function LemniscateClock(StartTime,Duration,DoRender)
% LemniscateClock(StartTime,Duration,Render)
% Plots 3 Lemniscates (hour, min, sec) 
% at StartTime in minutes
% for Duration in minutes
% DoRender == 1 does render to animated GIF
% -- Author ---
% Marc falkao Falk, Entropia Universe

    %lemnisacte param
    a=1; %scale parameter for Lemniscate, not used atm
    l = 2*a*5.2441; %circumference std lemniscate
    t = 0:.01:2*pi; %time vector
    %timers
    d = 24; %total hours
    tim = d; %multiplier for min
    tis = d*60; %multiplier for sec


    %simple param handling
    if nargin < 1
       StartTime = 0; %00:00
       Duration = 10; %6 min
       DoRender = 0;  %render off
    end

    if nargin == 1
       StartTime = 2*pi/d/60 * StartTime; 
       Duration = 10;
       DoRender = 0;
    end

    if nargin == 2
       StartTime = 2*pi/d/60 * StartTime; 
       Duration = 60 / Duration;
       DoRender = 0;
    end

    %define axis
    ax = axes('XLim',[-4 4],'YLim',[-4 4]);
    axis equal

    %== Clock ==
    hc = rectangle('Position',[-sqrt(2)*a,-sqrt(2)*a,2*sqrt(2)*a,2*sqrt(2)*a],'Curvature',[1,1]);
    hold on

    % Plot the numbers 1-12 on the screen
    % --Declare variables to be used in the plotting the clock numbers
    Clk_fSize = 12;                                  % controls the font size of the numbers of the clock
    Clk_fTheta = ((d-4)*pi/d/2:-2*pi/d:-3/2*pi)';           % sets the Theta for each number position, goes from pi/2 to -3/2pi
    Clk_fRad = sqrt(2)*a+.3;                                 % sets the Raduis for each number position
    Clk_numbas = (1:1:d)';
    Clk_nData = [Clk_fRad*cos(Clk_fTheta) Clk_fRad*sin(Clk_fTheta) Clk_numbas];
    text(Clk_nData(:,1),Clk_nData(:,2),num2str(Clk_nData(:,3)),...
        'horizontalAlignment','center','verticalAlignment','middle','FontSize',Clk_fSize);
    %== Tic Marks
    % Define the Length of the Tic marks
    TLenStart = sqrt(2)*a-.1;    % Start of the Tick mark (distance from origin)
    TLenStop = sqrt(2)*a;     % End of the Tick mark (distance from origin)
    [STX,STY,TTX,TTY] = ticMark(TLenStart,TLenStop);
    % Plot Skinny and Thick Tick marks on the clock face
    plot(TTX,TTY, 'linewidth',2,'color','k');
    %hour marker
    hh = plot([-sqrt(2)*a,-sqrt(2)*a-.1],[0,0], 'linewidth',2,'color','b');

    %== Leminscate ==
    h = plot(sqrt(2)*a*cos(t)./(1+sin(t).^2),2*pi/d*sqrt(2)*a*cos(t).*sin(t)./(1+sin(t).^2));
    axis(a*[-2.2 2.2 -2.2 2.2])
    hold off

    %transforms
    th = hgtransform('Parent',ax);
    thc = hgtransform('Parent',ax); %circle
    tm = hgtransform('Parent',th);
    ts = hgtransform('Parent',th);
    set(get(ax,'Parent'),'Renderer','opengl','DoubleBuffer','on')


    set(h,'Parent',th); %Hour Lamnisacte
    set(hc,'Parent',thc); %circle
    set(hh,'Parent',th); %hour marker
    hm = copyobj(h,tm);copyobj(hh,tm); %Min Lamnisacte
    hs = copyobj(h,ts);copyobj(hh,ts); %Sec Lamnisacte

    set(h,'Color','k');
    set(hm,'Color','b');
    set(hs,'Color','r');

    Sxy = makehgtform('scale',[1 2*pi/d*sqrt(2)*a 1]);
    Rz = makehgtform('zrotate',pi/2+StartTime); %Start at 0 hour+ StartTime
    set(th,'Matrix',Rz)


    drawnow;

    if DoRender == 1
        M = getframe;
        map = [0 0 0;.8 .8 .8; 1 0 0; 0 0 1; 1 1 1];
        im(:,:,1,1) = rgb2ind(M.cdata,map,'nodither');
    end

%end part1 insert part 2 thereafter to complete the m-file

%part 2
    %animation
    i = 2;
    for r = pi/2+StartTime:.0001:pi/2+StartTime+2*pi/d/Duration
        % Form z-axis rotation matrix 
        Rz = makehgtform('zrotate',-r);
        Rzm = makehgtform('zrotate',-r*tim);
        Rzs = makehgtform('zrotate',-r*tis);
        rm = (r -pi/2) * tim + pi/2;
        Txym = makehgtform('translate',sqrt(2)*a*[cos(rm)./(1+sin(rm).^2) 2*pi/d*cos(rm).*sin(rm)./(1+sin(rm).^2) 0]);
        rs = (r -pi/2) * tis + pi/2;
        Txys = makehgtform('translate',sqrt(2)*a*[cos(rs)/(1+sin(rs).^2) 2*pi/d*cos(rs).*sin(rs)./(1+sin(rs).^2) 0]);
        % Set transforms for both hgtransform objects 
        set(th,'Matrix',Rz)
        %with rotation

        set(tm,'Matrix',Txym*Rzm*eye(4))   
        set(ts,'Matrix',Txys*Rzs*eye(4))   

        drawnow,%pause(.1)
        if DoRender == 1
            M = getframe;
            im(:,:,1,i) = rgb2ind(M.cdata,map,'nodither');
        end
        i = i + 1;
    end

    if DoRender == 1        
      imwrite(im,map,'LemniscateClock_tmp.gif','DelayTime',0,'LoopCount',inf) 
    end

    function [STX,STY,TTX,TTY] = ticMark(TLenStart,TLenStop)
                %ticMark is given the distance from center to start the tick
                % marks (TLenStart) and the distance from origin to stop the
                % tick marks (TLenStop).
                %STTTheta 60 point array going clockwise skinny ticmarks
                STTheta = ((d-4)*pi/d/2:-2*pi/d/60:-3/2*pi);

                %Calculates X Y coordinates for all 60 skinny tick marks
                STX = [TLenStart*cos(STTheta') TLenStop*cos(STTheta')]'; 
                STY = [TLenStart*sin(STTheta') TLenStop*sin(STTheta')]';
                %TTTheta 12 point array going around clockwise thick tic marks
                TTTheta = ((d-4)*pi/d/2:-2*pi/d:-3/2*pi);
                %Calculates X Y coordinates for all 12 thick tic marks
                TTX = [TLenStart*cos(TTTheta') TLenStop*cos(TTTheta')]'; 
                TTY = [TLenStart*sin(TTTheta') TLenStop*sin(TTTheta')]';
    end %end ticmark function
end %main function