plot a 3d function (with three independent variable)

I am traying to plot in matlab like this picture! how can i do it? thank you

Answer 1

[Star Strider]

The isosurface function would likely be most apprroppriate.

See the documentation section on Volume Visualization for more options.

[Niloofar Moosavi]

hi, thanks for your answer but i want it with shadows like this picture i tried this code but it wasn't like my picture

[Star Strider]

My pleasure!

I have no idea what you intend by ‘shadows’, since all that is necessary to produce them is to create a lighting effect.

Example —

N = 50;
xv = linspace(-10,10, N);
yv = linspace(-10,10, N);
zv = linspace(-10,10, N);

vfcn = @(x,y,z) 4*x.^2 + 9*y.^2 + 4*z.^2;

[Xm,Ym,Zm] = meshgrid(xv,yv,zv);
Vm = vfcn(Xm,Ym,Zm);

figure
p = patch(isosurface(Xm, Ym, Zm, Vm,  36));
isonormals(Xm,Ym,Zm,Vm,p)
p.FaceColor = 'red';
p.EdgeColor = 'none';
daspect([1 1 1])
view(3); 
% axis tight
axis('equal')
camlight 
lighting gouraud
grid on
hold on
plot3([-5 5], [0 0], [0 0], '-k') 
plot3([0 0], [-5 5], [0 0], '-k') 
plot3([0 0], [0 0], [-5 5], '-k') 
hold off
text(-6, 0, 0, '$x$', 'Interpreter','latex', 'FontSize',20)
text(0, -6, 0, '$y$', 'Interpreter','latex', 'FontSize',20)
text(0, 0, 6, '$z$', 'Interpreter','latex', 'FontSize',20)

This is partially copied from the isosurface documentation.

[Niloofar Moosavi]

thank you so much and how can i unfill the graph like picture?

[Star Strider]

My pleasure!

If by ‘unfill’ you mean to see inside it, add this assignment —

p.FaceAlpha = 0.75;                                                 % See Inside The Volume!

so the revised code is now —

N = 50;
xv = linspace(-10,10, N);
yv = linspace(-10,10, N);
zv = linspace(-10,10, N);

vfcn = @(x,y,z) 4*x.^2 + 9*y.^2 + 4*z.^2;

[Xm,Ym,Zm] = meshgrid(xv,yv,zv);
Vm = vfcn(Xm,Ym,Zm);

figure
p = patch(isosurface(Xm, Ym, Zm, Vm,  36));
isonormals(Xm,Ym,Zm,Vm,p)
p.FaceColor = 'red';
p.EdgeColor = 'none';
p.FaceAlpha = 0.75;                                                 % See Inside The Volume!
daspect([1 1 1])
view(3); 
axis tight
camlight 
lighting gouraud
grid on
hold on
plot3([-5 5], [0 0], [0 0], '-k') 
plot3([0 0], [-5 5], [0 0], '-k') 
plot3([0 0], [0 0], [-5 5], '-k') 
hold off
text(-6, 0, 0, '$x$', 'Interpreter','latex', 'FontSize',20, 'Horiz','center', 'Vert','middle')
text(0, -6, 0, '$y$', 'Interpreter','latex', 'FontSize',20, 'Horiz','center', 'Vert','middle')
text(0, 0, 6, '$z$', 'Interpreter','latex', 'FontSize',20, 'Horiz','center', 'Vert','middle')

Change that value to something between 0 (fully transparent) and 1 (not at all transparent) to get the result you want.

.

[Niloofar Moosavi]

thanks alot

[Star Strider]

As always, my pleasure!