This is a Featured picture. Click here for more information.
This is a Quality image. Click here for more information.

File:Unnecessarily complicated gears a.gif

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search
Unnecessarily_complicated_gears_a.gif ‎(600 × 500 pixels, file size: 10.36 MB, MIME type: image/gif, looped, 170 frames, 6.8 s)

Summary[edit]

Description
English: Animation of Gears including epicyclic gears and a Rack and pinion.
Deutsch: Animation von Zahnrädern inkusive eines Planetengetriebes und einer Zahnstange.
Українська: Анімація коліщат, включаючи епіциклічну передачу та рейкову передачу.
Date
Source Own work
Author Jahobr
Matlab Logo.png
 This diagram was created with MATLAB by Jahobr:

Matlab

function unnecessarily_complicated_gears()
% source code for drawing unnecessarily complicated gearing
% the shape of the gears is not precise. It is a hack job that produces a GIF and a SVG
%
% 2017-06-20 Jahobr

teethSun  = 48; % 
teethPlan = 12; % 
teethRing = teethSun+teethPlan*2;
nPlan = 12; % number of planets

teethSun_top = 24;
teethHub_spoked = 60;
teethHub_back = 24;
teethBigSpoke = 96;
teethRackTrans_Bottom = 25;
teethRackTrans_Top = 25/5*4;
teethRackDriver  = 16;

modul_Epicyclic = 1;
modul_Hub_Spoke = 1.8;
modul_Sun_Hub = 1.5;
modul_LL = 0.8;
modul_top = 0.9;
modul_Rack = 1.4;

col.carrier   = roundToUINT8pos([0.1  0.7  0.1 ]); % green
col.sun       = roundToUINT8pos([0.95 0.65 0   ]); % yellow (obviously)
col.palnet    = roundToUINT8pos([0.2  0.2  1   ]); % blue   (obviously)
col.ring      = roundToUINT8pos([1    0.2  0.2 ]); % red
col.hub       = roundToUINT8pos([0.6  0.2  0.8 ]); % violet
col.spoke     = roundToUINT8pos([0.5  0.5  0.5 ]); % 
col.rackTrans = roundToUINT8pos([0.4  0.24 0.08]); % 
col.rack      = roundToUINT8pos([1    0.5  0.2 ]); % 
col.rackDrive = roundToUINT8pos([0.8  0.3  0.2 ]); % 
col.LL_1      = roundToUINT8pos([0.4  0.6  0.6 ]); % 
col.LL_2      = roundToUINT8pos([0.3  0.6  0.8 ]); % 
col.top       = roundToUINT8pos([0.5  0.7  1   ]); % 

diameterSun  = modul_Epicyclic.*teethSun;
diameterPlan = modul_Epicyclic.*teethPlan;
diameterCarr = diameterSun+diameterPlan;

dist_Sun_Hub = mean([modul_Sun_Hub*teethSun_top, modul_Sun_Hub*teethHub_spoked]);
centerHub = [dist_Sun_Hub*cosd(60) -dist_Sun_Hub*sind(60)];

dist_Hub_Spoke = mean([modul_Hub_Spoke*teethHub_back, modul_Hub_Spoke*teethBigSpoke]) ;
centerSpoke = [dist_Hub_Spoke*cosd(60) +dist_Hub_Spoke*sind(60)]+centerHub;

dist_Hub_RackTrans = mean([modul_Sun_Hub*teethHub_spoked, modul_Sun_Hub*teethRackTrans_Bottom]); 
centerRackTrans = [dist_Hub_RackTrans*cosd(53) +dist_Hub_RackTrans*sind(53)]+centerHub;

dist_RackTrans_col.rackDriver = mean([modul_Rack*teethRackTrans_Top, modul_Rack*teethRackDriver ]);
centerRackDriver = [dist_RackTrans_col.rackDriver*cosd(55) -dist_RackTrans_col.rackDriver*sind(55)]+centerRackTrans;

[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location

xlimValues = [-20 100];
ylimValues = [-60  40];

xRange = xlimValues(2)-xlimValues(1);
yRange = ylimValues(2)-ylimValues(1);

ySize = 500; % pixel
xSize = round(ySize/yRange*xRange); % pixel
scaleReduction = 2; % reduction for nice antialiasing
linW = 2.5; % LineWidth
nFrames = 170;

figHandle = figure(15674455); clf
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 xSize*scaleReduction ySize*scaleReduction]); % big start image for antialiasing later [x y width height]
%set(figHandle, 'GraphicsSmoothing','on') % requires at least version 2014b
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
set(axesHandle,'YColor',[1 1 1]) % remove outline
set(axesHandle,'XColor',[1 1 1]) % remove outlinexlim(xli);
xlim(xlimValues);ylim(ylimValues);
axis equal; drawnow;

angleCarrier = -linspace(0,pi*2/nPlan,nFrames+1); % define gear position in frames
angleCarrier = angleCarrier(1:end-1); % remove last frame, it would be double

anglePlan = angleCarrier.*( teethSun/teethPlan+1 ); % gear ratio
anglePlan = -anglePlan + (pi/teethPlan); % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT

angleSun = angleCarrier.*  (1+teethRing/teethSun); % gear ratio
angleSun = angleSun + 0; % ALLIGNMENT; THIS MAY NEED MANUAL ADJUSTMENT

angleRing = zeros(size(anglePlan));
reducedRGBimage = uint8(ones(ySize,xSize,3,nFrames)); % allocate

for iFrame = 1:nFrames
    cla(axesHandle);xlim(xlimValues);ylim(ylimValues); % fresh frame
    
    %% background wheels
    % Hub background wheel  24 teeth rotates 2, interacts with spoked
    drawCogWheel(centerHub,teethHub_back ,modul_Hub_Spoke,... % center, number of teeth, modul
        col.hub*0.6, linW,... % color, linewidth
        -angleSun(iFrame)/2.5,... % angle of rotaion
        NaN, 1, 3, 1); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % fine Spoked wheel 96 teeth rotates 2
    drawCogWheel(centerSpoke,teethBigSpoke, modul_Hub_Spoke,... % center, number of teeth, modul
        col.spoke, linW,... % color, linewidth
        angleSun(iFrame)/2.5/4 + pi/teethBigSpoke,... % angle of rotaion
        teethBigSpoke/2, 0.5, 0, 13.2); % nSpoke, spokeW, sideOffset, shaftDiameter
     
    %% %%%%%%%%%%     Epicyclic_Gearing    %%%%%%%%%%%%%%%%%%%%%
    % ring
    drawRingGear(teethRing,modul_Epicyclic,col.ring,linW,angleRing(iFrame))
    
    % sun
    drawCogWheel([0 0],teethSun ,modul_Epicyclic,... % center, number of teeth, modul
        col.sun, linW,... % color, linewidth
        angleSun(iFrame),... % angle of rotaion
        NaN, 0, 0, 0); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % planets
    angPlan = linspace(0,2*pi,nPlan+1);
    angPlan = angPlan(1:end-1);
    for iPlan = angPlan
        [X,Y] = pol2cart(iPlan+angleCarrier(iFrame) ,diameterCarr/2);
        drawCogWheel([X,Y],teethPlan,modul_Epicyclic,... % center, number of teeth, modul
            col.palnet, linW,... % color, linewidth
            anglePlan(iFrame),... % angle of rotaion
            NaN, 0, 0, 0); % nSpoke, spokeW, sideOffset, shaftDiameter
    end
    
    % carrier
    angCarr = linspace(0,2*pi,nPlan+1);
    [X,Y] = pol2cart([angCarr  fliplr(angCarr)]+angleCarrier(iFrame) ,[ones(size(angCarr))*diameterCarr/2.07 ones(size(angCarr))* diameterCarr/1.93]);
    patch(X,Y,col.carrier,'EdgeColor',[0 0 0],'LineWidth',linW) % full outer disc
    
    for iPlan = angPlan
        [X,Y] = pol2cart(iPlan+angleCarrier(iFrame) ,diameterCarr/2);
        circlePatch(X,Y,diameterPlan*0.25,col.carrier,linW);
        circlePatch(X,Y,diameterPlan*0.15,col.palnet, linW);
    end
    
    %% connection Epicyclic Gearing and hub
    % 24 teeth, rotates 5 teeth
    drawCogWheel([0 0],teethSun_top ,modul_Sun_Hub,... % center, number of teeth, modul
        1-(1-col.sun)*0.5, linW,... % color, linewidth
        angleSun(iFrame),... % angle of rotaion
        NaN, 0, 0, 3); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % spoked hub wheel: 60 teeth; rotates 5
    drawCogWheel(centerHub,teethHub_spoked ,modul_Sun_Hub,... % center, number of teeth, modul
        col.hub, linW,... % color, linewidth
        -angleSun(iFrame)/2.5 +pi/teethHub_spoked,... % angle of rotaion
        teethSun/2*2.5/5,... % 12 nSpoke,
        1, 5.5, 7); % spokeW, sideOffset, shaftDiameter
    
    %% chain of wheels on the Top
    % on top big spoked (wheel 96 teeth rotates 2) 48 teeth rotates 1
    drawCogWheel(centerSpoke,48 ,modul_top,... % center, number of teeth, modul
        1-(1-col.spoke)*0.7, linW,... % color, linewidth
        angleSun(iFrame)/2.5/4+0.2,... % angle of rotaion
        NaN, 1, 0, 7); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % top idler , meshing with small wheel big spoked; 17 teeth rotates 1
    drawCogWheel([57.35 31],17 ,modul_top,... % center, number of teeth, modul
        col.top, linW,... % color, linewidth
        -angleSun(iFrame)/2.5/4 * 48/17  - 0.067,... % angle of rotaion
        NaN, 1, 0, 3); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % last on top, meshing with idler; 23 teeth rotates 1
    drawCogWheel([42.34 41],23 ,modul_top,... % center, number of teeth, modul
        col.top*0.8, linW,... % color, linewidth
        angleSun(iFrame)/2.5/4 * 48/23  +0.12,... % angle of rotaion
        NaN, 1, 0, 3); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    %% Rack
    % Rack-Transmission; meshes in Hub-spoked 25 teeth rotates 5
    drawCogWheel(centerRackTrans,teethRackTrans_Bottom,modul_Sun_Hub,... % center, number of teeth, modul
        col.rackTrans, linW,... % color, linewidth
        angleSun(iFrame)/teethRackTrans_Bottom*teethSun_top +0.003,... % angle of rotaion
        NaN, 1, 0, 0); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % Rack-Transmission; meshes in Rack-driver; 15 teeth rotates 3
    drawCogWheel(centerRackTrans,teethRackTrans_Top,modul_Rack,... % center, number of teeth, modul
        1-(1-col.rackTrans)*0.7, linW,... % color, linewidth
        angleSun(iFrame)/teethRackTrans_Bottom*teethSun_top +0.157,... % angle of rotaion
        NaN, 1, 0, 2.5); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    % Rack-driver; idler between Rack-Transmission and Rack
    drawCogWheel(centerRackDriver,teethRackDriver ,modul_Rack,... % center, number of teeth, modul
        col.rackDrive, linW,... % color, linewidth
        -angleSun(iFrame)/teethRackTrans_Bottom*teethSun_top *15/12 +pi/teethRackDriver ,... % angle of rotaion
        NaN, 0.5, 0, 2); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    drawRack([centerRackDriver(1)+modul_Rack*teethRackDriver /2 centerRackDriver(2)],50,modul_Rack,col.rack,linW,-angleSun(iFrame)/teethRackTrans_Bottom*teethSun_top *modul_Rack/2*teethRackTrans_Top)
    
    %% lower left
    %  on top of hub; rotates 3 teeth
    drawCogWheel(centerHub,36 ,modul_LL,... % center, number of teeth, modul
        1-(1-col.hub)*0.9, linW,... % color, linewidth
        -angleSun(iFrame)/2.5,... % angle of rotaion
        NaN, 1, 3, 9); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    %  next to hub; lower left trasmission; bottom wheel; rotates 3 teeth
    drawCogWheel([centerHub(1)-28.8 centerHub(2)],36 ,modul_LL,... % center, number of teeth, modul
        col.LL_1*0.5, linW,... % color, linewidth
        angleSun(iFrame)/2.5 +pi/36,... % angle of rotaion
        NaN, 1, 0, 1); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    %  lower left trasmission; top wheel; rotates 2 teeth
    drawCogWheel([centerHub(1)-28.8 centerHub(2)],24 ,modul_LL,... % center, number of teeth, modul
        col.LL_1, linW,... % color, linewidth
        angleSun(iFrame)/2.5 ,... % angle of rotaion
        NaN, 1, 0, 4); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    %  lower left wheel; rotates 2 teeth; rotates 1 spoke
    drawCogWheel([centerHub(1)-57.6 centerHub(2)],48 ,modul_LL,... % center, number of teeth, modul
        col.LL_2, linW,... % color, linewidth
        -angleSun(iFrame)/2.5  /2 +pi/48,... % angle of rotaion
        24, 1, 0, 10); % nSpoke, spokeW, sideOffset, shaftDiameter
    
    %% save animation
    xlim(xlimValues); ylim(ylimValues); drawnow
    f = getframe(figHandle);
    reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % the size reduction: adds antialiasing
    
%     if iFrame == 10 % SVG
%         if ~isempty(which('plot2svg'))
%             plot2svg(fullfile(pathstr, [fname '_a.svg']),figHandle) % by Juerg Schwizer
%         else
%             disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
%         end
%     end

end

map = createImMap(reducedRGBimage,128,[0 0 0;1 1 1;struct2map(col)]); % 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, [fname '_a.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif
disp([fname '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit


function drawCogWheel(center,toothNumber,modul,colFilling,linW,startOffset,nSpoke,spokeW,sideOffset,shaftDia)
% DRAWTOOTHEDWHEEL - draw a simple Toothed Wheel
%  Input:
%    center:       [x y]
%    toothNumber:  scalar
%    modul:        scalar tooth "size"
%    colFilling:   color of filling [r g b]
%    linW:         LineWidth (scalar)
%    startOffset:  start rotation (scalar)[rad] 
%    nSpoke:       number of spokes; NaN for filled wheel (scalar integer) 
%    spokeW:       spoke width  [moduls]
%    sideOffset:   spoke side offset  [moduls]
%    shaftDia:     inner shaft diameter  [moduls]

effectiveRadius = modul*toothNumber/2; % effective effectiveRadius

outsideRadius =     effectiveRadius+1*  modul; %                +---+             +---+
upperRisingRadius = effectiveRadius+0.5*modul; %               /     \           /     \
% effective Radius                             %              /       \         /       \
lowerRisingRadius = effectiveRadius-0.5*modul; %             I         I       I         I
rootRadius =        effectiveRadius-1.1*modul; %     + - - - +         + - - - +         +

angleBetweenTeeth = 2*pi/toothNumber; % angle between 2 teeth

angleOffPoints = (0:angleBetweenTeeth/16:(2*pi));
angleOffPoints = angleOffPoints+startOffset; % apply rotation offset

angleOffPoints(7:16:end)  = angleOffPoints(7:16:end)  + 1/toothNumber^1.2; % hack to create smaller tooth tip
angleOffPoints(11:16:end) = angleOffPoints(11:16:end) - 1/toothNumber^1.2; % hack to create smaller tooth tip

angleOffPoints(8:16:end)  = (angleOffPoints(7:16:end) +  angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly
angleOffPoints(10:16:end) = (angleOffPoints(11:16:end) + angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly

angleOffPoints(6:16:end)  = angleOffPoints(6:16:end)  + 1/toothNumber^1.7; % hack to create slender upperRisingRadius
angleOffPoints(12:16:end) = angleOffPoints(12:16:end) - 1/toothNumber^1.7; % hack to create slender upperRisingRadius

radiusOffPoints = angleOffPoints; % allocate with correct site

radiusOffPoints(1:16:end)  = rootRadius;        % center bottom         I
radiusOffPoints(2:16:end)  = rootRadius;        % left bottom           I
radiusOffPoints(3:16:end)  = rootRadius;        % left bottom corner    +
radiusOffPoints(4:16:end)  = lowerRisingRadius; % lower rising bottom      \
radiusOffPoints(5:16:end)  = effectiveRadius;   % rising edge                 \
radiusOffPoints(6:16:end)  = upperRisingRadius; % upper rising edge              \
radiusOffPoints(7:16:end)  = outsideRadius;     % right top  corner                 +
radiusOffPoints(8:16:end)  = outsideRadius;     % right top                         I
radiusOffPoints(9:16:end)  = outsideRadius;     % center top                        I
radiusOffPoints(10:16:end) = outsideRadius;     % left top                          I
radiusOffPoints(11:16:end) = outsideRadius;     % left top  corner                  +
radiusOffPoints(12:16:end) = upperRisingRadius; % upper falling edge             /
radiusOffPoints(13:16:end) = effectiveRadius;   % falling edge                /
radiusOffPoints(14:16:end) = lowerRisingRadius; % lower falling edge       /
radiusOffPoints(15:16:end) = rootRadius;        % right bottom  corner  +
radiusOffPoints(16:16:end) = rootRadius;        % right bottom          I

[X,Y] = pol2cart(angleOffPoints,radiusOffPoints);
X = X+center(1); % center offset
Y = Y+center(2); % center offset

if ~isnan(nSpoke)
    for iSpoke = 1:nSpoke
        Xs = ([-1 1 1 -1]+sideOffset)*modul*spokeW;
        Ys =  [ 1 1 0  0]*(rootRadius-1*modul);
        [Xs,Ys] = rotateCordiantes(Xs,Ys,2*pi/nSpoke*iSpoke+startOffset);% apply rotation
        Xs = Xs+center(1); % center offset
        Ys = Ys+center(2); % center offset
        patch(Xs,Ys,colFilling*0.85,'EdgeColor',[0 0 0],'LineWidth',linW)
    end
    
    [Xc,Yc] = pol2cart(angleOffPoints,effectiveRadius-3*modul);
    Xc = Xc+center(1); % center offset
    Yc = Yc+center(2); % center offset

    [Xc,Yc] = poly2cw(Xc,Yc);
    [X,Y] = poly2cw(X,Y);
    [Xb,Yb] = polybool('subtraction', X,Y,Xc,Yc);
    Xb = Xb(~isnan(Xb)); % notNaN
    Yb = Yb(~isnan(Yb)); % notNaN
    patch(Xb,Yb,colFilling,'EdgeColor','none')
    
    plot(X, Y, 'linewidth',linW,'color',[0 0 0]); % extra line
    plot(Xc,Yc,'linewidth',linW,'color',[0 0 0]); % extra line

else % filled
    patch(X,Y,colFilling,'EdgeColor',[0 0 0],'LineWidth',linW)
end
if and(~isnan(shaftDia),shaftDia>0)
    circlePatch(center(1),center(2),shaftDia*modul,1-(1-colFilling)*0.85,linW);
end
% % effective Radius
% [X,Y] = pol2cart(angleOffPoints,effectiveRadius);
% X = X+center(1); % center offset
% Y = Y+center(2); % center offset
% plot(X,Y,'-.','color',[0 0 0]);


function [x,y] = rotateCordiantes(x,y,anglee)
% x coordinates of the center
% y coordinates of the center
% anglee angle of rotation in [rad]
rotM = [cos(anglee) -sin(anglee); sin(anglee) cos(anglee)];
x_y = rotM*[x(:)';y(:)'];
x = x_y(1,:);
y = x_y(2,:);


function drawRack(center,toothNumber,modul,col,linW,startOffset)
% x coordinates of the center
% y coordinates of the center
% r is the radius of the circle
% col patch color
% linW LineWidth
% startOffset initial shift
y = (0:toothNumber*8-2)*pi*modul/8;
y = y-mean(y)+center(2)+startOffset;
x = ones(size(y))*center(1);

x(1:8:end) = x(1:8:end)+1.1*modul; %     +   I
x(2:8:end) = x(2:8:end);           %   /     I
x(3:8:end) = x(3:8:end)-0.9*modul; % +       I
x(4:8:end) = x(4:8:end)-0.9*modul; % I       I
x(5:8:end) = x(5:8:end)-0.9*modul; % +       I
x(6:8:end) = x(6:8:end);           %   \     I
x(7:8:end) = x(7:8:end)+1.1*modul; %     +   I
x(8:8:end) = x(8:8:end)+1.1*modul; %     I   I

y(3:8:end) = y(3:8:end)+0.08*modul; %
y(5:8:end) = y(5:8:end)-0.08*modul; %

y = [y(1) y y(end)];
x = [x(1)+5*modul x x(end)+5*modul];
patch(x,y,col,'EdgeColor',[0 0 0],'LineWidth',linW);


function h = circlePatch(x,y,r,col,linW)
% x coordinates of the center
% y coordinates of the center
% r is the radius of the circle
% col patch color
% linW LineWidth
angleOffPoints = linspace(0,2*pi,200);
xc = x + r*cos(angleOffPoints);
yc = y + r*sin(angleOffPoints);
% h = plot(xc,yc,'color',col,'LineWidth',linW,'LineStyle',sty);
h = patch(xc,yc,col,'EdgeColor',[0 0 0],'LineWidth',linW);


function drawRingGear(toothNumber,modul,colFilling,linW,startOffset)
% subfunction for the outer static gear
%    toothNumber:  scalar
%    modul:        scalar tooth "size"
%    colFilling:   color of filling [r g b]
%    linW:         LineWidth (scalar)
%    startOffset:  start rotation (scalar)[rad] 
effectiveRadius = modul*toothNumber/2; % effective effectiveRadius

outsideRadius     = effectiveRadius-1*  modul; %                +---+             +---+
upperRisingRadius = effectiveRadius-0.5*modul; %               /     \           /     \
% effective Radius                             %              /       \         /       \
lowerRisingRadius = effectiveRadius+0.5*modul; %             I         I       I         I
rootRadius        = effectiveRadius+1.1*modul; %     + - - - +         + - - - +         +

angleBetweenTeeth = 2*pi/toothNumber; % angle between 2 teeth

angleOffPoints = (0:angleBetweenTeeth/16:(2*pi));

angleOffPoints = angleOffPoints+startOffset; % apply rotation offset

%% outerEdge
maxRadius = rootRadius*1.2; % definition of outer line
[Xout,Yout] = pol2cart(angleOffPoints,maxRadius);

% plot(axesHandle,X,Y,'linewidth',2,'color',[0 0 0]); % 

%% inner teeth
radiusOffPoints = angleOffPoints; % init

angleOffPoints( 7:16:end) = angleOffPoints(7:16:end)  + 1/toothNumber^1.2; % hack to create smaller tooth tip
angleOffPoints(11:16:end) = angleOffPoints(11:16:end) - 1/toothNumber^1.2; % hack to create smaller tooth tip

angleOffPoints( 8:16:end) = (angleOffPoints(7:16:end) +  angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly
angleOffPoints(10:16:end) = (angleOffPoints(11:16:end) + angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly

angleOffPoints( 6:16:end) = angleOffPoints(6:16:end)  + 1/toothNumber^1.7; % hack to create slender tooth
angleOffPoints(12:16:end) = angleOffPoints(12:16:end) - 1/toothNumber^1.7; % hack to create slender tooth

radiusOffPoints( 1:16:end) = rootRadius;        % center bottom         I
radiusOffPoints( 2:16:end) = rootRadius;        % left bottom           I
radiusOffPoints( 3:16:end) = rootRadius;        % left bottom corner    +
radiusOffPoints( 4:16:end) = lowerRisingRadius; % lower rising bottom      \
radiusOffPoints( 5:16:end) = effectiveRadius;   % rising edge                 \
radiusOffPoints( 6:16:end) = upperRisingRadius; % upper rising edge              \
radiusOffPoints( 7:16:end) = outsideRadius;     % right top corner                 +
radiusOffPoints( 8:16:end) = outsideRadius;     % right top                        I
radiusOffPoints( 9:16:end) = outsideRadius;     % center top                       I
radiusOffPoints(10:16:end) = outsideRadius;     % left top                         I
radiusOffPoints(11:16:end) = outsideRadius;     % left top corner                  +
radiusOffPoints(12:16:end) = upperRisingRadius; % upper falling edge             /
radiusOffPoints(13:16:end) = effectiveRadius;   % falling edge                /
radiusOffPoints(14:16:end) = lowerRisingRadius; % lower falling edge       /
radiusOffPoints(15:16:end) = rootRadius;        % right bottom corner   +
radiusOffPoints(16:16:end) = rootRadius;        % right bottom          I

[X,Y] = pol2cart(angleOffPoints,radiusOffPoints);

[Xout,Yout] = poly2cw(Xout,Yout);
[X,   Y   ] = poly2cw(X   ,Y   );
[Xb,Yb] = polybool('subtraction',Xout,Yout, X,Y);
Xb = Xb(~isnan(Xb)); % notNaN
Yb = Yb(~isnan(Yb)); % notNaN
patch(Xb,Yb,colFilling,'EdgeColor','none')

plot(X,   Y,   'linewidth',linW,'color',[0 0 0]); % draw teeth outline
plot(Xout,Yout,'linewidth',linW,'color',[0 0 0]); % draw outer circle


function map = struct2map(RGB)
% RGB: struct of depth 1 with [r g b] in each field
fNames = fieldnames(RGB);
nNames = numel(fNames);
map = NaN(nNames,3); % allocate
for iName = 1:nNames
    map(iName,:) = RGB.(fNames{iName}); % 
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];


function RGB = roundToUINT8pos(RGB)
% Round rgb [0 to 1] to values that matches nicely to a uint8 compatible pos
% This not strictly necessary, but it makes later colormap-work less
% ambiguous and can help to avoid dithering of larger areas.
% Input / output:   RGB: [r g b]
RGB   = round( RGB.*255)./255; % round it to possible uint8 color

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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 his or her 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.

Quality images logo.svg
Quality image
This image has been assessed using the Quality image guidelines and is considered a Quality image.

العربية | جازايرية | беларуская | беларуская (тарашкевіца)‎ | български | বাংলা | català | čeština | Cymraeg | Deutsch | Schweizer Hochdeutsch | Zazaki | Ελληνικά | English | Esperanto | español | eesti | euskara | فارسی | suomi | français | galego | עברית | हिन्दी | hrvatski | magyar | Հայերեն | italiano | 日本語 | ქართული | 한국어 | Kurdî | Lëtzebuergesch | lietuvių | македонски | മലയാളം | मराठी | Bahasa Melayu | Nederlands | polski | português | português do Brasil | rumantsch | română | русский | sicilianu | slovenčina | slovenščina | српски / srpski | svenska | தமிழ் | తెలుగు | ไทย | Türkçe | українська | vèneto | Tiếng Việt | 中文 | 中文（简体）‎ | 中文（繁體）‎ | +/−

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current19:27, 14 October 2017Thumbnail for version as of 19:27, 14 October 2017600 × 500 (10.36 MB)Jahobr (talk | contribs)color pallet better
19:05, 13 September 2017Thumbnail for version as of 19:05, 13 September 2017600 × 500 (11.53 MB)Jahobr (talk | contribs)GraphicsSmoothing with matlab 2017
10:41, 20 June 2017Thumbnail for version as of 10:41, 20 June 2017600 × 500 (10.44 MB)Jahobr (talk | contribs)User created page with UploadWizard
  • You cannot overwrite this file.

The following 80 pages uses this file:

File usage on other wikis

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Unnecessarily_complicated_gears_a.gif&oldid=318679109"