File:Voronoi growth euclidean.gif
Voronoi_growth_euclidean.gif (500 × 500 pixels, file size: 1.24 MB, MIME type: image/gif, looped, 200 frames, 10 s)
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Summary
DescriptionVoronoi growth euclidean.gif | Deutsch: Voronoi-Diagramm erstellt durch Wachstum mit dem Euklidischer Abstand (bzw. p-Norm mit p=2) aus neun Zentren. English: Voronoi diagram crated by the growth from nine seeds using the Euclidean distance (or Minkowski distance with p=2.) |
Date | |
Source | Own work |
Author | Jahobr |
Other versions |
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GIF development InfoField | |
Source code InfoField | MATLAB codefunction 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]; |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 20:35, 1 October 2017 | ![]() | 500 × 500 (1.24 MB) | Jahobr | code update; additional Point |
01:32, 29 July 2017 | ![]() | 500 × 500 (1.19 MB) | Jahobr | User created page with UploadWizard |
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