How can I plot 3D surface x^3 + y^3 + z^3 = 1, where x, y, z are in unit closed interval in MATLAB ?.

I want to plot a surface x^3 + y^3 + z^3 = 1, where x, y, z are in unit closed interval. The MATLAB is not displaying the plot. Perhaps there occur some complex roots. Please help me to write its code. Thanks in advance.

Answer 1

[madhan ravi]

syms x y z

fimplicit3(x^3+y^3+z^3==1,[-1 1 -1 1 -1 1])

[Amna Habib]

MATLAB responses: Undefined function or variable 'fimplicit3'.

[madhan ravi]

type ver in command window and paste the result here

[Amna Habib]

---------------------------------------------------------------------------------------------
MATLAB Version: 8.5.0.197613 (R2015a)
MATLAB License Number: ••••••
Operating System: Microsoft Windows 8.1 Pro Version 6.3 (Build 9600)
Java Version: Java 1.7.0_60-b19 with Oracle Corporation Java HotSpot(TM) Client VM mixed mode
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[madhan ravi]

I suggest you to upgrade to 2016b or later because fimplicit3 was introduced in 2016b see https://www.mathworks.com/help/matlab/release-notes.html?rntext=fimplicit3&startrelease=R2015a&endrelease=R2018b&groupby=release&sortby=descending&searchHighlight=

[Amna Habib]

Ok Thanks. But this is not an implicit function ever. Can you tell another command instead fimplicit3 for my version.

[madhan ravi]

"But this is not an implicit function ever

It is! you need to know the difference between implicit and explicit function first before plotting.

x^2+y^2=1 is an implicit function

x=+-sqrt(1-x^2) is an explicit function

"Can you tell another command instead fimplicit3 for my version."

without this function I suspect it would be hard to construct the surface

[Amna Habib]

Ok. Thanks a lot. I will upgrade to latest version.

[madhan ravi]

Anytime :)

[Bruno Luong]

madhan: how the surface looks like? Can you post the image?

[madhan ravi]

sure Bruno

[Bruno Luong]

Thanks

madhan ravi's reply: Anytime :) @Bruno

Answer 2

[Bruno Luong]

[x,y,z]=ndgrid(linspace(-1,1,33));
v=x.^3+y.^3+z.^3-1;

close all
p = patch(isosurface(x,y,z,v,0));
p.FaceColor = 'red';
daspect([1 1 1])
view(120,-30); 
axis tight
camlight 
lighting gouraud

[madhan ravi]

cool @Bruno may I know how did you attach your image as an image instead of an attachment , I don't know how to attach an image not being an attachment?

[Bruno Luong]

I use the button "image" on the left of "attach file" button.

[madhan ravi]

thanks

[Amna Habib]

Very nice. I need this surface only in first octant, that is, all x, y and z varies from 0 to 1. Is only this change is require for it? [x,y,z]=ndgrid(linspace(0,1,33)) I am not expert in MATLAB till now.

[Bruno Luong]

Yes

[Amna Habib]

Thanks:)

[Amna Habib]

Please find attached file. I want to compare the spaces covered by respective surfaces. They are not clear yet. How can I remove their mesh?

[Bruno Luong]

To remove the mesh set

    h.LineStyle = 'none';

[x,y,z]=ndgrid(linspace(-1,1,65));

close all
ptab = [1 1.5 2 3 4];
for k=1:length(ptab)
    p = ptab(k);
    v = abs(x).^p+abs(y).^p+abs(z).^p-1;
    subplot(2,2,k);
    h = patch(isosurface(x,y,z,v,0));
    h.FaceColor = 'red';
    h.LineStyle = 'none';
    daspect([1 1 1])
    view(75,20);
    axis tight
    camlight
    lighting gouraud
    title(sprintf('Sphere in l_{%g}', p));
end

[Amna Habib]

Ok. Thank you for your guidance.

[Amna Habib]

i need help in plotting the function 'g'. Can you please correct this code.

I would be very thankful to you.

x = linspace(0, 1 );
f = @(x) (x<0.5) .* (7-3.* sqrt(-2.* (log(2.*x)))) + (x>=0.5).*(7+2.* sqrt(-2.* (log(2-(2.*x)))));
g = @(x) (x<0.5).* (7-5.* sqrt(-1.* (log(2-(2.*x))))) + (x>=0.5).*(7+4.* sqrt(-1.* (log(2.*x))));
figure
plot(x, [f(x); g(x)], 'linewidth', 1.5 )

Warning: Imaginary parts of complex X and/or Y arguments ignored.

[Les Beckham]

It depends on what you really want to plot. g(x) is complex. In a 2d plot you can't plot a complex vector against a real vector. So, you have a few choices (ignoring f(x) which seems to be plotting just fine):

x = linspace(0, 1 );
g = @(x) (x<0.5).* (7-5.* sqrt(-1.* (log(2-(2.*x))))) + (x>=0.5).*(7+4.* sqrt(-1.* (log(2.*x))));
figure
plot(g(x), 'linewidth', 1.5) % plot the imaginary part of g(x) against the real part
xlabel 'real(g(x))'
ylabel 'imag(g(x))'
grid on

figure
plot(x, abs(g(x)), 'linewidth', 1.5) % plot the magnitudes of g(x) against x
xlabel 'x'
ylabel 'abs(g(x))'
grid on

figure
plot(x, angle(g(x)), 'linewidth', 1.5) % plot the phase angles of g(x) against x
xlabel 'x'
ylabel 'angle(g(x))'
grid on

figure
% plot the real part of g(x) against x; note that this is what you got
% above, plot defaults to plotting the real part and throws away the
% imaginary part
plot(x, real(g(x)), 'linewidth', 1.5)
xlabel 'x'
ylabel 'real(g(x))'
grid on

figure
plot(x, imag(g(x)), 'linewidth', 1.5) % plot the imaginary part of g(x) against x
xlabel 'x'
ylabel 'imag(g(x))'
grid on

[Amna Habib]

Thanks a lot @Les Beckham

I got this point. I appreciate your effort. Well explained!

[Amna Habib]

if you feel easy please check this code too. This function is very simple but graph is different as compared to my manual calculations.

Thank you very much for your kindness!

x = linspace(0, 1 ).';
f = @(x) (x<0.5) .* (30.*x) + (x>=0.5).* (70.*x)-20 ;
g = @(x) (x<0.5).* 30.*(1-x) + (x>=0.5).* 50-(70.*x ) ;
figure
plot(x, [f(x), g(x)], 'linewidth', 1.5 )

[Torsten]

Maybe you mean

x = linspace(0, 1,100 ).';
f = @(x) (x<0.5) .* (30.*x) + (x>=0.5).* (70.*x-20 );
g = @(x) (x<0.5).* (30.*(1-x)) + (x>=0.5).* (50-70.*x ) ;
figure
plot(x, [f(x), g(x)], 'linewidth', 1.5 )

[Amna Habib]

Yes, exactly. The same is required.

Thanks a lot @Torsten.