function Voronoi_growth % source code that produces a GIF. % % 2017-07-29 Jahobr (reworked 2017-10-03)   [pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location   imageMax = [500, 500]; % pixel (height width) scaleReduction = 5; % the size reduction: adds antialiasing nFrames = 200;  seedsDef = [... relative to image size     0.28    0.26; ... 1     0.30    0.05; ... 2     0.03    0.07; ... 3     0.77    0.67; ... 4     0.22    0.82; ... 5     0.46    0.42; ... 6     0.16    0.05; ... 7     0.80    0.07; ... 8     0.80    0.70]; %  9  rawIndexImage.colormap = [...     0     0     1.00;... 1 blue     0     0.50  0   ;... 2 dark green     0.75  0.75  0   ;... 3 yellow     0     0.70  0.80;... 4 cyan     0.80  0     0.80;... 5 magenta     1.00  0.50  0.10;... 6 orange     0.70  0.20  0.20;... 7 brown     1.00  0.1   0.1 ;... 8 red     0.55  1.00  0   ;... 9 bright green     0     0     0   ;... black (seeds)     1     1     1   ];%  white (background)  nSeeds = size(seedsDef,1);  figHandle1 = figure(2347541);clf;hold on xlim([0 1]); ylim([0 1]);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%              SVG                  %%%%%%%%%%%%%%%%%%%%  paddingSeeds = [... the main seeds grow to inifinity; so no path can be drawn; this extra seeds act as boundary     +3   0.0; ... nSeeds+1     +3   +3 ; ... nSeeds+2     0.0  +3 ; ... nSeeds+3     -3   +3 ; ... nSeeds+4     -3   0.0; ... nSeeds+5     -3   -3 ; ... nSeeds+6     0.0  -3 ; ... nSeeds+7     +3   -3 ]; %  nSeeds+8  figHandle2 = figure(12554461); clf; % text rendering-figure set(figHandle2,'Units','pixel'); set(figHandle2,'Position',[1 1 imageMax(2) imageMax(1)]); % big start image for antialiasing later [x y width height] axesHandle = axes; hold(axesHandle,'on') set(axesHandle,'Position',[0 0 1 1]); % stretch axis bigger as figure, [x y width height] set(axesHandle,'XTick',NaN) % get rid of ticks set(axesHandle,'YTick',NaN) % get rid of ticks set(axesHandle,'TickLength',[0 0]) % get rid of ticks xlim([0 1]); ylim([0 1]);  [v,c] = voronoin([seedsDef;paddingSeeds]); for iSeed = 1:nSeeds % scetch of points     p = patch('Faces',c{iSeed},'Vertices',v,'FaceColor',rawIndexImage.colormap(iSeed,:),'EdgeColor','none'); end plot(seedsDef(:,1),seedsDef(:,2),'.k','MarkerSize',30); if ~isempty(which('plot2svg'))     plot2svg(fullfile(pathstr, 'Voronoi_static_euclidean.svg'),figHandle2) % by Juerg Schwizer else     disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/'); end  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%         Voronoi_growth            %%%%%%%%%%%%%%%%%%%%  seeds = round(seedsDef.*(ones(nSeeds,1)*imageMax).*scaleReduction); % convert unit from "rel" to pixel  [X,Y] = meshgrid(1:imageMax(2)*scaleReduction,1:imageMax(1)*scaleReduction); % pixel coordinates  versionList{1} = 'minkowski_p0_125'; p(1) = 0.125; versionList{2} = 'minkowski_p0_707'; p(2) = 2^-0.5; versionList{3} = 'cityblock';        p(3) = 1; versionList{4} = 'minkowski_p1_25';  p(4) = 1.25; versionList{5} = 'euclidean';        p(5) = 2; versionList{6} = 'minkowski_p3';     p(6) = 3; versionList{7} = 'chebychev';        p(7) = Inf;  for versionNr = 1:numel(versionList)     curVers = versionList{versionNr};          [MinDistMat,MinPointIndexMat] = pdist2(seeds,[X(:),Y(:)],'minkowski',p(versionNr),'Smallest',1);          MinDistMat       = reshape(MinDistMat,      imageMax*scaleReduction); % minimum dist-matrix from pixel next point     MinPointIndexMat = reshape(MinPointIndexMat,imageMax*scaleReduction); % index nearest neighbour to each pixel          distancePoint = imageMax(1)*scaleReduction*(0.01 + 0.0012/p(versionNr)^3); % black start point size     distanceList = linspace(distancePoint, max(MinDistMat(:))+eps,nFrames); % growths steps from start point to full coverage      rawIndexImage.cdata = ones(imageMax*scaleReduction)*nSeeds+2; % all in background color          reducedRGBimage = ones(imageMax(1),imageMax(2),3,nFrames); % allocate          for iFrame = 1:nFrames         currentGrowthDist = distanceList(iFrame);         colorPixel = MinDistMat <= currentGrowthDist; % in Range                  if iFrame == 1             rawIndexImage.cdata(colorPixel) = nSeeds+1; % start-Point color         else             rawIndexImage.cdata(colorPixel) = MinPointIndexMat(colorPixel); % area color (using the index)         end                  MinDistMat(colorPixel) = Inf; % mark as "done"                  rawRGBimage = ind2rgb(rawIndexImage.cdata,rawIndexImage.colormap);          tempImage = d_imReduceSize(rawRGBimage,scaleReduction); % the size reduction: adds antialiasing                  figure(figHandle1);clf         image(flipud(tempImage)); % show current state                  reducedRGBimage(:,:,:,iFrame) = tempImage;     end          map = d_createImMap(reducedRGBimage,64,rawIndexImage.colormap(1:end,:)); % colormap          im = uint8(ones(imageMax(1),imageMax(2),1,nFrames));     for iFrame = 1:nFrames         im(:,:,1,iFrame) = flipud(rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'));     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  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%             p-Sweep               %%%%%%%%%%%%%%%%%%%%  p_sweep = 4.^([(-1.5:0.02:2.5) Inf]); nFrames = numel(p_sweep); reducedRGBimage = ones(imageMax(1),imageMax(2),3,nFrames); % allocate rawIndexImage.cdata = ones(imageMax*scaleReduction)*nSeeds+2; % all in background color  figure(figHandle2); clf; % text rendering-figure set(figHandle2,'Units','pixel'); %set(figHandle2,'GraphicsSmoothing','on') % requires at least version 2014b set(figHandle2,'Position',[1 1 imageMax(2) imageMax(1)]); % big start image for antialiasing later [x y width height] set(figHandle2,'Color'  ,'white'); % white background axesHandle = axes; hold(axesHandle,'on'); set(axesHandle,'Position',[0 0 1 1]); % stretch axis bigger as figure, [x y width height] axis off; % invisible axes (no ticks) xlim([0 1]); ylim([0 1]); drawnow;  for iFrame = 1:nFrames     % pause(0.1)     [MinDistMat,MinPointIndexMat] = pdist2(seeds,[X(:),Y(:)],'minkowski',p_sweep(iFrame),'Smallest',1);                  MinDistMat       = reshape(MinDistMat,      imageMax*scaleReduction); % minimum dist-matrix from pixel next point     MinPointIndexMat = reshape(MinPointIndexMat,imageMax*scaleReduction); % index nearest neighbour to each pixel     rawIndexImage.cdata = MinPointIndexMat; % area color (using the index)      distancePoint = imageMax(1)*scaleReduction*(0.01 + 0.0012/p_sweep(iFrame)^3); % black start point size      colorPixel = MinDistMat <= distancePoint; % in Range     rawIndexImage.cdata(colorPixel) = nSeeds+1; % start-Point color      rawRGBimage = ind2rgb(flipud(rawIndexImage.cdata),rawIndexImage.colormap);     tempImage = d_imReduceSize(rawRGBimage,scaleReduction); % the size reduction: adds antialiasing      figure(figHandle2); cla % text rendering-figure     text(0.983,0.983,sprintf('p=%6.3f',p_sweep(iFrame)),'FontName','FixedWidth','FontSize',imageMax(1)/20,'FontWeight','bold','HorizontalAlignment','right','VerticalAlignment','top')     drawnow;     f = getframe(figHandle2);     tempImage = tempImage-(1-double(f.cdata)./255); % combine voronoi & text     tempImage(tempImage<0) = 0; % correct too dark pixel     reducedRGBimage(:,:,:,iFrame) = tempImage;              figure(figHandle1);clf     image(tempImage); % show current state     drawnow; end  map = d_createImMap(reducedRGBimage,64,rawIndexImage.colormap(1:end-1,:)); % colormap without white; sweep-animation is fully filled  im = uint8(ones(imageMax(1),imageMax(2),1,nFrames)); for iFrame = 1:nFrames     im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'); end  imwrite(im,map,fullfile(pathstr, 'Voronoi_p_sweep.gif'),'DelayTime',1/10,'LoopCount',inf) % save gif disp(['Voronoi_p_sweep.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%            Seed-Movement              %%%%%%%%%%%%%%%%%%  ellipseDiameter = [... relative to image size     0.8    0.8; ... 1 blue     0.6    0.75;... 2 dark green     0.9    0.1; ... 3 yellow     0.7    0.25;... 4 cyan     0.7    0.5; ... 5 magenta     0.6    0.6; ... 6 orange     0.2    0.9; ... 7 brown     0.35   0.8; ... 8 red     0.8    0.5];%   9 bright green      angleOffset = pi/180*[230;  260;  185;  310;  140;  225;  260;  280;  45]; %                     1b    2da-g 3y    4c    5m    6o    7br   8r    9br-g direction =          [1;    1;    1;   -1;    1;   -1;   -1;    1;   -1 ];  imageMax = [350, 350]; % pixel (height width) scaleReduction = 5; % the size reduction: adds antialiasing nFrames = 408;  [X,Y] = meshgrid(1:imageMax(2)*scaleReduction,1:imageMax(1)*scaleReduction); % pixel coordinates  figure(figHandle1);clf;hold on angleList = linspace(0,2*pi,nFrames+1); angleList = angleList(1:end-1);  for iFrame = 1:nFrames     cla     xlim([0 1]); ylim([-1 0]);     for iSeed = 1:nSeeds % scetch of points         angle = angleList*direction(iSeed)+angleOffset(iSeed);         xp=cos(angle)*ellipseDiameter(iSeed,1)/2;         yp=sin(angle)*ellipseDiameter(iSeed,2)/2;         trajectX(iSeed,:)=xp-xp(1)+seedsDef(iSeed,1);         trajectY(iSeed,:)=yp-yp(1)+seedsDef(iSeed,2); %         plot(trajectX(iSeed,:),-trajectY(iSeed,:),'.','Color',rawIndexImage.colormap(iSeed,:)); %         plot(trajectX(iSeed,iFrame),-trajectY(iSeed,iFrame),'p','Color',rawIndexImage.colormap(iSeed,:));     end     drawnow; pause(.05) end  reducedRGBimage = ones(imageMax(1),imageMax(2),3,nFrames); % allocate  trajectX = round(trajectX*imageMax(2)*scaleReduction); % in pixel x or horizontal trajectY = round(trajectY*imageMax(1)*scaleReduction); % in pixel y of vertical  for versionNr = 1:numel(versionList)     curVers = versionList{versionNr};     for iFrame = 1:nFrames         % pause(0.1)         [MinDistMat,MinPointIndexMat] = pdist2([trajectX(:,iFrame),trajectY(:,iFrame)],[X(:),Y(:)],'minkowski',p(versionNr),'Smallest',1);                  MinDistMat       = reshape(MinDistMat,      imageMax*scaleReduction); % minimum dist-matrix from pixel next point         MinPointIndexMat = reshape(MinPointIndexMat,imageMax*scaleReduction); % index nearest neighbour to each pixel         rawIndexImage.cdata = MinPointIndexMat; % area color (using the index)                  distancePoint = imageMax(1)*scaleReduction*(0.01 + 0.0012/p(versionNr)^3); % black start point size         colorPixel = MinDistMat <= distancePoint; % in Range         rawIndexImage.cdata(colorPixel) = nSeeds+1; % start-Point color                  rawRGBimage = ind2rgb(rawIndexImage.cdata,rawIndexImage.colormap);         tempImage = d_imReduceSize(rawRGBimage,scaleReduction); % the size reduction: adds antialiasing         reducedRGBimage(:,:,:,iFrame) = tempImage;                  figure(figHandle1);clf         image(flipud(tempImage)); % show current state         drawnow;     end          map = d_createImMap(reducedRGBimage,128,rawIndexImage.colormap(1:end-1,:)); % colormap without white; sweep-animation is fully filled          im = uint8(ones(imageMax(1),imageMax(2),1,nFrames));     for iFrame = 1:nFrames         im(:,:,1,iFrame) = flipud(rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'));     end          imwrite(im,map,fullfile(pathstr, ['Voronoi_move_' curVers '.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif     disp(['Voronoi_move_' curVers '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit end  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%              PNG                  %%%%%%%%%%%%%%%%%%%%  imageMax = [2000, 2000]; % pixel (height width) scaleReduction = 5; % the size reduction: adds antialiasing  seeds = round(seedsDef.*(ones(nSeeds,1)*imageMax).*scaleReduction); % convert unit from "rel" to pixel [X,Y] = meshgrid(1:imageMax(2)*scaleReduction,1:imageMax(1)*scaleReduction); % pixel coordinates  for versionNr = 1:numel(versionList)     curVers = versionList{versionNr};          [MinDistMat,MinPointIndexMat] = pdist2(seeds,[X(:),Y(:)],'minkowski',p(versionNr),'Smallest',1);          MinDistMat       = reshape(MinDistMat,      imageMax*scaleReduction); % minimum dist-matrix from pixel next point     MinPointIndexMat = reshape(MinPointIndexMat,imageMax*scaleReduction); % index nearest neighbour to each pixel     distancePoint = imageMax(1)*scaleReduction*(0.01 + 0.0012/p(versionNr)^3); % black start point size     colorPixel = MinDistMat <= distancePoint; % in Range     MinPointIndexMat(colorPixel) = nSeeds+1; % start-Point color          rawRGBimage = flipud(ind2rgb(MinPointIndexMat,rawIndexImage.colormap));     im = d_imReduceSize(rawRGBimage,scaleReduction); % the size reduction: adds antialiasing          imwrite(im,fullfile(pathstr, ['Voronoi_static_' curVers '.png'])) % save png     disp(['Voronoi_static_' curVers '.png saved']) % Category:Animated GIF files exceeding the 50 MP limit end  function im = d_imReduceSize(im,redSize) % Input: %  im:      image, [imRows x imColumns x nChannel x nStack] (double) %                      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:  double([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 = 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 = sqrt(im./redSize^2); % mean; re-normalize brightness: "scale linear to the human eye"; back in uint8   function map = d_createImMap(imRGB,nCol,startMap) % d_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] (double) %   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 = permute(imRGBcolumn,[1 3 2]); % "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];