How can plot 1D manifold in 3d space

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M 2022-6-21

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https://ww2.mathworks.cn/matlabcentral/answers/1744555-how-can-plot-1d-manifold-in-3d-space

回答： Torsten 2022-6-21

采纳的回答： Torsten

Hi, I have to plot a 1D manifold based on the equations below, x=[0,0.3], y=[0,1], z=[0,0.5]

other related equations are:

The 1D manifold in 3D space should be something like the red curve in the figure below:

For the convenience, the code of equations are:

g=(0:05).^4./z+(0:05).^4;

x=g;

p=0.255.*(z.^2./z.^2+(0.055).^2);

m1=0.15.^2./(p.^2+0.15.^2);

m2=z.^4./z.^4+0.1.^4;

m3=p.^2./p.^2+0.15.^2;

b=m2.*m3.*x;

a=m1.*(1-m2.*g);

f=1./1+0.4.*(1+a./b);

Thanks in advance for any help.

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M 2022-6-21

Sure, thanks again, I will check it and if it works I will accept your answer

M 2022-6-21

编辑：M 2022-6-21

@Torsten ,my problem is almost solved with your code, but because your answer is in the comment, I can't accept it as the best answer, so please write it as an answer if you like, then it would be chosen as the accepted answer, thanks.

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采纳的回答

Torsten 2022-6-21

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syms x y z

p=0.255*z.^2./(z.^2+(0.055)^2);

m1=0.15^2./(p.^2+0.15^2);

m2=z.^4./(z.^4+0.1^4);

m3=p.^2/(p.^2+0.15^2);

g = 0.05^4./(z+0.05^4);

a = m1.*(1-m2.*g);

b = m2.*m3.*x;

f = 1./(1+0.4*(1+a./b));

u = 0.18*f.*(5.5*y-6.5*z)-0.002*z.^2./(0.01+z.^2);

v = x - 0.05^4./(z+0.05^4) ;

u = subs(u,x,g);

Y = solve(u==0,y)

Y =

Y = matlabFunction(Y);

z = 0.1:0.1:1;

y = Y(z);

x = 0.05^4./(z+0.05^4);

plot3(x,y,z)

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