function R2_D2_14(arg)
% R2_D2, version 1.4, March 5, 2023.
% Rotations and Dilations in Two dimensions.
%
% See: https://blogs.mathworks.com/ ...
%      cleve/2023/03/03/r2-d2-rotations-and-dilations-in-two-dimensions/

%   Copyright 2016-2023 Cleve Moler

    ishouse = nargin == 0 || strcmp(arg,'house');
    if ishouse
        H = house;
    else
        H = hand;
    end
    
    theta = 0; 
    sigma = 1;
    U = [cosd(theta) -sind(theta); sind(theta) cosd(theta)];
    S = sigma*eye(2,2);
    A = U*S;
    X = A*H;
    Y = X;
    initialize_graphics(ishouse);
    Ut = framed_matrix(.1);
    St = framed_matrix(.4);
    At = framed_matrix(.7);
    d2d = dot2dot(X);
    
    % End of main program.  Motion functions take charge.

% ------------------------------------------------------

    function initialize_graphics(ishouse)
        clf
        shg
        set(gcf, ...
            'position',get(0,'screensize'), ...
            'windowbuttondownfcn',@down, ...
            'windowbuttonupfcn',@up)

        pushbut(  'exit',[.86 .90 .12 .06],'close(gcf)')       
        pushbut(  'info',[.86 .82 .12 .06],@infocb)
        pushbut( 'start',[.86 .74 .12 .06],@(~,~) R2_D2_14) 
        toggbut(   'tbd',[.86 .66 .12 .06],@house_hand);
        toggbut('rotate',[.86 .58 .12 .06],@action);
        toggbut('dilate',[.86 .50 .12 .06],@action);
        toggbut(  'both',[.86 .42 .12 .06],@action);
        pushbut(     '-',[.86 .34 .03 .06],@dtcb) 
        pushbut(     '3',[.90 .34 .04 .06],[]) 
        pushbut(     '+',[.95 .34 .03 .06],@dtcb) 
        hh = findobj('string','tbd');
        if ishouse
            hh.String = 'house';
            hh.Value = 0;
            hh.BackgroundColor = gray;
        else
            hh.String = 'hand';
            hh.Value = 1;
            hh.BackgroundColor = bluegreen;
        end      
        axes('position',[0 0 1 1],'vis','off')
        text(.35,.15,'*','fontsize',30,'fontweight','bold');
        text(.65,.15,'=','fontsize',30,'fontweight','bold');
    end % initialize graphics 

    function house_hand(arg,~)
        if arg.Value == 1
            arg.BackgroundColor = bluegreen;
            arg.String = 'hand';
            R2_D2_14('hand')
        else
            arg.BackgroundColor = gray;
            arg.String = 'house';
            R2_D2_14('house')
        end
    end    

    function Mt = framed_matrix(xmin)
        txt = @(x,y,t) text(x,y,t, ...
            'fontsize',20, ...
            'fontweight','bold', ...
            'horiz','left');
        framed_axis([xmin .02 .2 .25]);
        Mt = [txt(.12,.65,'1.00')
              txt(.12,.35,'  0 ')
              txt(.62,.65,'  0 ')
              txt(.62,.35,'1.00')];
    end % framed_matrix

    function d2d = dot2dot(X,d2d)
        % DOT2DOT  Connect the points from a 2-by-n array.
        X(:,end+1) = X(:,1);
        if nargin == 1
            axes('position',[.18 .34 .62 .62])
            d2d = plot(X(1,:),X(2,:),'.-', ...
                'markersize',18, ...
                'linewidth',2);
            axis(10*[-1 1 -1 1])
            axis off
            axis square
            set(gca,'clipping','off')
        else
            set(d2d,'xdata',X(1,:),'ydata',X(2,:))
        end
    end % dot2dot  

    function action(arg,~)
        job = arg.String;
        thetamax = 90;
        t = 0;
        tag = findobj('tag','3');
        dt = str2num(tag.String);
        if want_gif
            uic = get(gcf,'children');
            set(uic(1:10),'vis','off')
        end
        while arg.Value == 1
           arg.BackgroundColor = bluegreen;
           if strcmp(job,'rotate') || strcmp(job,'both')
               U = [cosd(t) -sind(t); sind(t) cosd(t)];
           end
           if strcmp(job,'dilate') || strcmp(job,'both')
               S = (3/4)^(t/45)*eye(2,2);
           end
           A = U*S;
           Y = A*X;
           update(U,Ut);
           update(S,St);
           update(A,At)
           dot2dot(Y,d2d);
           drawnow
           if want_gif
               gif_frame
           end
           if abs(t+dt) > thetamax
               pause(0.1)
               dt = -dt;
           end
           dt = sign(dt)*str2num(tag.String);
           t = t + dt;
           if want_gif && t == 0 && dt > 0
               break
           end
        end
        if want_gif
            gif_frame('wrap')
            set(uic(1:10),'vis','on')
        end
        arg.BackgroundColor = 'w';        
    end

    function dtcb(arg,~)
        tag = findobj('tag','3');
        dt = str2num(tag.String);
        if dt > 1
            if arg.String == '+'
               dt = dt+1;
            else
               dt = dt-1;
            end
            tag.String = num2str(dt);
        elseif dt < 1
            if arg.String == '+' 
               dt = dt/(1-dt);
            else
               dt = dt/(1+dt);
            end
            tag.String = ['1/' num2str(1/dt)];
        elseif arg.String == '+' 
            tag.String = '2';
        else
            tag.String = '1/2';
        end
    end

    function infocb(~,~)
        web('https://blogs.mathworks.com/cleve/2023/03/03/r2-d2-rotations-and-dilations-in-two-dimensions/')
    end

    function motion(varargin)
        % WindowsButtonMotionFunction

        z = read_mouse;
        w = U'*z;
        if inregion(w(1),w(2),Y(1,:),Y(2,:)) == 0
            theta = 90 - atan2d(z(2),z(1));
            U = [cosd(theta) -sind(theta); sind(theta) cosd(theta)];
        else
            sigma = norm(w)/4;
            S = sigma*eye(2,2);
        end
        A = U*S;
        X = A*H;
        dot2dot(X,d2d);
        update(U,Ut)
        update(S,St)
        update(A,At)
    end % motion

    function update(M,Mt)
        for k = 1:4
            Mt(k).String = sprintf('%5.2f',M(k));
        end
    end % update

    function down(varargin)
        % Called at the start of mouse movement.
        % Activate the motion function.
        set(gcf,'windowbuttonmotionfcn',@motion)
    end % down
  
    function up(varargin)
        % Called at the end of mouse movement.
        % Deactivate motion function.
        set(gcf,'windowbuttonmotionfcn',[])
        set(gcf,'windowbuttondownfcn',@down)
    end % up

    function z = read_mouse
        % Current horizontal and vertical coordinates of the mouse.
        cp = get(gca,'currentpoint');
        z = cp(1,1:2)';
    end % read_mouse

    function H = house   
        H = [ -6  -6  -7   0   7   6   6  -3  -3   0   0
              -7   2   1   8   1   2  -7  -7  -2  -2  -7 ];
    end

    function H = hand
       H = ...
         [3.15  4.43  6.13  7.65  7.52  6.75  5.60  4.45  3.07  2.60 ...
          2.73  3.22  3.39  2.84  2.10  1.48  0.68  0.81  0.66 -0.33 ...
         -0.99 -1.04 -1.17 -1.81 -2.63 -3.39 -3.86 -3.49 -3.13 -4.78 ...
         -6.00 -6.95 -7.12 -5.82 -4.76 -4.52 -4.00;
         -9.00 -6.55 -4.39 -2.21 -1.26 -0.95 -1.56 -2.85 -3.00 -1.70 ...
          0.59  3.66  6.79  7.92  7.41  4.25  0.79  4.96  8.36  9.06 ...
          8.09  4.68  0.90  4.15  7.45  7.80  6.97  3.35 -0.44  1.87 ...
          3.81  3.92  3.04 -0.07 -2.29 -5.62 -9.00];
    end

    function pushbut(string,position,callback)
        uicontrol(Style = "pushbutton", ...
            String = string, ...
            Tag = string, ...
            Units = "normalized", ...
            Position = position, ...
            Callback = callback, ...
            Fontsize = 20, ...
            Fontweight = "bold", ...
            BackgroundColor = gray);
    end
    
    function tb = toggbut(str,position,callback)
        tb = uicontrol(Style = "toggle", ...
            String = str, ...
            Units = "normalized", ...
            Position = position, ...
            Callback = callback, ... 
            Value = 0, ...
            Fontsize = 20, ...
            Fontweight = "bold", ...
            BackgroundColor = gray);
    end

    function wg = want_gif
        d = dir;
        ds = string({d.name})';
        wg = any(contains(ds,"xx.gif"));
    end 

end