File:LissajousCurvesWithGears a1 b2 p00 p025 p05.gif

function [] = LissajousCurvesWithGears()
% Source code for drawing gears that produce lissajous curves.
% The shape of the gears is not precise, it creates a decent GIF and a SVG.
%
% 2017-05-01 Jahobr

module = 1; % gear size
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location

RGB.black      = [0   0   0  ];
RGB.white      = [1   1   1  ];
RGB.cyan       = [0   0.6 0.7]; % for phase shift 0.125
RGB.green      = [0   0.7 0  ]; % for phase shift 0.25
RGB.blue       = [0   0   1  ]; % for phase shift 0.5
RGB.red        = [1   0   0  ]; % for phase shift 0.0
RGB.violet     = [0.6 0.2 0.8]; % for horizontal line
RGB.brightGrey = [0.8 0.8 0.8]; % upper two Idler & "LeftRight gear"
RGB.grey       = [0.5 0.5 0.5]; % lower left "UpDown gear"

RGB.paleCyan   = 1-(1-RGB.cyan)  *0.85; % dotted line
RGB.paleGreen  = 1-(1-RGB.green) *0.85; % dotted line 
RGB.paleBlue   = 1-(1-RGB.blue)  *0.85; % dotted line 
RGB.paleRed    = 1-(1-RGB.red)   *0.85; % dotted line 
RGB.paleViolet = 1-(1-RGB.violet)*0.85; % dotted line 

RGB.violetGreyMix1 = sqrt(mean([RGB.paleViolet.^2;RGB.grey.^2;      RGB.grey.^2],1)); % experience shows that matlab does not create...
RGB.violetGreyMix2 = sqrt(mean([RGB.paleViolet.^2;RGB.paleViolet.^2;RGB.grey.^2],1)); %...nice mix colors in this combination; enforced

RGB = structfun(@(q)round(q*255)/255, RGB, 'UniformOutput',false); % round to values that are nicely uint8 compatible

versionList ={};
versionList{end+1} = 'a1_b1_p00';
versionList{end+1} = 'a1_b1_p025';
versionList{end+1} = 'a1_b1_p05';
versionList{end+1} = 'a1_b1_p00_p025_p05';
versionList{end+1} = 'a1_b2_p00';
versionList{end+1} = 'a1_b2_p025';
versionList{end+1} = 'a1_b2_p05';
versionList{end+1} = 'a1_b2_p00_p025_p05';
versionList{end+1} = 'a1_b3_p00';
versionList{end+1} = 'a1_b3_p025';
versionList{end+1} = 'a1_b3_p05';
versionList{end+1} = 'a1_b3_p00_p025_p05';
versionList{end+1} = 'a1_b4_p00';
versionList{end+1} = 'a1_b4_p025';
versionList{end+1} = 'a1_b4_p05';
versionList{end+1} = 'a1_b4_p00_p025_p05';
versionList{end+1} = 'a2_b3_p00';
versionList{end+1} = 'a2_b3_p0125';
versionList{end+1} = 'a2_b3_p025';
versionList{end+1} = 'a2_b3_p00_p0125_p025';
versionList{end+1} = 'a3_b4_p00';
versionList{end+1} = 'a3_b4_p025';
versionList{end+1} = 'a3_b4_p05';
versionList{end+1} = 'a3_b4_p00_p025_p05';

for versionNr = 1:numel(versionList)
    curVers = versionList{versionNr};
    
    switch curVers(1:5)
        case 'a1_b1'
            a=1; b=1;
            teeth = [48*a/b 48 48]; % [leftBottom leftTop rightTop]
        case 'a1_b2'
            a=1; b=2;
            teeth = [48*a/b 48 48]; % [leftBottom leftTop rightTop]
        case 'a1_b3'
            a=1; b=3;
            teeth = [48*a/b 50 48]; % [leftBottom leftTop rightTop]
        case 'a1_b4'
            a=1; b=4;
            teeth = [48*a/b 50 48]; % [leftBottom leftTop rightTop]
        case 'a2_b3'
            a=2; b=3;
            teeth = [48*a/b 48 48]; % [leftBottom leftTop rightTop]
        case 'a3_b4'
            a=3; b=4;
            teeth = [48*a/b 48 48]; % [leftBottom leftTop rightTop]
        otherwise
            error('not defined')
    end
    ratio = a/b; 
    rotToRepetition = lcm(a,b)/a; % Least common multiple, to produce a closed curve
    nFrames = 180*rotToRepetition; % 180 frames per rotation
    MegaPixelTarget = 100*10^6; % Category:Animated GIF files exceeding the 100 MP limit
    xySize = floor(sqrt(MegaPixelTarget/nFrames)); %  gif size in pixel
    screenSize = get(groot,'Screensize')-[0 0 5 20]; % [1 1 width height] (minus tolerance for figure borders)
    scaleReduction = min(...% reduction for nice antialiasing (for >1 you need a 4K monitor or a virtural combination of several monitors using "Nvidia Surround" to fit the figure)
        floor(screenSize(4)/xySize), floor(screenSize(3)/xySize)); 
    if scaleReduction == 0;   error('"MegaPixelTarget" not possible; use smaller target or bigger monitor'); end % check
    
    diameter = module.*teeth;
    
    %      ---     ---
    %    /  2  \ /  3  \
    %   ( Idler X   LR  ) Left-Right-Wheel
    %    \     / \     /
    %     >---<    ---
    %    /  1  \
    %   (   UD  )   + 0/0 of coordinates
    %    \     /
    %      --- Up-Down-Wheel
    
    center_UD_wheel = [-diameter(3) 0]; % wheel for Up-Down movement
    center_LR_wheel = [0  diameter(3)]; % wheel for Left-Right movement
    [xout,yout] = circcirc(center_UD_wheel(1),center_UD_wheel(2),mean(diameter(1:2)),center_LR_wheel(1),center_LR_wheel(2),mean(diameter(2:3))); % Intersections
    [centerIdler(2),ind] = max(yout);
    centerIdler(1) = xout(ind);

    
    figPosition = [1 1 xySize*scaleReduction xySize*scaleReduction]; % big start image for antialiasing later [x y width height]
    figHandle = figure(15554461); clf
    axesHandle = axes; hold(axesHandle,'on')
    set(figHandle,'Units','pixel');
    set(figHandle,'MenuBar','none',  'ToolBar','none'); % free real estate for a maximally large image
    set(figHandle,'Position',figPosition); % big start image; reduction allows for subpixel LineWidth
    set(figHandle,'GraphicsSmoothing','on') % requires at least version 2014b
    set(figHandle,'Color',RGB.white); % white background
    drawnow
    if ~all(get(figHandle, 'Position')==figPosition)
        error('figure Position could not be set')
    end
    liSc = xySize*scaleReduction/1000; % LineWidth scale; LineWidth is absolut, a bigger images needs thicker lines to keep them in proportion

    xLimits = [-1.55  0.55]*diameter(3); % ADJUST
    yLimits = [-0.55  1.55]*diameter(3); % ADJUST
    set(axesHandle,'Position',[0 0 1 1]); % stretch axis as big as figure, [x y width height]
    xlim(xLimits); ylim(yLimits); % set axis limits
    axis off % invisible axes (no ticks)
    axis equal; drawnow;
    
    angles_UD_wheel = linspace(0, rotToRepetition *2*pi,nFrames+1); % angles for wheel responsible for Up-Down
    angles_UD_wheel = angles_UD_wheel(1:end-1); % remove last frame, it would be double
    nShift = find(angles_UD_wheel>pi/6,1,'first');
    angles_UD_wheel = circshift(angles_UD_wheel,nShift,2); % shift a view frames to get good visibility of all lines in frame 1
    
    idlerRatio  = teeth(1)/teeth(2);
    anglesIdler = angles_UD_wheel.*idlerRatio;
    angles_LR_wheel = angles_UD_wheel*ratio;
    
    switch curVers(1:5)
        case 'a1_b1'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *0;   % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        case 'a1_b2'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *-0.01; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *0.36; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        case 'a1_b3'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *0.43; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *-0.21; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        case 'a1_b4'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *-0.34; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *-0.29; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        case 'a2_b3'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *-0.29; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *-0.23; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        case 'a3_b4'
            anglesIdlerToothAllign  = anglesIdler + (2*pi/teeth(2)) *0.62; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            angles_LR_wheelToothAllign = angles_LR_wheel +(2*pi/teeth(3)) *0.03; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
        otherwise
            error('not defined')
    end
    
    curvePoints = linspace(0,2*pi,500);
    yCurvePoints00   = NaN(size(curvePoints)); % defaults
    yCurvePoints0125 = NaN(size(curvePoints)); % defaults
    yCurvePoints025  = NaN(size(curvePoints)); % defaults
    yCurvePoints05   = NaN(size(curvePoints)); % defaults
    
    if contains(curVers,'p00')   % Phase shift 0
        yCurvePoints00   = sin(b*curvePoints     )*0.9*diameter(3)/2; % Lissajous curve
    end
    if contains(curVers,'p0125') % Phase shift 1/8*pi = 0.125*pi
        yCurvePoints0125 = sin(b*curvePoints-pi/8)*0.9*diameter(3)/2; % Lissajous curve
    end
    if contains(curVers,'p025')  % Phase shift 1/4*pi = 0.25*pi
        yCurvePoints025  = sin(b*curvePoints-pi/4)*0.9*diameter(3)/2; % Lissajous curve
    end
    if contains(curVers,'p05')   % Phase shift 1/2*pi = 0.5*pi
        yCurvePoints05   = sin(b*curvePoints-pi/2)*0.9*diameter(3)/2; % Lissajous curve
    end
    
    
    xCurvePoints  = sin(a*    curvePoints     )*0.9*diameter(3)/2; % Lissajous curve
    
    x_y_Crank = [-module*2 -module*2 0.9*diameter(3)/2+module 0.9*diameter(3)/2+module;...
        -module*2  module*2           module                  -module];
    
    anglesPSmakerXw = linspace(0,pi,64+1)*ratio-pi/2; % marker for possible phase shifts

    reducedRGBimage = ones(xySize,xySize,3,nFrames, 'uint8'); % allocate
    
    for iFrame = 1:nFrames
        cla(axesHandle)
        
        plot([-1 0.51]*diameter(3),[ 0  0   ]*diameter(3),'-','Color',RGB.brightGrey,'LineWidth',3*liSc) % horizontal coordinateSystem
        plot([ 0  0  ]*diameter(3),[1  -0.51]*diameter(3),'-','Color',RGB.brightGrey,'LineWidth',3*liSc) % vertival coordinateSystem
        
        drawSpurWheel(center_UD_wheel,teeth(1),module,RGB.grey      ,2.5*liSc,RGB.black, angles_UD_wheel(iFrame)); % Up-Down-Wheel [at lower left]  (fast)
        drawSpurWheel(centerIdler,    teeth(2),module,RGB.brightGrey,2.5*liSc,RGB.black,-anglesIdlerToothAllign(iFrame)); % Idler-Wheel [at top left]
        drawSpurWheel(center_LR_wheel,teeth(3),module,RGB.brightGrey,2.5*liSc,RGB.black, angles_LR_wheelToothAllign(iFrame)); % Left-Right-Wheel [at top right] (slow)
        
        x_UD_Crank = cos(angles_UD_wheel(iFrame))*0.9*diameter(3)/2+center_UD_wheel(1); % Up-Down-Wheel
        y_UD_Crank = sin(angles_UD_wheel(iFrame))*0.9*diameter(3)/2+center_UD_wheel(2); % Up-Down-Wheel
        
        if ratio < 1 % draw extra crank
            rotM = [cos(angles_UD_wheel(iFrame)) -sin(angles_UD_wheel(iFrame)); -sin(-angles_UD_wheel(iFrame)) cos(angles_UD_wheel(iFrame))]; % rotation matrix
            vecTemp = rotM*x_y_Crank; % rotate crank
            patch(vecTemp(1,:)+center_UD_wheel(1),vecTemp(2,:)+center_UD_wheel(2),RGB.grey,'EdgeColor',RGB.black,'LineWidth',2*liSc) % raw the crank trapezoid
        end
        
        x_LR_Crank00   = NaN; y_LR_Crank00   = NaN; % Left-Right-Wheel (defaults)
        x_LR_Crank0125 = NaN; y_LR_Crank0125 = NaN; % Left-Right-Wheel (defaults)
        x_LR_Crank025  = NaN; y_LR_Crank025  = NaN; % Left-Right-Wheel (defaults)
        x_LR_Crank05   = NaN; y_LR_Crank05   = NaN; % Left-Right-Wheel (defaults)
        
        if contains(curVers,'p00') % Phase shift 0
            x_LR_Crank00   =  sin(           angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(1); % Left-Right-Wheel (if used)
            y_LR_Crank00   = -cos(           angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(2); % Left-Right-Wheel (if used)
        end
        if contains(curVers,'p0125') % Phase shift 1/8*pi = 0.125*pi
            x_LR_Crank0125 =  sin(pi/8*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(1); % Left-Right-Wheel (if used)
            y_LR_Crank0125 = -cos(pi/8*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(2); % Left-Right-Wheel (if used)
        end
        if contains(curVers,'p025') % Phase shift 1/4*pi = 0.25*pi
            x_LR_Crank025  =  sin(pi/4*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(1); % Left-Right-Wheel (if used)
            y_LR_Crank025  = -cos(pi/4*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(2); % Left-Right-Wheel (if used)
        end
        if contains(curVers,'p05') % Phase shift 1/2*pi = 0.5*pi
            x_LR_Crank05   =  sin(pi/2*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(1); % Left-Right-Wheel (if used)
            y_LR_Crank05   = -cos(pi/2*ratio+angles_LR_wheel(iFrame))*0.9*diameter(3)/2+center_LR_wheel(2); % Left-Right-Wheel (if used)
        end
        
        plot([center_UD_wheel(1) x_UD_Crank ],[center_UD_wheel(2) y_UD_Crank ],'-','Color',RGB.black ,'LineWidth',3*liSc) % base line
        plot([0 sin(angles_LR_wheel(iFrame))*0.9*diameter(3)/2]+center_LR_wheel(1),[0 -cos(angles_LR_wheel(iFrame))*0.9*diameter(3)/2]+center_LR_wheel(2),'-','Color',RGB.black,'LineWidth',3*liSc) % base line
        
        for mark = 1:a-1
            [X,Y] = pol2cart(2*mark*pi/a +angles_UD_wheel(iFrame),[0.9 0.6]*diameter(1)/2);
            X = X+center_UD_wheel(1); % center offset
            Y = Y+center_UD_wheel(2); % center offset
            plot(X,Y,'-','Color',RGB.black,'LineWidth',3*liSc) % rotation marker line
        end
        
        for mark = 1:b-1
            [X,Y] = pol2cart(2*mark*pi/b +angles_LR_wheel(iFrame)-pi/2,[0.9 0.6]*diameter(3)/2);
            X = X+center_LR_wheel(1); % center offset
            Y = Y+center_LR_wheel(2); % center offset
            plot(X,Y,'-','Color',RGB.black,'LineWidth',3*liSc) % rotation marker line
        end
        
        [X,Y] = pol2cart(anglesPSmakerXw+angles_LR_wheel(iFrame),0.9*diameter(3)/2);
        X = X+center_LR_wheel(1); % center offset
        Y = Y+center_LR_wheel(2); % center offset
        plot(X,Y,'-','Color',RGB.grey,'LineWidth',5*liSc) % marker for possible phase shifts
        plot(X(1:8:end), Y(1:8:end) ,'.','Color',RGB.grey,'MarkerSize',30*liSc) % marker for possible phase shifts
        plot(X(1:16:end),Y(1:16:end),'.','Color',RGB.grey,'MarkerSize',45*liSc) % marker for possible phase shifts
        
        plot(xCurvePoints,yCurvePoints0125,'-','Color',RGB.cyan ,'LineWidth',5*liSc) % Lissajous curve
        plot(xCurvePoints,yCurvePoints025, '-','Color',RGB.green,'LineWidth',5*liSc) % Lissajous curve
        plot(xCurvePoints,yCurvePoints05,  '-','Color',RGB.blue ,'LineWidth',5*liSc) % Lissajous curve
        plot(xCurvePoints,yCurvePoints00,  '-','Color',RGB.red  ,'LineWidth',5*liSc) % Lissajous curve
        
        plot([x_UD_Crank max(max(x_LR_Crank00,x_LR_Crank0125),max(x_LR_Crank025,x_LR_Crank05))],[y_UD_Crank y_UD_Crank],':','Color',RGB.paleViolet,'LineWidth',6*liSc) % left crank  to curve
             
        plot([x_LR_Crank0125 x_LR_Crank0125],[y_LR_Crank0125 y_UD_Crank],'.:','Color',RGB.paleCyan, 'LineWidth',6*liSc,'MarkerEdgeColor',RGB.cyan ,'MarkerSize',55*liSc) % crank to curve - verical
        plot([x_LR_Crank025  x_LR_Crank025], [y_LR_Crank025  y_UD_Crank],'.:','Color',RGB.paleGreen,'LineWidth',6*liSc,'MarkerEdgeColor',RGB.green,'MarkerSize',55*liSc) % crank to curve - verical
        plot([x_LR_Crank05   x_LR_Crank05],  [y_LR_Crank05   y_UD_Crank],'.:','Color',RGB.paleBlue, 'LineWidth',6*liSc,'MarkerEdgeColor',RGB.blue ,'MarkerSize',55*liSc) % crank to curve - verical
        plot([x_LR_Crank00   x_LR_Crank00],  [y_LR_Crank00   y_UD_Crank],'.:','Color',RGB.paleRed,  'LineWidth',6*liSc,'MarkerEdgeColor',RGB.red  ,'MarkerSize',55*liSc) % crank to curve - verical
        
        plot(x_UD_Crank,y_UD_Crank ,'.','Color',RGB.violet,'MarkerSize',55*liSc) % color marker on crank
        plot([x_LR_Crank00 x_LR_Crank0125 x_LR_Crank025 x_LR_Crank05],[y_UD_Crank y_UD_Crank y_UD_Crank y_UD_Crank],'o','Color',RGB.violet,'MarkerSize',16*liSc,'LineWidth',4*liSc) % traking points on top of the curve
        
        %% save animation
        xlim(xLimits); ylim(yLimits); % set axis limits
        drawnow
        %  pause(0.01)
        
        if iFrame == 1 % save svg
        %         if ~isempty(which('plot2svg'))
        %             posSave = get(figHandle, 'Position');
        %             set(figHandle, 'Position',[1 1 800 800]); % big start image for antialiasing later [x y width height]
        %             plot2svg(fullfile(pathstr, [fname '_' curVers '.svg']),figHandle) % by Juerg Schwizer
        %             set(figHandle, 'Position',posSave); % reset size
        %         else
        %             disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
        %         end
        end

        f = getframe(figHandle);
        reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % allows subpixel lines
   
    end

    if numel(strfind(curVers,'p')) >= 3 % many curves at once
        nColors = 64;
    else
        nColors = 32;
    end
    
    RGBcurrent = RGB; % copy colormap; to be pruned to the used colors
    if isnan(x_LR_Crank0125)
        RGBcurrent = rmfield(RGBcurrent,{'cyan','paleCyan'}); % remove unused colors
    end
    if isnan(x_LR_Crank025)
        RGBcurrent = rmfield(RGBcurrent,{'green','paleGreen'}); % remove unused colors
    end
    if isnan(x_LR_Crank05)
        RGBcurrent = rmfield(RGBcurrent,{'blue','paleBlue'}); % remove unused colors
    end
    if isnan(x_LR_Crank00)
        RGBcurrent = rmfield(RGBcurrent,{'red','paleRed'}); % remove unused colors
    end

    startMap = cell2mat(struct2cell(RGBcurrent)); % struct2colormap; % list of map colors that are not allowed to be changed
    map = createImMap(reducedRGBimage,nColors,startMap);  % full colormap
    im = uint8(ones(xySize,xySize,1,nFrames)); % allocate
    
    for iFrame = 1:nFrames
        im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'); % rgb to colormap image
    end
    
    imwrite(im,map,fullfile(pathstr, [fname '_' curVers '.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif
    disp([fname '_' curVers '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
end

function drawSpurWheel(center,toothNumber,module,fillC,linW,linC,startOffset)
% DRAWSPURWHEEL - draw a simple Toothed Wheel
%    center:       [x y]
%    toothNumber:  scalar
%    module:       scalar tooth "size"
%    fillC:   color of filling [r g b]
%    linW:         LineWidth
%    linC:         LineColor
%    startOffset:  start rotation (scalar)[rad]

effectiveRadius = module*toothNumber/2; % effective effectiveRadius

outsideRadius =     effectiveRadius+1*  module; %                +---+             +---+
upperRisingRadius = effectiveRadius+0.5*module; %               /     \           /     \
% effective Radius                              %              /       \         /       \
lowerRisingRadius = effectiveRadius-0.5*module; %             I         I       I         I
rootRadius =        effectiveRadius-1.1*module; %     + - - - +         + - - - +         +

angleBetweenTeeth = 2*pi/toothNumber; % angle between 2 teeth

angleOffPoints = (0:angleBetweenTeeth/16:(2*pi));


angleOffPoints = angleOffPoints+startOffset; % apply rotation offset

angleOffPoints(7:16:end) =  angleOffPoints(7:16:end)  + 1/toothNumber^1.2; % hack to create smaller tooth tip
angleOffPoints(11:16:end) = angleOffPoints(11:16:end) - 1/toothNumber^1.2; % hack to create smaller tooth tip

angleOffPoints(8:16:end)  = (angleOffPoints(7:16:end) +  angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly
angleOffPoints(10:16:end) = (angleOffPoints(11:16:end) + angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly

angleOffPoints(6:16:end) =  angleOffPoints(6:16:end)  + 1/toothNumber^1.7; % hack to create slender upperRisingRadius
angleOffPoints(12:16:end) = angleOffPoints(12:16:end) - 1/toothNumber^1.7; % hack to create slender upperRisingRadius

radiusOffPoints = angleOffPoints; % allocate with correct site

radiusOffPoints(1:16:end)  = rootRadius;        % center bottom         I
radiusOffPoints(2:16:end)  = rootRadius;        % left bottom           I
radiusOffPoints(3:16:end)  = rootRadius;        % left bottom corner    +
radiusOffPoints(4:16:end)  = lowerRisingRadius; % lower rising bottom      \
radiusOffPoints(5:16:end)  = effectiveRadius;   % rising edge                 \
radiusOffPoints(6:16:end)  = upperRisingRadius; % upper rising edge              \
radiusOffPoints(7:16:end)  = outsideRadius;     % right top  corner                 +
radiusOffPoints(8:16:end)  = outsideRadius;     % right top                         I
radiusOffPoints(9:16:end)  = outsideRadius;     % center top                        I
radiusOffPoints(10:16:end) = outsideRadius;     % left top                          I
radiusOffPoints(11:16:end) = outsideRadius;     % left top  corner                  +
radiusOffPoints(12:16:end) = upperRisingRadius; % upper falling edge             /
radiusOffPoints(13:16:end) = effectiveRadius;   % falling edge                /
radiusOffPoints(14:16:end) = lowerRisingRadius; % lower falling edge       /
radiusOffPoints(15:16:end) = rootRadius;        % right bottom  corner  +
radiusOffPoints(16:16:end) = rootRadius;        % right bottom          I

[X,Y] = pol2cart(angleOffPoints,radiusOffPoints);
X = X+center(1); % center offset
Y = Y+center(2); % center offset
patch(X,Y,fillC,'EdgeColor',linC,'LineWidth',linW)
plot(X,Y,'.','MarkerSize',2*linW,'Color',linC); % extra dots make corners look smoother


% %% effective Radius
% circle(center(1),center(2),effectiveRadius,linC,'-.',linW);

%% shaft
shaftRadius = module*6 /2; % small radius, assuming the effective radius a 6-tooth wheel would have
circle(center(1),center(2),shaftRadius,linC,'-',linW);


function h = circle(x,y,r,col,sty,linW)
% x:    coordinates of the center
% y:    coordinates of the center
% r:    is the radius of the circle
% sty:  LineStyle
% linW: LineWidth
angleOffPoints = linspace(0,2.001*pi,300);
xc = x + r*cos(angleOffPoints);
yc = y + r*sin(angleOffPoints);
h = plot(xc,yc,'Color',col,'LineWidth',linW,'LineStyle',sty);


function im = imReduceSize(im,redSize)
% Input:
%  im:      image, [imRows x imColumns x nChannel x nStack] (unit8)
%                      imRows, imColumns: must be divisible by redSize
%                      nChannel: usually 3 (RGB) or 1 (grey)
%                      nStack:   number of stacked images
%                                usually 1; >1 for animations
%  redSize: 2 = half the size (quarter of pixels)
%           3 = third the size (ninth of pixels)
%           ... and so on
% Output:
%  im:     [imRows/redSize x imColumns/redSize x nChannel x nStack] (unit8)
%
% an alternative is : imNew = imresize(im,1/scaleReduction ,'bilinear');
%        BUT 'bicubic' & 'bilinear'  produces fuzzy lines
%        IMHO this function produces nicer results as "imresize"
 
[nRow,nCol,nChannel,nStack] = size(im);

if redSize==1;  return;  end % nothing to do
if redSize~=round(abs(redSize));             error('"redSize" must be a positive integer');  end
if rem(nRow,redSize)~=0;     error('number of pixel-rows must be a multiple of "redSize"');  end
if rem(nCol,redSize)~=0;  error('number of pixel-columns must be a multiple of "redSize"');  end

nRowNew = nRow/redSize;
nColNew = nCol/redSize;

im = double(im).^2; % brightness rescaling from "linear to the human eye" to the "physics domain"; see youtube: /watch?v=LKnqECcg6Gw
im = reshape(im, nRow, redSize, nColNew*nChannel*nStack); % packets of width redSize, as columns next to each other
im = sum(im,2); % sum in all rows. Size of result: [nRow, 1, nColNew*nChannel]
im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image. Size of result: [nColNew*nChannel, nRow, 1]
im = reshape(im, nColNew*nChannel*nStack, redSize, nRowNew); % packets of width redSize, as columns next to each other
im = sum(im,2); % sum in all rows. Size of result: [nColNew*nChannel, 1, nRowNew]
im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image back. Size of result: [nRowNew, nColNew*nChannel, 1]
im = reshape(im, nRowNew, nColNew, nChannel, nStack); % putting all channels (rgb) back behind each other in the third dimension
im = uint8(sqrt(im./redSize^2)); % mean; re-normalize brightness: "scale linear to the human eye"; back in uint8


function map = createImMap(imRGB,nCol,startMap)
% createImMap creates a color-map including predefined colors.
% "rgb2ind" creates a map but there is no option to predefine some colors,
%         and it does not handle stacked images.
% Input:
%   imRGB:     image, [imRows x imColumns x 3(RGB) x nStack] (unit8)
%   nCol:      total number of colors the map should have, [integer]
%   startMap:  predefined colors; colormap format, [p x 3] (double)

imRGB = permute(imRGB,[1 2 4 3]); % step1; make unified column-image (handling possible nStack)
imRGBcolumn = reshape(imRGB,[],1,3,1); % step2; make unified column-image

fullMap = double(permute(imRGBcolumn,[1 3 2]))./255; % "column image" to color map 
[fullMap,~,imMapColumn] = unique(fullMap,'rows'); % find all unique colors; create indexed colormap-image
% "cmunique" could be used but is buggy and inconvenient because the output changes between "uint8" and "double"

nColFul = size(fullMap,1);
nColStart = size(startMap,1);
disp(['Number of colors: ' num2str(nColFul) ' (including ' num2str(nColStart) ' self defined)']);

if nCol<=nColStart;  error('Not enough colors');        end
if nCol>nColFul;   warning('More colors than needed');  end

isPreDefCol = false(size(imMapColumn)); % init
 
for iCol = 1:nColStart
    diff = sum(abs(fullMap-repmat(startMap(iCol,:),nColFul,1)),2); % difference between a predefined and all colors
    [mDiff,index] = min(diff); % find matching (or most similar) color
    if mDiff>0.05 % color handling is not precise
        warning(['Predefined color ' num2str(iCol) ' does not appear in image'])
        continue
    end
    isThisPreDefCol = imMapColumn==index; % find all pixel with predefined color
    disp([num2str(sum(isThisPreDefCol(:))) ' pixel have predefined color ' num2str(iCol)]);
    isPreDefCol = or(isPreDefCol,isThisPreDefCol); % combine with overall list
end
[~,mapAdditional] = rgb2ind(imRGBcolumn(~isPreDefCol,:,:),nCol-nColStart,'nodither'); % create map of remaining colors
map = [startMap;mapAdditional];