پەڕگە:GoldenSpiralLogarithmic color in.gif
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GoldenSpiralLogarithmic_color_in.gif (٤٥٠ × ٤٥٠ پیکسڵ، قەبارەی پەڕگە: ١٫٥١ مێگابایت، جۆری ئێم ئای ئێم ئی: image/gif، looped، ٢٤٥ frames، ٤٫٩چ)
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کورتە
وەسفGoldenSpiralLogarithmic color in.gif |
English: Logarithmic golden spiral |
ڕێکەوت | |
سەرچاوە | بەرھەمی خۆم |
بەرھەمھێنەر | Jahobr |
وەشانەکانی تر |
|
GIF genesis InfoField | |
کۆدی سەرچاوە InfoField | MATLAB codefunction GoldenSpiralLogarithmic()
% source code for drawings the animations
%
% 2018-06-07 Jahobr
fps = 50;
nFrames = 245;
xySize = 450; % gif size in pixel
scaleReduction = 2; % the size reduction: adds antialiasing
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
figHandle = figure(2324455);
clf
axesHandle = axes;
hold(axesHandle,'on')
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 xySize*scaleReduction xySize*scaleReduction]); % big start image for antialiasing later [x y width height]
set(figHandle, 'GraphicsSmoothing','on') % requires at least version 2014b
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]
axis equal; drawnow;
phi = (1+sqrt(5))/2;
b = log(phi)/(pi/2);
thetaXextreme = atan(b)+pi/2*(2:-2:-20);
rXextreme = phi.^(thetaXextreme*2/pi);
[Xextreme,yXext] = pol2cart(thetaXextreme,rXextreme);
thetaYextreme = atan(b)+pi/2*(1:-2:-21);
rYextreme = phi.^(thetaYextreme*2/pi);
[xYext,Yextreme] = pol2cart(thetaYextreme,rYextreme);
theta = pi/2*(3:-0.02:-20); % curve points
r = phi.^(theta*2/pi); % radii
[X,Y] = pol2cart(theta,r); % cartesian coordinate system
for useColor = [false true]
cla(axesHandle);
for m = 1:numel(Xextreme)-2
if useColor
cmap = [0.0 0.0 0.0;... 1 spiral color; black
0.3 0.3 0.3;... 2 box-edge color; grey
1.0 0.8 0.8;... 3 box-filling; pale red
1.0 1.0 0.7;... 4 box-filling; pale yellow
0.8 1.0 0.8;... 5 box-filling; pale green
0.8 0.8 1.0]; % 6 box-filling; pale blue
cmap = round(cmap.*255)./255; % round to uint8 positions
curVers = '_color';
if Xextreme(m)<0
colFilling = cmap(3,:); % pale red
else
colFilling = cmap(4,:); % pale yellow
end
patch([Xextreme(m) Xextreme(m) Xextreme(m+2) Xextreme(m+2) Xextreme(m)],...
[ Yextreme(m+1) Yextreme(m) Yextreme(m) Yextreme(m+1) Yextreme(m+1)],...
colFilling,'EdgeColor',cmap(2,:),'LineWidth',3)
if Yextreme(m)<0
colFilling = cmap(5,:); % pale green
else
colFilling = cmap(6,:); % pale blue
end
patch([Xextreme(m+2) Xextreme(m+2) Xextreme(m+1) Xextreme(m+1) Xextreme(m+2)],...
[ Yextreme(m+2) Yextreme(m) Yextreme(m) Yextreme(m+2) Yextreme(m+2)],...
colFilling,'EdgeColor',cmap(2,:),'LineWidth',3)
else
cmap = [0.0 0.0 1.0;... 1 spiral color; blue
0.0 0.0 0.0;... 2 box-edge color; black
1.0 1.0 1.0]; % 3 box-filling; white
cmap = round(cmap.*255)./255; % round to uint8 positions
curVers = '';
plot([Xextreme(m) Xextreme(m) Xextreme(m+2) Xextreme(m+2) Xextreme(m)],...
[ Yextreme(m+1) Yextreme(m) Yextreme(m) Yextreme(m+1) Yextreme(m+1)],...
'-','color',cmap(2,:),'LineWidth',3)
plot([Xextreme(m+2) Xextreme(m+2) Xextreme(m+1) Xextreme(m+1) Xextreme(m+2)],...
[ Yextreme(m+2) Yextreme(m) Yextreme(m) Yextreme(m+2) Yextreme(m+2)],...
'-','color',cmap(2,:),'LineWidth',3)
end
end
plot(X,Y,'.-','linewidth',5,'color',cmap(1,:),'Markersize',5*3.4) % plot spiral
scale = linspace(log(-Xextreme(3)),log(-Xextreme(5)),nFrames+1); % start with an area fully covered, zoom in till repetition
scale = exp(scale); % logarithmic sale
scale = scale(1:end-1); % cut off doubled frame
RGBimageStack = uint8(ones(xySize*scaleReduction,xySize*scaleReduction,3,nFrames)); % allocate
for iFrame = 1:nFrames
axis equal
xlim([-scale(iFrame) scale(iFrame)]) % zoom
ylim([-scale(iFrame) scale(iFrame)]) % zoom
drawnow expose; % causes graphics and user-interface objects to refresh with all pending changes
% save SVG
if iFrame == 1 % only once
if ~isempty(which('plot2svg'))
posSave = get(figHandle, 'position');
set(figHandle, 'position',[1 1 800 800]); % big start image for antialiasing later [x y width height]
plot2svg(fullfile(pathstr, [fname curVers '.svg']),figHandle) % by Juerg Schwizer
set(figHandle, 'position',posSave); % reset size
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]
else
disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
end
end
%% save animation
f = getframe(figHandle);
RGBimageStack(:,:,:,iFrame) = f.cdata; % store
end
reducedRGBimage = imReduceSize(RGBimageStack,scaleReduction); % the size reduction: adds better antialiasing
map = createImMap(reducedRGBimage,32,cmap); % colormap
im = uint8(ones(xySize,xySize,1,nFrames)); % allocate colormap indexed image
for iFrame = 1:nFrames
im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'); % RGB to colormap indexed image
end
imwrite(im,map,fullfile(pathstr, [fname curVers '_in.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif
disp([fname curVers '_in.gif has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
imwrite(im(:,:,:,iFrame:-1:1),map,fullfile(pathstr, [fname curVers '_out.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif
%% save MP4 and WebM
cd(pathstr); % set path to working folder
videoFileName = [fname curVers '_in'];
vid = VideoWriter(videoFileName,'MPEG-4'); % Prepare the new file
vid.FrameRate = fps;
vid.Quality = 100; % quality in [0% 100%]
open(vid);
for iRep = 1:5 % loops
for iFrame = 1:nFrames
writeVideo(vid,RGBimageStack(:,:,:,iFrame));
end
end
close(vid); %
disp('conversion from MP4 to WebM (Matlab currently does not support webm)');
try
dosCommand = ['!ffmpeg -i ' videoFileName '.mp4 '... % Command and source
'-c:v libvpx-vp9 -crf 30 -b:v 0 -deadline best '...% constant (best) quality; see: https://trac.ffmpeg.org/wiki/Encode/VP9
videoFileName '.webm']; % conversion target
eval(dosCommand); % run conversion from mp4 to webm
catch
disp(['"ffmpeg.exe" not available in path "' pathstr '" (or other problem); see https://ffmpeg.zeranoe.com/builds/']);
end
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];
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