File:Fowler Ellipsograph a.gif
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Fowler_Ellipsograph_a.gif (600 × 260 pixels, file size: 4.54 MB, MIME type: image/gif, looped, 330 frames, 13 s)
File information
Structured data
Captions
Summary[edit]
DescriptionFowler Ellipsograph a.gif |
English: Fowler Ellipsograph
Deutsch: Ellipsenzeichner (Ellipsenzirkel) nach Fowler
|
Date | |
Source | Own work |
Author | Jahobr |
Other versions |
|
GIF development InfoField | |
Source code InfoField | MATLAB codefunction [] = Fowler_Ellipsograph()
% The shape of the gears is not precise, it creates a decent GIF and a SVG.
%
% 2017-05-30 Jahobr
modul=1;
col.green = round([0.1 0.7 0.1 ]*255)/255; % pin
col.darkGreen = round([0 0.3 0 ]*255)/255; % frame
col.darkGrey = round([0.5 0.5 0.65]*255)/255; % wheels
col.grey = round([0.8 0.8 0.8 ]*255)/255; % wheels
col.grey2 = round([0.7 0.7 0.7 ]*255)/255; % slider
col.E = round([1 0 0 ]*255)/255; % red
teeth = [60 60];
diameter = modul.*teeth;
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
nFrames = 330; % frames per rotation
scaleReduction = 3; % reduction for nice antialiasing
xSize = 600; % pixel
ySize = 260; % pixel
figHandle = figure(15554461); clf
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 [xSize ySize]*scaleReduction]); % big start image for antialiasing later [x y width height]
set(figHandle, 'GraphicsSmoothing','on') % requires at least version 2014b
axesHandle = axes;
hold(axesHandle,'on')
xlimValues = [-1.05 2.05]*diameter(1); % ADJUST
ylimValues = [-0.7 0.7] *diameter(1); % ADJUST
set(axesHandle,'position',[-0.05 -0.05 1.1 1.1]); % stretch axis bigger as figure, easy way to get rid of ticks [x y width height]
xlim(xlimValues); ylim(ylimValues); % set axis limits
axis equal; drawnow;
angles_wheels = linspace(0.2*pi, 2.2*pi,nFrames+1); % angles for wheel
angles_wheels = angles_wheels(1:end-1); % remove last frame, it would be double
leftCrank = diameter(1)*0.2;
rightCrank = diameter(1)*0.35;
reducedRGBimage = uint8(ones(ySize,xSize,3,nFrames)); % allocate
for iFrame = 1:nFrames
cla(axesHandle)
curAngle = angles_wheels(iFrame);
plotBox(0.5*diameter(1), 0,1.4*diameter(1),0.578*diameter(1),0,[1 1 1],col.darkGreen,15) % outer frame
plotBox(0.5*diameter(1)+leftCrank*cos(-curAngle), 0, 1.05*diameter(1),0.556*diameter(1),0,[0.8 0.8 1],[0 0 0.5],5) % sliging blue box
center_L_wheel = [leftCrank*cos(-curAngle) 0]; % Left wheel
center_R_wheel = [leftCrank*cos(-curAngle)+mean(diameter) 0]; % Right wheel
drawCogWheel(axesHandle,center_L_wheel,teeth(1),modul,col.darkGrey,-curAngle); % left cogwheel
drawCogWheel(axesHandle,center_R_wheel,teeth(2),modul,col.darkGrey, curAngle-(pi/teeth(2))); % right cogwheel
circlePatch(center_L_wheel(1),center_L_wheel(2),diameter(1)*0.47,col.grey,'k',3) % grey circle
circlePatch(center_R_wheel(1),center_R_wheel(2),diameter(2)*0.47,col.grey,'k',3) % grey circle
plotBox(center_L_wheel(1),center_L_wheel(2),eps,diameter(1)*0.1, curAngle,[1 1 1],'k',3) % missuse box to plot a line
plotBox(center_R_wheel(1),center_R_wheel(2),eps,diameter(1)*0.1,-curAngle,[1 1 1],'k',3) % missuse box to plot a line
plotBox(center_L_wheel(1),center_L_wheel(2),diameter(1)*0.45,diameter(1)*0.05, curAngle,[1 1 1],'k',3) % plot slit
plotBox(center_R_wheel(1),center_R_wheel(2),diameter(1)*0.45,diameter(1)*0.05,-curAngle,[1 1 1],'k',3) % plot slit
plotBox(0,leftCrank*sin(curAngle),diameter(1)*0.08,diameter(1)*0.048, curAngle,col.grey2,'k',3) % left crank slider
circlePatch(0,leftCrank*sin(curAngle),diameter(2)*0.04,col.green,'k',3) % green crank pin
plotBox(center_R_wheel(1)+cos(curAngle)*rightCrank,center_R_wheel(2)-sin(-curAngle)*rightCrank,diameter(1)*0.08,diameter(1)*0.048,-curAngle,col.grey2,'k',3) % right pen slider
plot( [1 1]*0.06*diameter(1),[1 -1]*0.57*diameter(1),'-','color',col.darkGreen,'LineWidth',15) % vertical guide
plot(-[1 1]*0.06*diameter(1),[1 -1]*0.57*diameter(1),'-','color',col.darkGreen,'LineWidth',15) % vertical guide
ellipse(diameter(1),0,rightCrank+leftCrank,rightCrank,col.E,7)
plot(center_R_wheel(1)+cos(curAngle)*rightCrank,center_R_wheel(2)-sin(-curAngle)*rightCrank,'.','color',col.E,'MarkerSize',60) % pen marker
%% save animation
xlim(xlimValues); ylim(ylimValues); drawnow; % set axis limits
if iFrame == 1 % save SVG
if ~isempty(which('plot2svg'))
plot2svg(fullfile(pathstr, [fname '_a.svg']),figHandle) % by Juerg Schwizer, See http://www.zhinst.com/blogs/schwizer/
else
disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
end
end
f = getframe(figHandle);
reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % the size reduction: adds antialiasing
end
map = createImMap(reducedRGBimage,32,[1 1 1;struct2map(col)]); % colormap
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, [fname '_a.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif
disp([fname '_a.gif has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
function drawCogWheel(axesHandle,center,toothNumber,modul,colFilling,startOffset)
% DRAWTOOTHEDWHEEL - draw a simple Toothed Wheel
%
% Input:
% axesHandle:
% center: [x y]
% toothNumber: scalar
% modul: scalar tooth "size"
% colFilling: color of filling [r g b]
% startOffset: start rotation (scalar)[rad]
effectiveRadius = modul*toothNumber/2; % effective effectiveRadius
outsideRadius = effectiveRadius+1* modul; % +---+ +---+
upperRisingRadius = effectiveRadius+0.5*modul; % / \ / \
% effective Radius % / \ / \
lowerRisingRadius = effectiveRadius-0.5*modul; % I I I I
rootRadius = effectiveRadius-1.1*modul; % + - - - + + - - - + +
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,colFilling,'EdgeColor',[0 0 0],'LineWidth',2)
% plot(axesHandle,X,Y,'-x','linewidth',2,'color',[0 0 0]);
% %% effective Radius
% [X,Y] = pol2cart(angleOffPoints,effectiveRadius);
% X = X+center(1); % center offset
% Y = Y+center(2); % center offset
% plot(axesHandle,X,Y,'-.','color',[0 0 0]);
function circlePatch(x,y,r,colFa,colEd,linw)
% x coordinates of the center
% y coordinates of the center
% r is the radius of the circle
% colFa face color [r g b]
% colEd edge color [r g b]
% linw line width
angleOffPoints = linspace(0,2*pi,300);
xc = x + r*cos(angleOffPoints);
yc = y + r*sin(angleOffPoints);
patch(xc,yc,colFa,'linewidth',linw,'EdgeColor',colEd); %
function plotBox(x,y,wi,hi,rot,colFa,colEd,linw)
% x coordinates of the center
% y coordinates of the center
% wi half of width
% hi half of height
% rot dotation in [rad]
% colFa face color [r g b]
% colEd edge color [r g b]
% linw line width
% joint in the middle of an edge to get nice corners
xs = [-wi -wi wi wi -wi -wi]; % x slit
ys = [ 0 -hi -hi hi hi 0]; % y slit
rotM = [cos(-rot) -sin(-rot); sin(-rot) cos(-rot)];
vecTemp = rotM*[xs; ys]; % rotate slit
xs = vecTemp(1,:)+x;
ys = vecTemp(2,:)+y;
patch(xs,ys,colFa,'EdgeColor',colEd,'LineWidth',linw); %
function ellipse(x,y,a,b,col,linw)
% x coordinates of the center
% y coordinates of the center
% a radius1
% b radius2
% col color [r g b]
% linw line width
angleOffPoints = linspace(0,2.001*pi,300);
xe = x + a*cos(angleOffPoints);
ye = y + b*sin(angleOffPoints);
plot(xe,ye,'-','linewidth',linw,'color',col);
function map = struct2map(RGB)
% RGB: struct of depth 1 with [r g b] in each field
fNames = fieldnames(RGB);
nNames = numel(fNames);
map = NaN(nNames,3); % allocate
for iName = 1:nNames
map(iName,:) = RGB.(fNames{iName}); %
end
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:
% imNew: unit8([imRows/redSize x imColumns/redSize x nChannel x nStack])
%
% an alternative is : imNew = imresize(im,1/reduceImage,'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 colores; 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 colores
[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[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:58, 24 October 2017 | 600 × 260 (4.54 MB) | Jahobr (talk | contribs) | graph smoothing, | |
15:56, 30 May 2017 | 600 × 260 (4.68 MB) | Jahobr (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 3 pages use this file: