2-D graph help

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Ogen
Ogen 2016-2-10
评论： Star Strider 2016-3-6
Hi everyone. I would like to produce a graph like the one shown in the picture on MatLAB. Any help with writing the script will be greatly appreciated. The radius of each band increases from the central point 0,0.

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Star Strider
Star Strider 2016-2-10
One possibility:
w = linspace(0, 2*pi);
c = [cos(w); sin(w)];
r = [1 2 3];
figure(1)
plot(r(1)*c(1,:), r(1)*c(2,:))
hold on
plot(r(2)*c(1,:), r(2)*c(2,:))
plot(r(3)*c(1,:), r(3)*c(2,:))
hold off
axis equal
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Ogen
Ogen 2016-2-10
Furthermore, would it be possible to explain the equation used for the first section so I understand the maths? Thanks
Star Strider
Star Strider 2016-2-10
My pleasure.
The mushroom cloud problem would seem to be a computational fluid dynamics problem far beyond the scope of my knowledge. However, if you want to plot a cone plotting the radius at different heights, and perhaps the shape of the cloud itself, I would investigate the cylinder function. It, possibly in combination with the sphere function, could give you the result you want. This code uses both:
[Xc,Yc,Zc] = cylinder(0.5, 20);
[Xs,Ys,Zs] = sphere(20);
Xsm = Xs * 2;
Ysm = Ys * 2;
Zsm = Zs + 2;
figure(1)
surf(Xc,Yc,Zc)
hold on
surf(Xsm,Ysm,Zsm)
hold off
grid on
axis equal
view([-35 20])
to produce:

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Ogen
Ogen 2016-2-10
Wow that does sound complicated! I like the look of the graph you have plotted so I will definitely have a more detailed look. Your help is very much appreciated and helped to kick start my project, cheers.
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Ogen
Ogen 2016-3-6
Thanks for the reply. Would my code be able to be created into an animation plot using the drawnow and getframe functions as I have tried and I can't seem to crack it.
Star Strider
Star Strider 2016-3-6
My pleasure.
The drawnow function is useful inside a loop, so that you calculate and draw each frame and animate it in real time. This works best if the calculations creating the image are reasonably fast, and the resolution relatively low.
The getframe function and its friends allow you to create a movie out of your MATLAB images. This is best if the calculations for each frame take a while, are relatively high resolution, and so are not suited to real time display. If you have detailed images that take some time to render and you don’t need to change the parameters of the simulation in real time, this is likely the better option.
It all depends on what you want to depict. I last did this sort of thing many years ago when MATLAB, and PCs in general, were slower, so getframe was the best option for me. I've used drawnow recently with good results, but with simpler code.

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Ogen
Ogen 2016-2-10
How do you change the height of the cylinder and sphere?
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Star Strider
Star Strider 2016-2-11
As always, my pleasure.
Star Strider
Star Strider 2016-2-11

UPDATE — I did some Web searching, and discovered Dr. Jos Stam’s website at the University of Toronto http://www.dgp.toronto.edu/people/stam/reality/Research/pub.html. See specifically ‘Real-Time Fluid Dynamics for Games’. There’s also a CDROM, but I doubt the code’s written in MATLAB, so you’d have to adapt it. I found it through Mushroom Cloud Physics on ‘gamedev.net’. (I’m a gamer, so I can’t explain this not occurring to me earlier, other than that I do primarily medieval-themed games where mushroom clouds are rare and dragons are plentiful.)

If I find anything else, I’ll post it here.

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