 -s  c ];
        case 'y', R = [ c  0  s  
                        0  1  0
                       -s  0  c ];
        case 'z', R = [ c  s  0  
                       -s  c  0
                        0  0  1 ];
    end
    fmat = findobj('tag','fmat');
    if ~isempty(fmat)
        fmat.String = mat3(R);
    end
end
%% lib\Start_here.m
function Start_here(~,~)
    Qube
end
%% lib\apply.m
function apply(Qxx,~)
    if nargin == 1
        len = str2double(Qxx(2:3));
    else
        len = 3;
    end
    stk2 = blanks(0);
    while ~isempty(peek)
        stk2 = [stk2 pop];
    end
    Q = qstate('Q');
    %Qshow(Q)
    ops1 = findobj('callback',@ops1);
    while ~isempty(stk2)
        tp = top(stk2);
        op = stk2(tp);
        stk2(tp) = [];
        Q = Qmove(op,Q);   
        Qshow(Q)
        drawnow
        drawnow
        push(op)
        show_stack(qstate('stack'))
    end
    qstate('Q',Q)
end
%% lib\axfsig.m
function [ax,f,sig] = axfsig(op)
% [ax,f,sig] = axfsig(op), ax-th axis, f-th face, sig sign.
    W = ["L" "M" "R" "X"
         "F" "S" "B" "Y"
         "D" "E" "U" "Z"]; 
    opsm = 'RFUYZSE';
    n = str2double(qstate('nstr'));
    [ax,f] = find(op(1)==W);
    ax = char('w'+ax);
    if f == 3
        f = n;
    elseif f == 4
        f = 1:n;
    end
    if op(2) == ' '
        sig = 1;
    elseif op(2) == ''''
        sig = -1;
    else
        sig = 2;
    end
    if any(op(1) == opsm)
        sig = -sig;
    end
end
%% lib\bs.m
function bs(~,~)
% bs, backspace, inverse of first op in stack
    op = pop;
    if ~isempty(op)
        Q = qstate('Q');
        opt = prime(op);
        Q = Qmove(opt,Q);
        qstate('Q',Q)
        % qstate('stack2',[qstate('stack2') op])
    end  
end
%% lib\dpmcb.m
function dpmcb(arg,~)
    % dpm, degrees  per fractional rotation.
    if nargin == 0
        arg = findobj('callback',@dpmcb);
    end
    switch arg.String
        case '90', dpm = '0';
        case '30', dpm = '90';
        case '10', dpm = '30';
        case '3', dpm = '10';
        case '1', dpm = '3';
        case '0', dpm = '1';
        otherwise, dpm = '10';
    end
    arg.String = dpm;
    qstate('dpm',str2double(dpm))
    Qshow(qstate('Q'))
    set(findobj('callback',@dpmcb),'string',dpm)
end
%% lib\fmat.m
function fmat(R)
    fmatt = findobj('tag','fmat');
    if ~isempty(fmatt)
        fmatt.String = mat3(R);
    end
end
%% lib\framed_mat.m
function framed_mat(pos)
    fs = qstate('font');
    if fs > 7
        fs = fs;
    elseif fs < 12
        fs = fs;
    end
    uicontrol( ...
        'style','frame', ...
        'units','normalized', ...
        'position',pos, ...
        'backgroundcolor',0.25*[1 1 1])
    del = .0015;
    uicontrol( ...
        'style','text', ...
        'units','normalized', ...
        'position',pos+[del del -2*del -2*del], ...
        'fontname','Lucida Sans Typewriter', ...
        'fontsize', fs, ...
        'fontweight','bold', ...
        'horizontalalignment','left', ...
        'backgroundcolor','w', ...
        'string',mat3(eye(3,3)), ...
        'tag','fmat')
end
%% lib\initaxis.m
function initaxis(n)
    axis((n+0.5)*[-1 1 -1 1 -1 1]);
    axis off
    axis vis3d
    view(3)
    rotate3d on
    set(gca,'clipping','off', ...
       'userdata',n)
end
%% lib\key.m
function key(arg,~)
    if nargin == 2
        op = arg.String;
    else
        op = arg;
    end
    Q = qstate('Q');
    Q = Qmove(op,Q);
    push(op)
    qstate('Q',Q)
end
%% lib\mat3.m
function txt = mat3(M)
    txt = newline;
    for k = 1:3
        for j = 1:3
            if M(k,j) == 0
                txt = [txt sprintf('%6.0f',abs(M(k,j)))];
            elseif M(k,j) == round(M(k,j))
                txt = [txt sprintf('%6.0f',M(k,j))];
            else
                txt = [txt sprintf('%6.2f',M(k,j))];
            end
        end
        txt = [txt newline];
    end
end
%% lib\modecb.m
function modecb(arg,~)
    if nargin == 0
        arg = findobj('callback',@modecb);
    end
    switch arg.String
        case 'rubik', mode = 'color';
        otherwise, mode = 'rubik';
    end
    arg.String = mode;
    qstate('mode',mode)
    Qshow(qstate('Q'))
    set(findobj('callback',@modecb),'string',mode)
end
%% lib\nstrcb.m
function nstrcb(arg,~)
    if nargin == 0
        arg = findobj('callback',@nstrcb);
    end
    n = str2double(arg.String);
    if isnan(n)
        n = 3;
    end
    if isequal(get(gcf,'selectiontype'),'alt')
        n = n+1;
    else 
        n = n-1;
    end
    if n < 1
        n = 7;
    end
    nstr = num2str(n);
    arg.String = nstr;
    qstate('nstr',nstr)
    Q = Q0(nstr);
    qstate('Q',Q)
    Qshow(Q)
    initaxis(n)
end
%% lib\ops1.m
function ops1(arg,~)
    arg.Value = 0;
    arg.String = '0';
end
%% lib\ops2.m
function ops2(arg,~)
    arg.Value = 0;
    arg.String = '0';
end
%% lib\peek.m
function op = peek
    % peek   return top op
    stk = qstate('stack');
    tp = top(stk);
    op = stk(tp);
end
%% lib\pop.m
function op = pop
    % pop   remove op from top of stack
    stk = qstate('stack');
    tp = top(stk);
    op = stk(tp);
    stk(tp) = []; % delete top element
    show_stack(stk)
    qstate('stack',stk)
end
%% lib\prime.m
function op = prime(op)
    % op = op'
    if isempty(op)
        return
    elseif isscalar(op)
        op = [op char(' ' + '''' - op)];         
    elseif op(2) ~= '2'
        op(2) = char(' ' + '''' - op(2));
    end
end
%% lib\push.m
function push(op,~)
    % push  insert op on top of stack
    stk = qstate('stack');
    op(op==' ') = [];
    op = [op ' '];
    lop = length(op);
    ops1 = findobj('callback',@ops1);
    metric = findobj('callback',@Qmetric);
    if isequal(metric(end).String,'1/2') && ...
            length(stk) >= lop && isequal(stk(end-lop+1:end),op)
        stk = stk(1:end-lop);
        op = [op(1) '2 '];
        ops1.Value = ops1.Value - 1;
        ops1.String = num2str(ops1.Value);
    end
    stk = [stk op];
    show_stack(stk)
    qstate('stack',stk)
end 
%% lib\pushbut.m
function pushbut(string,position,callback)
    uicontrol(Style = "pushbutton", ...
        String = string, ...
        Tag = string, ...
        Units = "normalized", ...
        Position = position, ...
        Callback = callback, ...
        Fontsize = qstate('font'), ...
        Fontweight = "bold", ...
        BackgroundColor = 'w');
end
%% lib\qstate.m
function vout = qstate(item,vin)
    % qstate(name,set_value)
    % get_value = qstate(name)
    
    items = {'Q','stack','stack2','speed','types','mode','nstr', ...
        'scram','font','gif','video'}; 
    nstr = '3';
    defaults = {Q0(nstr),'','',10,0:7,'rubik',nstr,'4',24,[],[]};
    
    state = get(gcf,'userdata');
    if isempty(state)
        state = defaults;
        set(gcf,'userdata',defaults)
    end
    for k = 1:length(items)
        if isequal(item,items{k})
            if nargin == 2
                state{k} = vin;
                set(gcf,'userdata',state)
            else
                vout = state{k};
            end
            return
        end
    end
end
%% lib\qtrim1.m
function x = qtrim1(x)
    % X X'-> [].
    x = split(strip(x))';
    k = length(x)-1;
    while k > 0
        if x(k) == erase((x(k+1)+"'"),"''")
            x(k:k+1) = [];
            k = k-1;
        end
        k = k-1;
    end
    x = join(x);
end
%% lib\qtrim2.m
function x = qtrim2(x)
    % X X -> X2
    x = split(strip(x))';
    k = length(x)-1;
    while k > 0
        if x(k) == x(k+1)
            x(k+1) = [];
            x(k) = erase(x(k)+"2","'");
        end
        k = k-1;
    end
    x = join(x);
end
%% lib\quarter.m
function Qout = quarter(ax,f,sig,Q)
    if abs(sig) == 2
        Qout = quarter(ax,f,sig/2,Q);
        Q = Qout;
        Qout = quarter(ax,f,sig/2,Q);
    else
        Qout = Q;
        n = size(Q.V,1);
        R = Rk(ax,sig*90);
        switch ax
            case 'x'
                for j = 1:n
                    for k = 1:n
                        for i = f
                            if sig < 0
                                Qout.V{i,k,n+1-j} = Q.V{i,j,k}*R;
                                Qout.C{i,k,n+1-j} = Q.C{i,j,k};
                            else
                                Qout.V{i,n+1-k,j} = Q.V{i,j,k}*R;
                                Qout.C{i,n+1-k,j} = Q.C{i,j,k};
                            end
                        end
                    end
                end
            case 'y'
                for j = 1:n
                    for k = 1:n
                        for i = f
                            if sig < 0
                                Qout.V{j,i,n+1-k} = Q.V{k,i,j}*R;
                                Qout.C{j,i,n+1-k} = Q.C{k,i,j};
                            else
                                Qout.V{n+1-j,i,k} = Q.V{k,i,j}*R;
                                Qout.C{n+1-j,i,k} = Q.C{k,i,j};
                            end
                        end
                    end
                end
            case 'z'
                for j = 1:n
                    for k = 1:n
                        for i = f
                            if sig < 0
                                Qout.V{j,n+1-k,i} = Q.V{k,j,i}*R;
                                Qout.C{j,n+1-k,i} = Q.C{k,j,i};
                            else
                                Qout.V{n+1-j,k,i} = Q.V{k,j,i}*R;
                                Qout.C{n+1-j,k,i} = Q.C{k,j,i};
                            end
                        end
                    end
                end
        end   
    end
end
%% lib\qzero.m
function q0 = qzero
    % Unit cubelet.
    q0 = [-1 -1 -1
          -1 -1  1
          -1  1 -1
          -1  1  1
           1 -1 -1
           1 -1  1
           1  1 -1 
           1  1  1];
end
%% lib\randdo.m
function randdo(~,~)
    op = random_op;
    Q = qstate('Q');
    Q = Qmove(op,Q);
    push(op)
    qstate('Q',Q)
end
%% lib\random_op.m
function op = random_op
    % alfa = 'LMRUEDFSBXYZ';
    alfa = 'LRUDFB';
    op = blanks(2);
    op(1) = alfa(randi(length(alfa)));
    if rand > 0.5
        op(2) = '''';
    end
end
%% lib\scramble.m
function scramble(arg,~)
    if nargin == 0
        cnt = inf;
        arg = findobj('callback',@scramcb);
        arg.Value = 1;
    elseif nargin == 1
        cnt = str2double(arg.String);
        arg = findobj('callback',@scramble);
        arg.Value = 1;
    else
        scram = findobj('callback',@scramcb);
        if isequal(scram.String,'scram')
            cnt = inf;
        else
            cnt = str2double(scram.String);
        end
    end
    v = arg.Value;
    arg.BackgroundColor = 1-v*[.70 .25 .07];
    c = 0;
    while arg.Value > 0 && c < cnt
        randdo(arg)
        drawnow
        c = c+1;
    end
    arg.Value = 0;
    arg.BackgroundColor = 'w';
end
%% lib\scramcb.m
function scramcb(arg,~)
    % scram, number of random rotations.
    if nargin == 0
        arg = findobj('callback',@scramcb);
    end
    switch arg.String
        case 'inf', scram = '2';
        case '2', scram = '3';
        case '3', scram = '4';
        case '4', scram = '8';
        case '8', scram = '20';
        case '20', scram = 'inf';
        otherwise, scram = '3';
    end
    arg.String = scram;
    qstate('scram',str2double(scram))
    Qshow(qstate('Q'))
    set(findobj('callback',@scramcb),'string',scram)
end
%% lib\show_stack.m
function show_stack(stk)
    stacker = findobj('callback',@stacker);
    %{
    if length(stk) > 72
        stk = [stk(1:18) ' ... ' stk(end-29:end)];
    end
    %}
    if ~isempty(stacker)
        stacker.String = stk;
    end
end
%% lib\speedcb.m
function speedcb(arg,~)
    % speed, degrees  per fractional rotation.
    if nargin == 0
        arg = findobj('callback',@speedcb);
    end
    switch arg.String
        case '45', speed = '90';
        case '30', speed = '45';
        case '10', speed = '30';
        case '3', speed = '10';
        case '1', speed = '3';
        case '90', speed = '1';
        otherwise, speed = '10';
    end
    arg.String = speed;
    qstate('speed',str2double(speed))
    Qshow(qstate('Q'))
    set(findobj('callback',@speedcb),'string',speed)
end
%% lib\stacker.m
function stacker(arg,~)
    arg.String = '';
    qstate('stack','')
end
%% lib\textbut.m
function textbut(string,position,tag)
    uicontrol(Style = "pushbutton", ...
        String = string, ...
        Units = "normalized", ...
        Position = position, ...
        Tag = tag, ...
        Fontsize = qstate('font'), ...
        Fontweight = "bold", ...
        BackgroundColor = 'w');
end
%% lib\toggbut.m
function toggbut(str,position,callback)
    v = isequal(str,' ''');
    uicontrol(Style = "toggle", ...
        String = str, ...
        Units = "normalized", ...
        Position = position, ...
        Callback = callback, ... 
        Value = v, ...
        Fontsize = qstate('font'), ...
        Fontweight = "bold", ...
        BackgroundColor = 'w');
end
%% lib\tooltips.m
function tooltips
    tip = @(x,y,z) set(findobj(x,y),'tooltip',z);
    tip("string",   "<=",     "Apply inverse of most recent rotation.") 
    tip("string",   "<==",    "Unscramble with repeated <='s.")
    tip("string",   "=>",     "One random rotation.")
    tip("string",   "==>",    "Scramble with scram =>'s.")
    tip("string",   "n",      "nxnxn cube.")
    tip("string",   "speed",  "Fractional rotation")
    tip("string",   "types",  "Center=0, face=1, edge=2, corner=3.")
    tip("string",   "metric", "Quarter- or half-turn metric.")
    tip("string",   "scram",  "Number of =>'s in ==>.")
    tip("string",   "solve",  "Breadcrumbs algorithm.")
    tip("string",   "order",  "Number of repetitions to return to Q0.")
    tip("string",   "Q0",     "Initial configuration.")
    tip("string",   "Q20",    "Superflip.")
    tip("string",   "Q26",    "Superflip * fourscore.")
    tip("string",   "viz",    "Visibility of gui controls.")
    tip("string",   "info",   "help, blog.")
    tip("string",   "apply",  "Apply stack.")
    tip("string",   "start",  "Call Qube.")
    tip("string",   "metric", "Quarter- or Half-Turn Metric.")
    tip("tag",      "score",  "Nuclear norm distance to Q0.")
    tip("tag",      "fmat",   "Rotations.")
    tip("callback", @modecb,  "Rubik or Color Cube.")
    tip("callback",  @ops1,   "Total number of ops.")
    tip("callback",  @ops2,   "Number of order or solve ops.")
    tip("callback", @stacker, "Stack of ops, click to clear.")
    tip("callback", @fraccb,  "Number of fractional steps in rotation.")
    tip("callback", @typescb, "Show center, face, edge, corner cubelets.")
end
%% lib\top.m
function top = top(s)
   % indices of first op in stack    
   k = find((s ~= ' ') & (s ~= '''') & (s ~= '2'),2,'last');
   if length(k) > 1
       top = k(2):length(s);
   else
       top = 1:length(s);
   end
end
%% lib\types.m
function t = types(arg)
    % cubelet types
    f = @(n) n+(n+3)+(n>5);
    s = qstate('types');
    t = (s(1) <= arg) && (arg <= f(s(end)));
end
%% lib\typescb.m
function typescb(arg,~)
    if nargin == 0
        arg = findobj('callback',@typescb);
    end
    nstrcb = findobj('callback',@nstrcb);
    nstr = nstrcb.String;
    if nstr == 'n'
        nstr = '3';
    end
    n = str2double(nstr);
    nn = n + (n>3) + (n>5); 
    a = str2num(arg.String);
    if isempty(a)
        a = 0:3;
    elseif isscalar(a) && a == nn
        a = a-1:nn;
    elseif isscalar(a)
        a = min(a+1,nn);
    elseif a(1) > 0
        a = a(1)-1:a(end);
    else 
        a = 0:a(end)-1;
    end
    astr = [num2str(a(1)) ':' num2str(a(end))];
    arg.String = astr;
    qstate('types',min(a):max(a))
    Qshow
    n = str2double(qstate('nstr'));
    initaxis(n)
end
%% lib\unscramble.m
function unscramble(arg,~)
% undo.  bs until stack is empty.
    if nargin < 1
        arg = findobj('callback',@unscramble);
        arg.Value = 1;
    end
    while arg.Value > 0 && ~isempty(peek)
        bs(arg)
        drawnow
    end
    arg.BackgroundColor = 'w'; 
    arg.Value = 0;
end
%% lib\video_frame.m
function video_frame(~,~)
    writeVideo(qstate('video'),getframe(gcf))
end

%% EOF