File:Lever in balance hyperbola.gif

function 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