File:Lever in balance hyperbola.gif
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Lever_in_balance_hyperbola.gif (500 × 450 pixels, file size: 2.94 MB, MIME type: image/gif, looped, 221 frames, 12 s)
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[edit]DescriptionLever in balance hyperbola.gif |
Deutsch: Hebel |
Date | |
Source | Own work |
Author | Jahobr |
Other versions |
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GIF development InfoField | |
Source code InfoField | MATLAB codefunction lever_in_balance()
% source code that produces a GIF and a SVG
%
% 2017-11-01 Jahobr
rampUpDown = [0:0.1:1 linspace(1,2,90) 2:-0.2:0]; % speed profile
rampUpDown = cumsum(rampUpDown); % distance
rampUpDown = rampUpDown(1:end-1); % remove redundant point
rampUpDown = rampUpDown./rampUpDown(end); % normalize (0 to 1)
xPosList = [(0.5+rampUpDown./2) (1+rampUpDown(2:end))]; % x position with intermediate stop
nFrames = numel(xPosList);
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
leverThickness = 0.05;
leverLength = [-1.1 2.1];
leverOff = 0.17; % lever offset
xH = 0.3 : 0.01 : 2.3; % Hyperbola
yH = 1./xH; % Hyperbola
%% create figure
figHandle = figure(15677755); clf
set(figHandle,'Units','pixel');
set(figHandle,'GraphicsSmoothing','on') % requires at least version 2014b
axesHandle = axes;
hold(axesHandle,'on')
versionList{1} = 'hyperbola'; % full version with force vectors and hyperbola
versionList{2} = 'weights'; % reduced; just lever and weights
for versionNr = 1:numel(versionList)
cla(axesHandle) % fresh frame
saveName = [fname '_' versionList{versionNr}];
RGB = struct;
RGB.black = [0 0 0 ];
RGB.white = [1 1 1 ];
RGB.leverEdge = [0.55 0.27 0.08]; % brown
RGB.leverFace = [0.70 0.5 0.35]; % brown
RGB.weight = [0.6 0.6 0.6]; % grey
RGB.weight2 = [0.7 0.7 0.7]; % grey shine
RGB.weight3 = [0.8 0.8 0.8]; % grey glare
RGB.coordinate = [0.3 0.3 0.3]; % grey
if versionNr == 1
xSize = 500; % size in pixel
ySize = 450; % size in pixel
scaleReduction = 2; % the size reduction: adds antialiasing
xLimits = [-1.42 2.38];
yLimits = [-0.98 2.25];
RGB.LForce = [0 0 0.8]; % blue
RGB.RForce = [1 0 0 ]; % red
RGB.LText = [0 0 0.3]; % blue
RGB.RText = [0.2 0 0]; % red
RGB.LArea = [0.7 0.7 1]; % blue
RGB.RArea = [1 0.7 0.7]; % red
RGB.Hyper = [1 0.7 0.7]; % red
else
xSize = 900; % size in pixel
ySize = 250; % size in pixel
scaleReduction = 2; % the size reduction: adds antialiasing
xLimits = [-1.42 2.38];
yLimits = [-0.95 0.1];
end
RGB = structfun(@(q)round(q*255)/255, RGB, 'UniformOutput',false); % round to values that are nicely uint8 compatible
liSc = xSize*scaleReduction/1000;
set(figHandle,'Position',[1 1 [xSize ySize]*scaleReduction]); % 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(xLimits); ylim(yLimits); axis equal; drawnow;
%% plot loop
reducedRGBimage = uint8(ones(ySize,xSize,3,nFrames)); % allocate
for iFrame = 1:nFrames
cla(axesHandle) % fresh frame
xPos = xPosList(iFrame);
if versionNr == 1
forceR = 1/xPos;
weightL = 1000/9.81; %
weightR = 1000*forceR/9.81; %
plotBox([-1 0],[0 1],RGB.LArea,'none',1)
plotBox([ 0 xPos],[0 1/xPos],RGB.RArea,'none',1)
else
weightL = 100;
weightR = 100/xPos;
end
plot(leverLength+0.05,[0 0],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % horizontal arrow
plot(leverLength(2)+0.05+[-0.08 0 -0.08],[-0.02 0 0.02],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % Arrowhead
plot(leverLength(2)+0.05+[-0.08 -0.02 -0.08],[-0.02 0 0.02],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % Arrowhead
plotBox(leverLength,[-leverThickness 0]-leverOff,RGB.leverFace,RGB.leverEdge,2.5*liSc) % lever
for scale = ceil(leverLength(1)) :0.1: floor(leverLength(2))
if scale*2 == round(scale*2)
plot([scale scale],[-0.007 -leverThickness+0.007]-leverOff,'Color',RGB.leverEdge,'LineWidth',5*liSc) % bar scale
plot([scale scale],[-0.02 +0.02],'-','Color',RGB.coordinate,'LineWidth',5*liSc) % coordinate scale
text(scale,-0.01, num2str(scale),...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.coordinate, 'FontUnits','pixel', 'FontSize',33*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','top');
else
plot([scale scale],[-0.009 -leverThickness+0.009]-leverOff,'Color',RGB.leverEdge,'LineWidth',2.5*liSc) % bar scale
plot([scale scale],[-0.015 +0.015],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % coordinate scale
end
end
if versionNr == 1
text(2.03,0.03,'[m]',...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.coordinate, 'FontUnits','pixel', 'FontSize',33*liSc,...
'HorizontalAlignment','left', 'VerticalAlignment','bottom');
plot(xH,yH,':','Color',[1 0.1 0.1],'LineWidth',7*liSc) % Hyperbola
plot([0 0],[0 2.15],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % vertical arrow
plot([-0.02 0 0.02],[2.07 2.15 2.07],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % Arrowhead
plot([-0.02 0 0.02],[2.07 2.13 2.07],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % Arrowhead
for scale = 0:0.1:2.0
if scale*2 == round(scale*2)
plot([-0.02 +0.02],[scale scale],'-','Color',RGB.coordinate,'LineWidth',5*liSc) % coordinate scale
if scale >0
text(-0.03,scale, num2str(scale,'%3.1f'),...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.coordinate, 'FontUnits','pixel', 'FontSize',33*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','middle');
end
else
plot([-0.015 +0.015],[scale scale],'-','Color',RGB.coordinate,'LineWidth',2.5*liSc) % coordinate scale
end
end
text(-0.05,2.12, 'F [kN]',...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.coordinate, 'FontUnits','pixel', 'FontSize',33*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','middle');
text(-0.5,1, '1.00 m',...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.LText, 'FontUnits','pixel', 'FontSize',45*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','cap');
text(-0.98,0.1, '1.00 kN',...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.LText, 'FontUnits','pixel', 'FontSize',45*liSc,...
'HorizontalAlignment','left', 'VerticalAlignment','bottom');
text(-0.5,0.46, '$${\bf M_L}$$',...
'interpreter','Latex',...
'Color',RGB.LText, 'FontUnits','pixel', 'FontSize',70*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','middle');
plot([-1 -1],[0.04 1],'-','Color',RGB.LForce,'LineWidth',5.0*liSc)
plot([-0.02 0 0.02]-1,[0.09 0.01 0.09],'-','Color',RGB.LForce,'LineWidth',2.5*liSc) % Arrowhead
plot([-0.02 0 0.02]-1,[0.09 0.04 0.09],'-','Color',RGB.LForce,'LineWidth',2.5*liSc) % Arrowhead
text(xPos/2,forceR, [num2str(xPos,'%1.2f') ' m'],...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.RText, 'FontUnits','pixel', 'FontSize',45*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','cap');
text(xPos-0.02,0.1, [num2str(forceR,'%1.2f') ' kN'],...
'FontWeight','bold', 'FontName','Helvetica Narrow',...
'Color',RGB.RText, 'FontUnits','pixel', 'FontSize',45*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','bottom');
text(xPos/2,forceR*0.46, '$${\bf M_R}$$',...
'interpreter','Latex',...
'Color',RGB.RText, 'FontUnits','pixel', 'FontSize',70*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','middle');
plot([xPos xPos], [0.04 forceR],'-','Color',RGB.RForce,'LineWidth',5.0*liSc)
plot([-0.02 0 0.02]+xPos,[0.09 0.01 0.09],'-','Color',RGB.RForce,'LineWidth',2.5*liSc) % Arrowhead
plot([-0.02 0 0.02]+xPos,[0.09 0.04 0.09],'-','Color',RGB.RForce,'LineWidth',2.5*liSc) % Arrowhead
text(2.15,2, '$${\bf M_L+M_R =0}$$',...
'interpreter','Latex',...
'FontUnits','pixel', 'FontSize',70*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','middle');
text(0.95,1.7, '$${\bf M_L}$$',...
'interpreter','Latex',...
'FontUnits','pixel', 'FontSize',50*liSc,...
'HorizontalAlignment','left', 'VerticalAlignment','middle');
text(2.15,1.7, '$${\bf =+1\,kNm}$$',...
'interpreter','Latex',...
'FontUnits','pixel', 'FontSize',50*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','middle');
text(0.95,1.5, '$${\bf M_R}$$',...
'interpreter','Latex',...
'FontUnits','pixel', 'FontSize',50*liSc,...
'HorizontalAlignment','left', 'VerticalAlignment','middle');
text(2.15,1.5, '$${\bf =-1\,kNm}$$',...
'interpreter','Latex',...
'FontUnits','pixel', 'FontSize',50*liSc,...
'HorizontalAlignment','right', 'VerticalAlignment','middle');
end
bearing(0,-leverThickness-leverOff,0.3)
disc(0,-leverThickness-leverOff, 0.02,RGB.white,RGB.black,2.5*liSc)
plotWeight(-1, -leverOff,weightL)
plotWeight(xPos,-leverOff,weightR)
%% save animation
xlim(xLimits); ylim(yLimits); drawnow; % set axis limits
f = getframe(figHandle);
reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % the size reduction: adds antialiasing
if any(xPos == [0.5 1 2]) % SVG
disp(['x=' num2str(xPos) ' at Frame ' num2str(iFrame)]);
if ~isempty(which('plot2svg'))
plot2svg(fullfile(pathstr, [saveName '_1-' num2str(xPos) '.svg']),figHandle) % by Juerg Schwizer
else
disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
end
end
end
startMap = cell2mat(struct2cell(RGB)); % struct2colormap; % list of map colors that are not allowed to be changed
map = createImMap(reducedRGBimage,32,startMap); % colormap
im = uint8(ones(ySize,xSize,1,nFrames)); % allocate
for iFrame = 1:nFrames
im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither');
end
imwrite(im,map,fullfile(pathstr, [saveName '.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif
disp([saveName '.gif has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
end
function plotWeight(x,y,weight)
% x [left right]
% y [top bottom]
% force in kN
le = 0.11; % ropeLength
density = 2500; % adjust
% V = weight/density = 4/3*pi*r^3
r = nthroot( (weight*3)/(density*4*pi), 3); % radius
disc(x, y-le-r/6, r/3, RGB.weight, RGB.black, 2.5*liSc) % handle (material)
disc(x, y-le-r/6, r/6, RGB.white, RGB.black, 2.5*liSc) % handle (hole)
disc(x, y-le-r*1.25, r, RGB.weight, RGB.black, 2.5*liSc) % body
disc(x-r*0.4, y-le-r*0.75, r/3, RGB.weight2, 'none' , 1) % shine
disc(x-r*0.45,y-le-r*0.7, r/5, RGB.weight3, 'none' , 1) % glare
text(x, y-le-r*1.05, num2str(weight,'%5.1f'),...
'FontWeight','bold', 'FontName','Helvetica',...
'Color',RGB.black, 'FontUnits','pixel', 'FontSize',200*r*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','middle');
text(x, y-le-r*1.65, 'kg',...
'FontWeight','bold', 'FontName','Helvetica',...
'Color',RGB.black, 'FontUnits','pixel', 'FontSize',200*r*liSc,...
'HorizontalAlignment','center', 'VerticalAlignment','middle');
plot([x x],y+[0.03 -le-0.03],'Color',RGB.black,'LineWidth',6*liSc);
end
function bearing(x,y,sizze)
% x coordinates of the center
% y coordinates of the center
% size
plot([0 -0.5 0.5 0]*sizze+x,[0 -0.8660 -0.8660 0]*sizze+y,'k','LineWidth',5*liSc,'Color',RGB.black); % Triangle % 0.8660 = sqrt(3)*0.5
plot([-0.7 0.7]*sizze+x,[-0.87 -0.87]*sizze+y,'k','LineWidth',5*liSc,'Color',RGB.black); % base line
for iLine = -0.6:0.2:0.7
plot(([-0.1 0.1]+iLine)*sizze+x,[-1.07 -0.87]*sizze+y,'k','LineWidth',3*liSc,'Color',RGB.black); % Hatching
end
end
end
function disc(x,y,r,colFa,colEd,linWi)
% x coordinates of the center
% y coordinates of the center
% r is the radius of the circle
% colFa FaceColor
% colEd EdgeColor
% linWi LineWidth
angleOffPoints = linspace(0,2*pi,300);
xc = x + r*sin(angleOffPoints);
yc = y + r*cos(angleOffPoints);
patch(xc,yc,'k','LineWidth',linWi,'EdgeColor',colEd,'FaceColor',colFa); % ,'FaceAlpha',0.2% transparencc does onl work in 'renderer','OpenGL' but that fails in combination with "getframe"
end
function plotBox(x,y,colFa,colEd,linw)
% x [left right]
% y [top bottom]
% colFa face color [r g b]
% colEd edge color [r g b]
% linw line width
xs = [x(1) x(1) x(2) x(2) x(1) x(1)]; % x
ys = [mean(y) y(1) y(1) y(2) y(2) mean(y)]; % y joint in the middle of an edge to get nice corners
patch(xs,ys,colFa,'EdgeColor',colEd,'LineWidth',linw); %
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:
% 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
end
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];
end
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Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 12:31, 19 November 2017 | 500 × 450 (2.94 MB) | Jahobr (talk | contribs) | sign changed; text better | |
20:31, 1 November 2017 | 500 × 450 (2.76 MB) | Jahobr (talk | contribs) | User created page with UploadWizard |
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