function Tusi_couple_ellipses() % source code for Tusi_couple_ellipses % produces a GIF and a SVG % % 2017-04-10 Jahobr (update 14.03.2021)  rBase = 1; % base radius nFrames = 340; angleSmall = linspace(0,2*pi,nFrames+1); % define gear position in frames angleSmall = angleSmall(1:end-1); % remove last frame, it would be double  figHandle = figure(15674455); whitebg(figHandle,[246 248 249]./250) % color backbground clf axesHandle = axes; hold(axesHandle,'on') set(figHandle, 'Units','pixel'); set(figHandle, 'Position',[1 1 1000 1000]); % big start image for antialiasing later [x y width height] 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([-1.2 1.2]); ylim([-1.2 1.2]); axis equal; drawnow; axis off % invisible axes (no ticks) set(figHandle, 'Color',[1 1 1]); % white background  reducedRGBimage = uint8(ones(500,500,3,nFrames)); % allocate  for iFrame = 1:nFrames          currentAngle = angleSmall(iFrame);          cla(axesHandle) % fresh frame               xs = cos(currentAngle)*0.5*rBase;     ys = sin(currentAngle)*0.5*rBase;          circle_patch(0,0,rBase,[1 1 1]) % outer circle backbground     circle_patch(xs,ys,rBase/2,[0.95 0.95 0.95])  % inner circle backbground          plot(rBase*cos(currentAngle),rBase*sin(currentAngle),'.m','MarkerSize',40) % touching point / Instant centre of rotation     plot(0,0,'+','MarkerSize',15,'LineWidth',4,'Color',[0.5 0.5 0.5]); % center marker          %% draw center circle      colD    = [0.5 0.5 0.5]; %     circle(0,0,rBase/2,colD,4);               %% draw inner ellipse     colG = [0.1 0.7 0.1]; % green     randiusA = 0.6;     ellipse(0,0,randiusA,1-randiusA,colG);     xpG = randiusA*cos(currentAngle);     ypG =(rBase-randiusA)*sin(currentAngle);     plot([xs xpG],[ys ypG],':','LineWidth',4,'Color',colG); % radial line           %% draw medium ellipse     colC    = [0  0.9 0.9]; % cyan         randiusA = 0.85;     h(3) = ellipse(0,0,randiusA,rBase-randiusA,colC,pi/4);     xpC = xs+sin(currentAngle)*(randiusA-rBase/2);     ypC = ys+cos(currentAngle)*(randiusA-rBase/2);     plot([xs xpC],[ys ypC],':','LineWidth',4,'Color',colC); % radial line          %% draw outer ellipse     colR     = [1 0 0]; % red     randiusA = 1.35;     h(1) = ellipse(0,0,randiusA,rBase-randiusA,colR,-pi/4);     xpR = xs-sin(currentAngle)*(randiusA-rBase/2);     ypR = ys-cos(currentAngle)*(randiusA-rBase/2);     plot([xs xpR],[ys ypR],':','LineWidth',4,'Color',colR); % radial line          %% draw verical Line (degenerated ellipse)     plot([0 0],[rBase,-rBase],'-b','LineWidth',4) % vertical line     plot([xs 0],[ys rBase*sin(currentAngle)],':b','LineWidth',4); % radial line      %% final touches          plot(xpG,ypG,'.','MarkerSize',40,'LineWidth',4,'Color',colG); % tracking point     plot(xpC,ypC,'.','MarkerSize',40,'LineWidth',4,'Color',colC); % tracking point     plot(xpR,ypR,'.','MarkerSize',40,'LineWidth',4,'Color',colR); % tracking point          circle(0,0,rBase,[0 0 0],5) % outer circle     circle(xs,ys,rBase/2,[0 0 0],5)  % inner circle     plot([xs 0],[ys rBase*sin(currentAngle)],'.:b','MarkerSize',40,'LineWidth',4); % tracking point on top of circles     plot(xs,ys,'.','MarkerSize',40,'LineWidth',4,'Color',colD); % tracking point                %% save animation     drawnow     pause(0.01)     saveName = 'Tusi_couple_ellipses';     f = getframe(figHandle);     reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,2); % the size reduction: adds antialiasing %          if iFrame == 72         plot2svg([saveName '.svg'],figHandle) % by Juerg Schwizer, See http://www.zhinst.com/blogs/schwizer/     end  end  map = createImMap(reducedRGBimage,128,[0 0 0; 1 1 1; 0.5 0.5 0.5; 0.95 0.95 0.95; colD; colG: colC; colR]); % colormap  im = uint8(ones(500,500,1,nFrames)); % allocate for iFrame = 1:nFrames     im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'); end  imwrite(im,map,[saveName '.gif'],'DelayTime',1/50,'LoopCount',inf) % save gif1 disp([saveName '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 100 MP limit  return %%  function circle(x,y,r,col,linw) % x coordinates of the center % y coordinates of the center % r is the radius of the circle angleOffPoints = linspace(0,2*pi,300); xc = x + r*cos(angleOffPoints); yc = y + r*sin(angleOffPoints); plot(xc,yc,'k','LineWidth',linw,'Color',col);  function circle_patch(x,y,r,col) % x coordinates of the center % y coordinates of the center % r is the radius of the circle angleOffPoints = linspace(0,2*pi,300); xc = x + r*cos(angleOffPoints); yc = y + r*sin(angleOffPoints); patch(xc,yc,col,'EdgeColor','none') %   function h = ellipse(x,y,a,b,col,theta) % x coordinates of the center % y coordinates of the center % a radius1 % b radius2 if nargin <= 5     theta = 0; end angleOffPoints = linspace(0,2*pi,300); xe = x + a*cos(angleOffPoints); ye = y + b*sin(angleOffPoints);  xe_rot =  xe*cos(theta) - ye*sin(theta); ye_rot =  xe*sin(theta) + ye*cos(theta); h = plot(xe_rot,ye_rot,'-','LineWidth',4,'Color',col);  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/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 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];