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Math Help - some serious mathproblem i need help with, sinusoidal spiral etc

  1. #1
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    some serious mathproblem i need help with, sinusoidal spiral etc

    First post here so i hope im in the right forum, but i sort of suck at math so cant be sure.

    My problem is that i need help with figuring out how to do the maths for a certain type of timer/clock.

    The clock looks sort of like this

    *edit* noticed an error i made, the image/clock should only have 12 hours just like a normal analog clock, NOT 24 as the image has.

    This is only the first 6 minutes of it and it also sligthtly wrong, the second hand should travel on the minute hand really.

    The timers hands are based on the following Lemniscate -- from Wolfram MathWorld

    What i need help with is how i can set a certain width and length for the arms of the hands.

    This i need due to that the timer is used in a game i play and it's an imperative part to being successfull. The timers size is also based on the different continents sizes in the game.

    each continent has this timer placed in the middle and here is one of the continents http://jaxmap.net/pdf/efull.pdf and each coord is 1m

    other continent is here http://jaxmap.net/pdf/afull.pdf

    I hope i made everything clear but if i havent please feel free to ask.

    If someone would be able to help me with this i would be very very gratefull

    Also if someone could calculate how long it would take the hands to go from exactly aligned 12 o clock to next fulyl aligned 12 o clock would be great, i think it should be ~4 days

    *edit again*

    The hour hand spins one turn as a regular clock ie 12 hour to make one full spin, the minute hand spins one spin and travels along the hour hands side in 60 minutes and the second hand does the same on the minute hand but in 60 secfonds.
    Last edited by iller; July 5th 2009 at 06:54 AM.
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  2. #2
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    some aditional info

    The timer is sort of placed on top of the map, and each time the first side of the timer passes over an area it raises the loot values in that area, and then when the timer passes with it's endpart it lowers the values again, that is why the width is important aswell.

    I also had a friend make the image of the timer in mathematica i think, and here is the code he used if that could be of any help

    Code:
    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
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  3. #3
    Super Member malaygoel's Avatar
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    Also if someone could calculate how long it would take the hands to go from exactly aligned 12 o clock to next fulyl aligned 12 o clock would be great, i think it should be ~4 days
    I think it should be 12 hours.
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  4. #4
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    Quote Originally Posted by malaygoel View Post
    I think it should be 12 hours.
    no not as the maps aint totally square, and also due to how the hands move on each other i belive they will take longer.. but i'm not sure though as i havent been able to check.
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  5. #5
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    I hope i made everything clear but if i havent please feel free to ask.
    ...
    Also if someone could calculate how long it would take the hands to go from exactly aligned 12 o clock to next fulyl aligned 12 o clock would be great, i think it should be ~4 days
    I do not know what you are trying to do or how you are using the clock.
    The maps make no real sense or direct connection with the use of the clock.

    How do you get 4 days?
    Of the three hands:

    Each time the second hand rotates 1 full turn it aligns with the 12 (or 24 as shown);

    Each time the minute hand rotates 1 full turn it should align with the 12 o'clock position;

    Each time the hour hand rotates 1 full turn it should align with the 12 o'clock position;

    At that point (12 hours) all three should simultaneously align with the 12 o'clock position.
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  6. #6
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    Quote Originally Posted by aidan View Post
    I do not know what you are trying to do or how you are using the clock.
    The maps make no real sense or direct connection with the use of the clock.

    How do you get 4 days?
    Of the three hands:

    Each time the second hand rotates 1 full turn it aligns with the 12 (or 24 as shown);

    Each time the minute hand rotates 1 full turn it should align with the 12 o'clock position;

    Each time the hour hand rotates 1 full turn it should align with the 12 o'clock position;

    At that point (12 hours) all three should simultaneously align with the 12 o'clock position.
    The clock is used in the game as a layer on top of the maps, every time a part of the clocks hands sides passes over an area the value of the loot goes up in that area and when the same hand passes again with the other side it gets lowered again. the maps was provided to give the size of the continents to get the size of the sides of the clock and length of them also.

    And as i said i'm not very good at logical thinking but i thought that due to that the map is not totally square the hands would not be totally uniform or what one could call it and thus lag behind a bit on some places so they got slightly out of synch.
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