How can plot 1D manifold in 3d space

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.

[M]

Please let me know if the question is not clear, then I will make it clearer.

[KSSV]

What is z?

[M]

z is a variable between 0 and 0.5 (approximately)

[Torsten]

My guess is that u=0 and v=0 defines your manifold. Is this correct ?

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)

[M]

yes, 1D manifold should be plotted based on u=0 and v=0

[Torsten]

Then see the plot above.

E.g. the y-z-plane is never reached by the curve because x cannot be 0 on the manifold, only for z=Infinity:

x - 0.05^4./(z+0.05^4) = 0

[M]

Thanks @Torsten for the answer, does the figure change if instead of x,y and z that was defined by syms, we use the data attached (curve3d)?

[Torsten]

The manifold is given by

y = f(z)
x = g(z)

where z can be prescribed and x and y are derived coordinate values.

How do your curve data come into play here ? Do you want to check how far they are apart from the given manifold ?

[M]

yes exactly I want to see which part of this curve are on the curve that I sent its data, but I don't know should we use its data in your code or not

[Torsten]

plot3 your data in the same graphics window as the manifold:

% My Code %
hold on
plot3(X,Y,Z)

where X,Y,Z are your 3 columns.

[M]

yes I did it..but they don't have common part however I am sure that they should have

[Torsten]

Then recheck your equations.

And don't let y become that large by changing the range for z (I did it above).

[M]

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

[M]

@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.

Answer 1

[Torsten]

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)