Archivo:Rose Curve animation with Gears n1 d1.gif
Tamaño de esta previsualización: 313 × 598 píxeles. Otras resoluciones: 125 × 240 píxeles · 511 × 977 píxeles.
Ver la imagen en su resolución original (511 × 977 píxeles; tamaño de archivo: 4,37 MB; tipo MIME: image/gif, bucleado, 200 frames, 10s)
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Resumen
DescripciónRose Curve animation with Gears n1 d1.gif |
English: Rose crated with gears.
The figures shape is determined by the gear ratio between the upper and the lower wheel.
Deutsch: Rosette erstellt mit Zahnrädern.
Die Figur ergibt sich aus dem Übersetzungsverhältnis zwischen dem oberen und dem unteren Rad.
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Fecha | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Fuente | Trabajo propio | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Autor | Jahobr | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Otras versiones |
[editar]
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GIF desarrollo InfoField | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Código fuente InfoField | MATLAB codefunction [] = Rose_Curve_animation_with_Gears()
% The shape of the gears is not precise, it creates a decent GIF and a SVG.
% The image is rendered horizontally, but saved rotated vertical.
% This allows the rendering of bigger base images,
% and therefor better (self made) antialiasing.
% The plot option "GraphicsSmoothing" made this partly redundant.
%
% After rendering the first frame gets a display time of 0.4 sec and
% the last frame of 2 sec (using "Jasc Animation Shop").
%
% 2017-07-12 Jahobr (update 2019-04-14 Jahobr)
RGB.black = [0 0 0 ];
RGB.white = [1 1 1 ];
RGB.red = [1 0 0 ];
RGB.blue = [0 0 1 ];
RGB.darkBlue = RGB.blue/1.5;
RGB.brightGrey = [0.8 0.8 0.8]; % gear
RGB.grey = [0.5 0.5 0.5]; % gear
RGB.darkGrey = [0.3 0.3 0.3]; % coordinate system
RGB = structfun(@(q)round(q*255)/255, RGB, 'UniformOutput',false); % round to values that are nicely uint8 compatible
versionList = [... % [n1 d1; n2 d2; ...]
1 1; ...
1 2; ...
1 3; ...
1 4; ...
1 5; ...
1 6; ...
1 7; ...
1 8; ...
1 9; ...
1 10;...
2 1; ...
% 2 2; ... % see [1 1];
2 3; ...
% 2 4; ... % see [1 2];
2 5; ...
% 2 6; ... % see [1 3];
2 7; ...
% 2 8; ... % see [1 4];
2 9; ...
% 2 10;... % see [1 5];
3 1; ...
3 2; ...
% 3 3; ... % see [1 1];
3 4; ...
3 5; ...
% 3 6; ... % see [1 2];
3 7; ...
3 8; ...
% 3 9; ... % see [1 3];
3 10;...
4 1; ...
% 4 2; ... % see [2 1];
4 3; ...
% 4 4; ... % see [1 1];
4 5; ...
% 4 6; ... % see [2 3];
4 7; ...
% 4 8; ... % see [1 2];
4 9; ...
% 4 10;... % see [2 5];
5 1; ...
5 2; ...
5 3; ...
5 4; ...
% 5 5; ... % see [1 1];
5 6; ...
5 7; ...
5 8; ...
5 9; ...
% 5 10;... % see [1 2];
6 1; ...
% 6 2; ... % see [3 1];
% 6 3; ... % see [2 1];
% 6 4; ... % see [3 2];
6 5; ...
% 6 6; ... % see [1 1];
6 7; ...
% 6 8; ... % see [3 4];
% 6 9; ... % see [2 3];
% 6 10;... % see [3 5];
];
module = 1; % gear size
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
figHandle = figure(15554461);
clf
set(figHandle,'Units','pixel');
set(figHandle,'MenuBar','none', 'ToolBar','none'); % free real estate for a maximally large image
set(figHandle,'Color',RGB.white); % white background
axesHandle = axes;
hold(axesHandle,'on')
axis equal
axis off % invisible axes (no ticks)
drawnow;
for versionNr = 1:size(versionList,1)
curVers = ['n' num2str(versionList(versionNr,1)) '_d' num2str(versionList(versionNr,2))]; % 'n1_d1'
n = versionList(versionNr,1);
d = versionList(versionNr,2);
k = n/d;
teeth = [60 NaN]; % use "highly composite number"
teeth(2) = teeth(1)/k;
if teeth(2)~= round(teeth(2))
error(curVers)
end
diameter = teeth.*module;
% % continuous rotation
% nFrames = 180*max(d,n); % 180 frames per rotation
% angles_L_wheel = linspace(0, d *2*pi,nFrames); % angles for wheel responsible for Up-Down
% angles_L_wheel = angles_L_wheel(1:end-1); % remove last frame, it would be double
% stop acc rot deacc stop
accFrames = 10; % frames for acceleration (first frame will be 0 last at full speed, so practicall it is accFrames-2)
nFrames = 180*max(d,n)+2*accFrames; % 180 frames per rotation
speed = [linspace(0,1,accFrames) ones(1,nFrames+1 -2*accFrames) linspace(1,0,accFrames)];
speed = speed(1:end-1); % last speed is 0, this does nothing in cumsum; (compensated by +1 frames in center)
angles_L_wheel = cumsum(speed)/sum(speed) *d*2*pi; % create position, normalize, scale
angles_L_wheel(end) = 0; % repalce "d*2*pi" with 0 to avoid rounding errors resulting in minimally crooked lines
center_L_wheel = [0 0]; % wheel for left movement
center_R_wheel = [mean(diameter) 0]; % wheel for right movement
curveAmplitude = 0.43*diameter(1);
if strcmp(curVers,'n1_d1')
xLimits = [-0.55*diameter(1) 0.55*diameter(1)+mean(diameter)]; % ADJUST
else
xLimits = [-0.55*diameter(1) 1.12*curveAmplitude+mean(diameter)]; % ADJUST
end
yLimits = [-0.55 0.55]*diameter(1); % ADJUST
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
liSc = ySize*scaleReduction/600; % LineWidth scale; LineWidth is absolut, a bigger images needs thicker lines to keep them in proportion
axis equal;
setXYlim(axesHandle,xLimits,yLimits); % reset limits and drawnow
angles_R_wheel = -angles_L_wheel*k;
if n==4
angles_R_wheelToothAllign = angles_R_wheel + pi/teeth(2); % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
else
angles_R_wheelToothAllign = angles_R_wheel; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT
end
yCurvePoints = curveAmplitude*cos(k*angles_L_wheel).*cos(angles_L_wheel); % rhodonea curve
xCurvePoints = curveAmplitude*cos(k*angles_L_wheel).*sin(angles_L_wheel); % rhodonea curve
reducedRGBimage = uint8(ones(xSize,ySize,3,nFrames)); % allocate
for iFrame = 1:nFrames
cla(axesHandle)
drawSpurWheel(center_L_wheel,teeth(1),module,RGB.brightGrey,2*liSc,RGB.black, angles_L_wheel(iFrame)+pi/teeth(1)); % upper left cogwheel (fast)
drawSpurWheel(center_R_wheel,teeth(2),module,RGB.grey ,2*liSc,RGB.black, angles_R_wheelToothAllign(iFrame)); % lower right cogwheel (slow)
% if curveAmplitude >= diameter(2)/2 % if the crank reaches the white area
% xCrank = [-module*2 0 module*2 module -module];
% yCrank = [ 0 -module*2 0 curveAmplitude+module curveAmplitude+module];
% [xCrank,yCrank] = rotateCordiantes(xCrank,yCrank,angles_R_wheel(iFrame));
% patch(xCrank+center_R_wheel(1),yCrank+center_R_wheel(2),[0.5 0.5 0.5],'EdgeColor',[0 0 0],'LineWidth',2) % raw the crank trapezoid
% end
xCoord = [-1 0 0]*curveAmplitude*1.08+center_L_wheel(1);
yCoord = [ 0 0 1]*curveAmplitude*1.08+center_L_wheel(1);
[xCoord,yCoord] = rotateCordiantes(xCoord,yCoord,angles_L_wheel(iFrame));
plot(xCoord,yCoord,'-','Color',RGB.black,'LineWidth',4*liSc) % coordinate system lines
xArrow = [0 -0.8 0.8]*module+center_L_wheel(1);
yArrow = [1.17 1.07 1.07]*curveAmplitude+center_L_wheel(2);
[xArrow,yArrow] = rotateCordiantes(xArrow,yArrow,angles_L_wheel(iFrame));
patch(xArrow,yArrow,RGB.black);
[xArrow,yArrow] = rotateCordiantes(xArrow,yArrow,pi/2);
patch(xArrow,yArrow,RGB.black);
xLine = [-1 1]*(diameter(2)/2-module*1.5);
yLine = [ 0 0]*(diameter(2)/2-module*1.5);
[xLine,yLine] = rotateCordiantes(xLine,yLine,angles_R_wheel(iFrame));
plot(xLine+center_R_wheel(1),yLine+center_R_wheel(2),'-','Color',RGB.darkGrey,'LineWidth',5*liSc) % coordinate system lines
[xLine,yLine] = rotateCordiantes(xLine,yLine,pi/2);
plot(xLine+center_R_wheel(1),yLine+center_R_wheel(2),'-','Color',RGB.darkGrey,'LineWidth',5*liSc) % coordinate system lines
x_R_Crank = cos(angles_R_wheel(iFrame)+pi/2)*curveAmplitude+center_R_wheel(1); % Up-Down
y_R_Crank = sin(angles_R_wheel(iFrame)+pi/2)*curveAmplitude+center_R_wheel(2); % Up-Down
plot([center_L_wheel(1) center_L_wheel(1)],[curveAmplitude -curveAmplitude],':','Color',RGB.darkBlue,'LineWidth',6*liSc) % base line
[x,y] = rotateCordiantes(xCurvePoints,yCurvePoints,angles_L_wheel(iFrame));
plot(x,y, '-','Color',RGB.red ,'LineWidth',3*liSc) % rose curve
plot(x(1:max(iFrame,1)),y(1:max(iFrame,1)), '-','Color',RGB.red ,'LineWidth',7*liSc) % rose curve
plot([center_R_wheel(1) x_R_Crank],[center_R_wheel(2) y_R_Crank],'.-','Color',RGB.darkBlue,'LineWidth',7*liSc) % base line
plot([0 x_R_Crank],[y_R_Crank y_R_Crank],':','Color',RGB.blue,'LineWidth',6*liSc) % base line
plot(x_R_Crank,y_R_Crank,'.','Color',RGB.blue ,'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker crank and curve
plot(0,y_R_Crank,'.','Color',RGB.red ,'MarkerSize',60*liSc,'LineWidth',7*liSc) % color marker crank and curve
plot(0,y_R_Crank,'o','Color',RGB.blue ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker crank and curve
%% save animation
setXYlim(axesHandle,xLimits,yLimits); % reset limits and drawnow
% pause(0.01)
% return
f = getframe(figHandle);
imtemp = imReduceSize(f.cdata,scaleReduction); % allows subpixel lines
reducedRGBimage(:,:,:,iFrame) = rot90(imtemp,3); % rotate image
% if iFrame == nFrames % save svg
% if ~isempty(which('plot2svg'))
% plot2svg(fullfile(pathstr, [fname '_' curVers '.svg']),figHandle) % by Juerg Schwizer
% else
% disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
% end
% end
end
startMap = cell2mat(struct2cell(RGB)); % struct2colormap; % list of map colors that are not allowed to be changed
map = createImMap(reducedRGBimage,32,startMap); % full colormap
im = uint8(ones(xSize,ySize,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 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)
plot(X,Y,'.','MarkerSize',2*linW,'Color',linC); % extra dots make corners look smoother
function [x,y] = rotateCordiantes(x,y,anglee)
% x: coordinates vertical
% y: coordinates horizontal
% anglee: angle of rotation in [rad]
rotM = [cos(anglee) -sin(anglee); sin(anglee) cos(anglee)];
x_y = rotM*[x(:)';y(:)'];
x = x_y(1,:);
y = x_y(2,:);
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];
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Licencia
Yo, el titular de los derechos de autor de esta obra, la publico en los términos de la siguiente licencia:
Este archivo está disponible bajo la licencia Creative Commons Dedicación de Dominio Público CC0 1.0 Universal. | |
La persona que ha asociado una obra a este documento lo dedica al dominio público mediante la cesión mundial de sus derechos bajo la ley de derechos de autor y todos los derechos legales adyacentes propios de dicha, en el ámbito permitido por ley. Puedes copiar, modificar, distribuir y reproducir el trabajo, incluso con objetivos comerciales, sin pedir aprobación del autor.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Elementos representados en este archivo
representa a
spur gear train inglés
Algún valor sin elemento de Wikidata
12 jun 2017
Historial del archivo
Haz clic sobre una fecha y hora para ver el archivo tal como apareció en ese momento.
Fecha y hora | Miniatura | Dimensiones | Usuario | Comentario | |
---|---|---|---|---|---|
actual | 17:29 14 abr 2019 | 511 × 977 (4,37 MB) | Jahobr | Wikimedia uses a 100MPx limit now. New render for this quality. | |
18:08 3 feb 2019 | 365 × 697 (2,91 MB) | Jahobr | better colormap | ||
02:19 23 sep 2017 | 360 × 690 (2,74 MB) | Jahobr | GraphicsSmoothing | ||
17:55 13 jun 2017 | 362 × 691 (2,49 MB) | Jahobr | minor fix of minimally crooked lines | ||
21:38 12 jun 2017 | 362 × 691 (2,49 MB) | Jahobr | User created page with UploadWizard |
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