Fitxer:Voronoi growth euclidean.gif
El contingut de la pàgina no s'admet en altres llengües.
Aparença
De la Viquipèdia, l'enciclopèdia lliure
Voronoi_growth_euclidean.gif (500 × 500 píxels, mida del fitxer: 1,24 Mo, tipus MIME: image/gif, en bucle, 200 fotogrames, 10 s)
![]() | Aquest fitxer i la informació mostrada a continuació provenen del dipòsit multimèdia lliure Wikimedia Commons.![]() |
Resum
DescripcióVoronoi 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.) |
Data | |
Font | Treball propi |
Autor | Jahobr |
Altres versions |
|
GIF genesis InfoField | |
Codi font 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];
|
Llicència
Jo, el titular dels drets d'autor d'aquest treball, el public sota la següent llicència:
![]() ![]() |
L'ús d'aquest fitxer és regulat sota les condicions de Creative Commons de CC0 1.0 lliurament al domini públic universal. |
La persona que ha associat un treball amb aquest document ha dedicat l'obra domini públic, renunciant en tot el món a tots els seus drets de d'autor i a tots els drets legals relacionats que tenia en l'obra, en la mesura permesa per la llei. Podeu copiar, modificar, distribuir i modificar l'obra, fins i tot amb fins comercials, tot sense demanar permís.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Llegendes
Afegeix una explicació d'una línia del que representa aquest fitxer
Elements representats en aquest fitxer
representa l'entitat
Algun valor sense element de Wikidata
29 jul 2017
Historial del fitxer
Cliqueu una data/hora per veure el fitxer tal com era aleshores.
Data/hora | Miniatura | Dimensions | Usuari/a | Comentari | |
---|---|---|---|---|---|
actual | 22:35, 1 oct 2017 | ![]() | 500 × 500 (1,24 Mo) | Jahobr | code update; additional Point |
03:32, 29 jul 2017 | ![]() | 500 × 500 (1,19 Mo) | Jahobr | User created page with UploadWizard |
Ús del fitxer
La pàgina següent utilitza aquest fitxer:
Ús global del fitxer
Utilització d'aquest fitxer en altres wikis:
- Utilització a de.wikipedia.org
- Utilització a en.wikipedia.org
- Utilització a fi.wikipedia.org
- Utilització a sl.wikipedia.org
- Utilització a zh-yue.wikipedia.org
- Utilització a zh.wikipedia.org