Plotting curves with increasing radius

Question

James 2013-8-21

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https://ww2.mathworks.cn/matlabcentral/answers/85283-plotting-curves-with-increasing-radius

采纳的回答： Walter Roberson

Dear all,

I wanted to know if there is any way to plot a curve with increasing radius. This curve has to go around a circle.

Thanks for your help.

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Image Analyst 2013-8-21

Bring up your diagram somehow on the computer, be it in Photoshop or whatever. Type alt-Printscreen to capture the current window into the clipboard. Go to http://snag.gy and type control-V to paste it in. Note the URL it gives you and come back here and tell us what it is.

James 2013-8-21

@ Image Analyst: Thank you telling me how to do that. Below is the URL for the image. Hope it helps. The figure is of 3 different curves. The center is a circle, the other two I have the data for them but I am not sure not to plot them.

http://snag.gy/oaYfV.jpg

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Answer 1

Walter Roberson 2013-8-21

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https://ww2.mathworks.cn/matlabcentral/answers/85283-plotting-curves-with-increasing-radius#answer_94780

Your sample diagram look like spirals to me, other than that the radius might not be increasing linearly.

Use pol2cart() to switch between an (r, theta) form vs (x,y) coordinates.

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Kelly Kearney 2013-8-21

在 MATLAB Online 中打开

I see a circle and two spirals. Is this what you're looking for?

    theta = linspace(pi/2+2*pi, pi/2, 100);
    r = cell(3,1);
    r{1} = ones(size(theta));  % The circle
    r{2} = linspace(1, 0.5, 60); % Spiral in
    r{3} = linspace(1, 1.5, 60); % Spiral out
    for ii = 1:3
        [x{ii}, y{ii}] = pol2cart(theta(1:length(r{ii})), r{ii});
    end
    xy = [x;y]; plot(xy{:}); axis equal;

James 2013-8-21

@Kelly Kearney: Thank you. That works perfect.

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Answer 2

Image Analyst 2013-8-21

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https://ww2.mathworks.cn/matlabcentral/answers/85283-plotting-curves-with-increasing-radius#answer_94782

You say "I have the data for them" so why don't you just use the plot() function and plot them? Am I missing something???

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James 2013-8-21

编辑：James 2013-8-21

在 MATLAB Online 中打开

I have cropped the curve and that does make it better but I cannot get it to plot the full circle. I tried using a circle function for the circle but that failed too. Here is my code:

vehicle.a = 1.4; vehicle.b = 1.6; vehicle.m = 1600; vehicle.k = 1.5;
vehicle.l = vehicle.a + vehicle.b; vehicle.I = vehicle.m*vehicle.k^2;
vehicle.Cf = 6e4; vehicle.Cr = 6e4; vehicle.Ct = vehicle.Cf + vehicle.Cr;
% steering characteristics of the vehicle
steer.u = 1:1:40;
steer.a = [1.4 1.5 1.6]; steer.b = [1.6 1.5 1.4];
for i = 1:3
    loop.a = steer.a(i);
    loop.b = steer.b(i);
    steer.s (:,i) = (loop.a*vehicle.Cf - loop.b*vehicle.Cr)/vehicle.Ct;
end
% Relations of turn radius and vehicle speed for constant steer angle
steer.delta = degtorad (3);
for j = 1:3
    loop.s = steer.s(j);
    for i = 1:40
        loop.Vx = steer.u(i);
        steer.R(i,j) = (vehicle.l/steer.delta)*(1-(((vehicle.Ct*loop.s*vehicle.m)/(2*vehicle.l^2*vehicle.Cf*vehicle.Cr))*loop.Vx^2));
    end
end
% Change in turn radius with vehivle speed
loop.R = 50;
for j = 1:3
    loop.s = steer.s(j);
    for i = 1:40
        loop.Vx = steer.u(i);
        steer.delta(i,j) = (vehicle.l/loop.R)*(1-(((vehicle.Ct*loop.s*vehicle.m)/(2*vehicle.l^2*vehicle.Cf*vehicle.Cr))*loop.Vx^2));
    end
end
for i = 1:3
    steer.r = abs(steer.delta(:,i));
    [loop.r,loop.theta] = spiral(steer.r);
    steer.radius(:,i) = loop.r(:,1);
    steer.theta(:,i) = loop.theta(:,1);
end
%Change of turning with increase of vehicle speed. 
figure (4)
hold on
plot(steer.radius(:,1),steer.theta(:,1),'r')
plot(steer.radius(:,2),steer.theta(:,2),'b')
plot(steer.radius(:,3),steer.theta(:,3),'g')
title('Change of turning with increase of vehicle speed')
axis('equal')
hold off

The code is not yet cleaned up but that is no problem. Thank you for for taking such an interest in helping me.

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Answer 3

David Sanchez 2013-8-21

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https://ww2.mathworks.cn/matlabcentral/answers/85283-plotting-curves-with-increasing-radius#answer_94775

在 MATLAB Online 中打开

Try this out:

[x,y] = meshgrid(1:150,1:100);
[th, rho] =  cart2pol(x - 75,y - 50); % convert to polar
% spiral centered at (75,50)
Img = sin(r/3 + th);
imagesc(Img); colormap(hot);
axis equal; axis off;