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Original file ‎(903 × 461 pixels, file size: 4.68 MB, MIME type: image/gif, looped, 240 frames, 4.8 s)

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Summary

Description

English: Two sets of gears. z₁=14 (red); z₂=42 (blue); z₃=14 (yellow); z₄=28 (green).

Français : Un train de deux engrenages : le premier, le pignon rouge et la roue bleue ; le second, le pignon orange et la roue verte.

Deutsch: Zwei Getriebestufen mit Zahnrädern. z₁ = 14 (rot); z₂=42 (blau); z₃ = 14 (gelb); z₄ = 28 (grün).

Antrieb links, Abtrieb rechts
i_Stufe1 = z₂ / z₁ = 42 / 14 = 3
i_Stufe2 = z₄ / z₃ = 24 / 14 = 2

i_Ges = i_Stufe1 · i_Stufe2 = 6

Date

5 December 2016

Source

Own work

Author

Jahobr

Other versions

static SVG version

GIF development

This diagram was created with MATLAB by Jahobr.

Source code

MATLAB code

Source code

function animatedGears()
% Source code for drawing gears
% The shape of the gears is not precise, it creates a decent GIF and a SVG.
%
% 2019-05-12 Jahobr

pathstr,fname = fileparts(which(mfilename)); % save files under the same name and at file location

RGB.bkgd   = 1   1   1  ]; % white background
RGB.black  = 0   0   0  ]; %
RGB.green  = 0.1 0.7 0.1]; %
RGB.yellow = 1   0.7 0  ]; %
RGB.blue   = 0.2 0.2 1  ]; %
RGB.red    = 1   0.2 0.2]; %
% violetRGB = [0.6 0.2 0.8]; %

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

figHandle = figure(15674459); clf
set(figHandle,'Units','pixel');
set(figHandle,'MenuBar','none',  'ToolBar','none'); % free real estate for a maximally large image
set(figHandle,'Color',RGB.bkgd); % white background
axesHandle = axes;
hold(axesHandle,'on')
axis off % invisible axes (no ticks)
axis equal;

for currentCase = 3:8
    switch currentCase
        case 1 % animatedGears
            saveName = 'animatedGears';
            nFrames = 240;
            
            teeth    = 14, 3*14, 14, 2*14];
            module   =  2,    2,  3,    3]; % gear size
            diameter = module.*teeth;
            
            center1 = 0                                       0];
            center2 = [(diameter(1)+diameter(2))/2             0];
            center3 = center2(1)+(diameter(3)+diameter(4))/2  0];
            
            xLimits = center1(1)-diameter(1)/2-2*module(1)           center3(1)+diameter(4)/2+module(4)+module(1)]; % use a rim of size "module(1)"
            yLimits = center3(2)-diameter(4)/2-module(4)-module(1)   center3(2)+diameter(4)/2+module(4)+module(1)]; % use a rim of size "module(1)"
            
            maxMovementOfTheSlowestTooth = 2*pi/teeth(4);
            anglesSlow = linspace(0,maxMovementOfTheSlowestTooth,nFrames+1);
            anglesSlow = anglesSlow(1:end-1); % remove last frame, it would be double
            secondRatio  = teeth(4)/teeth(3);
            anglesMedium = anglesSlow.*secondRatio;
            anglesMedium = anglesMedium + (2*pi/teeth(3)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            firstRatio = teeth(2)/teeth(1);
            anglesFast = anglesMedium.*firstRatio;
            anglesFast = anglesFast + (2*pi/teeth(1)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            
        case 2 % animated_3_Gear_Row
            saveName = 'animated_3_Gear_Row';
            nFrames  = 80;
            
            teeth    = 14, 2*14, 3*14];
            module   = 1,  1,    1]; % gear size
            diameter = module.*teeth;
            
            center1 = 0                                       0];
            center2 = [(diameter(1)+diameter(2))/2             0];
            center3 = center2(1)+(diameter(2)+diameter(3))/2  0];

            xLimits = center1(1)-diameter(1)/2-module(1)*2   center3(1)+diameter(3)/2+module(3)*2]; % use a rim of size "module(1)"
            yLimits = center3(2)-diameter(3)/2-module(3)*2   center3(2)+diameter(3)/2+module(3)*2];  % use a rim of size "module(1)"
            
            maxMovementOfTheSlowestTooth = 2*pi/teeth(3);
            anglesSlow = linspace(0,maxMovementOfTheSlowestTooth,nFrames+1);
            anglesSlow = anglesSlow(1:end-1); % remove last frame, it would be double
            secondRatio  = teeth(3)/teeth(2);
            anglesMedium = anglesSlow.*secondRatio;
            anglesMedium = anglesMedium + (2*pi/teeth(2)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            firstRatio = teeth(2)/teeth(1);
            anglesFast = anglesMedium.*firstRatio;
            anglesFast = anglesFast + (2*pi/teeth(1)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            
         case 3 % animated_internal_gear
            saveName = 'animated_internal_gear';
            nFrames  = 80;
            teeth    = 14, 3*14];

            module   = 1,  1]; % gear size
            diameter = module.*teeth;
            
            center1 = 0 (diameter(1)-diameter(2))/2];
            center2 = 0                           0];
            
            xLimits = center2(1)-diameter(2)/1.5   center2(1)+diameter(2)/1.5]; % 
            yLimits = center2(2)-diameter(2)/1.5   center2(2)+diameter(2)/1.5]; % 
            
            maxMovementOfTheSlowestTooth = 2*pi/teeth(2);
            anglesSlow = linspace(0,maxMovementOfTheSlowestTooth,nFrames+1);
            anglesSlow = anglesSlow(1:end-1); % remove last frame, it would be double
            ratio  = teeth(2)/teeth(1);
            anglesFast = anglesSlow.*ratio;
            anglesFast = anglesFast + (2*pi/teeth(1)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            
         case 4 % animated_rack_and_pinion
            saveName = 'animated_rack_and_pinion';
            nFrames  = 80;
            teeth    = 14, 2*14];

            module   = 1,  1]; % gear size
            diameter = module.*teeth;
            
            center1 = 0              0];
            center2 = 0 -diameter(1)/2];
            
            xLimits = center1(1)-diameter(1)*1.25       center1(1)+diameter(1)*1.25]; % 
            yLimits = center1(2)-diameter(1)   center1(2)+diameter(1)/2+module(1)*3]; % 
            
            maxMovementOfTheSlowestTooth = 2*pi/teeth(1);
            anglesSlow = linspace(0,maxMovementOfTheSlowestTooth,nFrames+1);
            anglesSlow = anglesSlow(1:end-1); % remove last frame, it would be double
            sideShift = anglesSlow.*diameter(1)/2;
            sideShift = sideShift + module(1)*3/8; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
            
        case 5 % animated_two_spur_gears
            saveName = 'animated_two_spur_gears_1_1';
            nFrames  = 80;
            teeth    = 14, 14];
            
        case 6 % animated_two_spur_gears
            saveName = 'animated_two_spur_gears_1_2';
            nFrames  = 80;
            teeth    = 14, 2*14];
            
        case 7 % animated_two_spur_gears
            saveName = 'animated_two_spur_gears_1_3';
            nFrames  = 80;
            teeth    = 14, 3*14];
            
        case 8 % animated_two_spur_gears
            saveName = 'animated_two_spur_gears_1_5';
            nFrames  = 80;
            teeth    = 14, 5*14];
    end
    
    if  contains(saveName,'animated_two_spur_gears') % all versions
        module   = 1,  1]; % gear size
        diameter = module.*teeth;
        
        center1 = 0                           0];
        center2 = [(diameter(1)+diameter(2))/2 0];
        
        xLimits = center1(1)-diameter(1)/2-module(1)*2   center2(1)+diameter(2)/2+module(2)*2]; % use a rim of size "module(1)"
        yLimits = center2(2)-diameter(2)/2-module(2)*2   center2(2)+diameter(2)/2+module(2)*2]; % use a rim of size "module(1)"
        
        maxMovementOfTheSlowestTooth = 2*pi/teeth(2);
        anglesSlow = linspace(0,maxMovementOfTheSlowestTooth,nFrames+1);
        anglesSlow = anglesSlow(1:end-1); % remove last frame, it would be double
        ratio  = teeth(2)/teeth(1);
        anglesFast = anglesSlow.*ratio;
        anglesFast = anglesFast + (2*pi/teeth(1)) *0.5; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
    end
    
    xRange = xLimits(2)-xLimits(1);
    yRange = yLimits(2)-yLimits(1);

    screenSize = get(groot,'Screensize')-0 0 5 20]; % [1 1 width height] (minus tolerance for figure borders)
    imageAspectRatio = xRange/yRange;
    MegaPixelTarget = 100*10^6; % Category:Animated GIF files exceeding the 100 MP limit
    pxPerImage = MegaPixelTarget/nFrames; % pixel per gif frame
    ySize = sqrt(pxPerImage/imageAspectRatio); % gif height
    xSize = ySize*imageAspectRatio; % gif width
    xSize = floor(xSize); ySize = floor(ySize); % full pixels
    scaleReduction = min(...% repeat as often as possible for nice antialiasing
        floor(screenSize(4)/ySize), floor(screenSize(3)/xSize)); 
    if scaleReduction == 0;   error('"MegaPixelTarget" not possible; use smaller target or bigger monitor'); end % check
    
    figPos = 1 1 xSize*scaleReduction ySize*scaleReduction]; % big start image for antialiasing later [x y width height]
    set(figHandle, 'Position', figPos); 
    if ~all(get(figHandle, 'Position') == figPos);   error('figure Position could not be set');   end % check

    setXYlim(axesHandle,xLimits,yLimits); % set limits and drawnow;
    
    reducedRGBimage = uint8(ones(ySize,xSize,3,nFrames)); % allocate

    liSc = mean([xSize ySize*scaleReduction)/350; % LineWidth scale; LineWidth is absolut, a bigger images needs thicker lines to keep them in proportion

    for iFrame = 1:nFrames
        cla(axesHandle)
        
        switch currentCase
            case 1 % animatedGears
                drawSpurWheel(center1,teeth(1),module(1),RGB.red   ,liSc,RGB.black,-anglesFast(iFrame));   % left cogwheel  (fast)
                drawSpurWheel(center2,teeth(2),module(2),RGB.blue  ,liSc,RGB.black, anglesMedium(iFrame)); % cogwheel  2 (center)
                drawSpurWheel(center2,teeth(3),module(3),RGB.yellow,liSc,RGB.black, anglesMedium(iFrame)); % cogwheel  3 (center)
                drawSpurWheel(center3,teeth(4),module(4),RGB.green ,liSc,RGB.black,-anglesSlow(iFrame));   % right cogwheel  (slow)
            case 2 % animated_3_Gear_Row
                drawSpurWheel(center1,teeth(1),module(1),RGB.red   ,liSc,RGB.black,-anglesFast(iFrame));   % left cogwheel  (fast)
                drawSpurWheel(center2,teeth(2),module(2),RGB.blue  ,liSc,RGB.black, anglesMedium(iFrame)); % cogwheel  2 (center)
                drawSpurWheel(center3,teeth(3),module(3),RGB.green ,liSc,RGB.black,-anglesSlow(iFrame));   % right cogwheel  (slow)
            case 3 % animated_internal gear
                drawSpurWheel(center1,teeth(1),module(1),RGB.red   ,liSc,RGB.black,-anglesFast(iFrame));   % left cogwheel  (fast)
                drawRingGear(teeth(2),module(2),RGB.green,liSc,RGB.black, -anglesSlow(iFrame));
            case 4 % animated_rack_and_pinion
                drawSpurWheel(center1,teeth(1),module(1),RGB.red   ,liSc,RGB.black,-anglesSlow(iFrame));   % left cogwheel  (fast)
                drawRack(center2,teeth(2),module(2),RGB.green,liSc,RGB.black,-sideShift(iFrame),0);
            case {5,6,7,8} % animated_two_spur_gears
                drawSpurWheel(center1,teeth(1),module(1),RGB.red   ,liSc,RGB.black,-anglesFast(iFrame));   % left cogwheel  (fast)
                drawSpurWheel(center2,teeth(2),module(2),RGB.green ,liSc,RGB.black, anglesSlow(iFrame));   % right cogwheel  (slow)
        end
        
        setXYlim(axesHandle,xLimits,yLimits); % reset limits and drawnow

        f = getframe(figHandle);
        reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % allows subpixel lines       
        
        if iFrame == 1 % SVG
            if ~isempty(which('plot2svg'))
                plot2svg(fullfile(pathstr, saveName '_Frame1.svg']),figHandle) % by Juerg Schwizer
            else
                disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
            end
        end
    end
    
    switch currentCase % 
        case 1 % animatedGears
            map = createImMap(reducedRGBimage,32,[RGB.bkgd; RGB.black; RGB.red; RGB.blue; RGB.yellow; RGB.green]); % colormap
        case 2 % animated_3_Gear_Row
            map = createImMap(reducedRGBimage,32,[RGB.bkgd; RGB.black; RGB.red; RGB.blue;             RGB.green]); % colormap
        case 3 % animated_internal gear
            map = createImMap(reducedRGBimage,16,[RGB.bkgd; RGB.black; RGB.red;                       RGB.green]); % colormap
        case 4 % animated_rack_and_pinion
            map = createImMap(reducedRGBimage,16,[RGB.bkgd; RGB.black; RGB.red;                       RGB.green]); % colormap
        case {5,6,7,8} % animated_two_spur_gears
            map = createImMap(reducedRGBimage,16,[RGB.bkgd; RGB.black; RGB.red;                       RGB.green]); % colormap
    end
    
    im = uint8(ones(ySize,xSize,1,nFrames)); % allocate
    for iFrame = 1:nFrames
        im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither');
    end
    
    imwrite(im,map,fullfile(pathstr, saveName '.gif']),'DelayTime',1/60,'LoopCount',inf) % save gif
    disp([saveName '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 100 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 Radius

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)

% % effective Radius
% [X,Y] = pol2cart(angleOffPoints,effectiveRadius);
% X = X+center(1); % center offset
% Y = Y+center(2); % center offset
% plot(X,Y,'-.','Color',linC);

%% shaft
shaftRadius = module*6 /2; % small radius, assuming the effective radius a 6-tooth wheel would have
X,Y = pol2cart(angleOffPoints,shaftRadius);
X = X+center(1); % center offset
Y = Y+center(2); % center offset
plot(X,Y,'LineWidth',linW,'Color',linC);
% plot(center(1),center(2),'.','Color',linC)


function drawRingGear(toothNumber,module,fillC,linW,linC,startOffset)
% DRAWRINGGEAR - draw a outer gear
%    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

%% outerEdge
maxRadius = rootRadius*1.2; % definition of outer line
Xout,Yout = pol2cart(angleOffPoints,maxRadius);

%% inner teeth
radiusOffPoints = angleOffPoints; % init

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

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);

Xout,Yout = poly2cw(Xout,Yout);
X,   Y    = poly2cw(X   ,Y   );
Xb,Yb = polybool('subtraction',Xout,Yout, X,Y);
Xb = Xb(~isnan(Xb)); % notNaN
Yb = Yb(~isnan(Yb)); % notNaN
patch(Xb,Yb,fillC,'EdgeColor','none')

plot(X,   Y,   'LineWidth',linW,'Color',linC); % draw teeth outline
plot(Xout,Yout,'LineWidth',linW,'Color',linC); % draw outer circle


function drawRack(center,toothNumber,module,fillC,linW,linC,startOffset,top)
%    center:       [x y]
%    toothNumber:  scalar
%    module:       scalar tooth "size"
%    fillC:        color of filling [r g b]
%    linW:         LineWidth
%    linC:         LineColor
%    startOffset: initial shift
%    top:         1=top 0=bottom
x = (0:toothNumber*4-2)*pi*module/4;
x = x-mean(x)+center(1)+startOffset;

y = zeros(size(x));

y(1:4:end) = y(1:4:end)+1.1*module; %    +###I bottom
y(2:4:end) = y(2:4:end)-1  *module; % +######I tip
y(3:4:end) = y(3:4:end)-1  *module; % +######I tip
y(4:4:end) = y(4:4:end)+1.1*module; %    +###I bottom

x(1:4:end) = x(1:4:end)-0.14*module; % bottom smaller
x(2:4:end) = x(2:4:end)+0.14*module; % tip smaller
x(3:4:end) = x(3:4:end)-0.14*module; % tip smaller
x(4:4:end) = x(4:4:end)+0.14*module; % bottom smaller

x = x(1)     x  x(end)];
y = 5*module y  5*module];

if ~top
    y = -y; % flip
end
y = y+center(2);
patch(x,y,fillC,'EdgeColor',linC,'LineWidth',linW);


function setXYlim(axesHandle,xLimits,yLimits)
% set limits; practically the axis overhangs the figure all around, to
% hide rendering error at line-ends.
% Input:
%   axesHandle:        
%   xLimits, yLimits:  [min max]
overh = 0.05; % 5% overhang all around; 10% bigger in x and y
xlim([+xLimits(1)*(1+overh)-xLimits(2)*overh  -xLimits(1)*overh+xLimits(2)*(1+overh)])
ylim([+yLimits(1)*(1+overh)-yLimits(2)*overh  -yLimits(1)*overh+yLimits(2)*(1+overh)])
set(axesHandle,'Position',[-overh -overh  1+2*overh 1+2*overh]); % stretch axis as bigger as figure, [x y width height]
drawnow;


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];

Licensing

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	The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. CC0falsefalse

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File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	15:33, 12 May 2019	903 × 461 (4.68 MB)	Jahobr	higher resolution
	15:32, 12 May 2019	815 × 420 (1.23 MB)	Jahobr	higher resolution
	15:31, 12 May 2019	1,546 × 808 (2.4 MB)	Jahobr	higher resolution
	08:15, 11 December 2016	815 × 420 (1.1 MB)	Jahobr	Reverted to version as of 08:10, 11 December 2016 (UTC). I could not solve the color-render-errors. This is the best version
	08:12, 11 December 2016	815 × 420 (958 KB)	Jahobr	Reverted to version as of 08:04, 11 December 2016 (UTC)
	08:10, 11 December 2016	815 × 420 (1.1 MB)	Jahobr	32 colores intead of 16
	08:04, 11 December 2016	815 × 420 (958 KB)	Jahobr	try to get rid of flicker (25 fps. colores changed)
	19:09, 7 December 2016	800 × 400 (1.17 MB)	Jahobr	fixed rim
	18:56, 7 December 2016	800 × 400 (1.21 MB)	Jahobr	teeth smoother
	14:23, 5 December 2016	800 × 400 (1.41 MB)	Jahobr	User created page with UploadWizard