Plotting a 3d figure for a function with 4 variables?

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M 2021-8-13

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https://ww2.mathworks.cn/matlabcentral/answers/897957-plotting-a-3d-figure-for-a-function-with-4-variables

评论： DGM 2021-8-19

Hi, I have a function with 4 variables (x,y,z,w) which means d(x,y,z,w)=0, and I have to plot a 3D figure for just 3 variable (x,y,z) without specific values. could you please tell me which matlab function is useful?

here is my code:

function [] = critical()
[x,y,z] = meshgrid(-4:0.1:4,-4:0.1:4,-4:0.1:4);
w=1;
%parameter
a=25;K=0.5;K_p=0.4;K_b=0.3; V_s=0.8;K_s=0.2; gamma=6;K_bar=1.5e-4;
%Function
phi_1 = y.^3 ./ ( y.^3 + K ^3 );
phi_2 = w.^2 ./ ( K_p^2 + w.^2);
phi_3= K_p^2 ./ ( K_p^2 + w.^2);
teta = phi_1 .* phi_2 .* z;
aa = phi_3 .* ( 1 - phi_3).*x;
b = teta./(teta+K_b*(teta+aa));
Beta=(1-K_bar*(gamma*(x-y)./y).^2)./(1+(K_s./y).^2);
alpha=a*b*gamma.*(x-(1+(1/gamma).*y))/V_s;
d=alpha-Beta;
fv=isosurface(x,y,z,d,0)
fv = isosurface(d,0)
fvc = isosurface(d,'blue')
pp = patch(isosurface(x,y,z,d,-0))
isonormals(x,y,z,d,pp)
set(pp,'FaceColor','red','EdgeColor','none');
view(3); 
axis tight
camlight
end

when I define w as a vector [w]=meshgrid(-4:0.1:4); it has this error:

Error using .*

Matrix dimensions must agree.

Error in criticalaki (line 11)

teta = phi_1 .* phi_2 .* z;

so I put w=1 which is not true and give me the figure below. but I want a soft figure like surface.

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Adam Danz 2021-8-15

在 MATLAB Online 中打开

Your code is copied below so that Matlab Central's Run Feature can produce the plot. I also added 4 semicolons to suppress unnecessary outputs. Lastly, I added the line you described to define w with meshgrid() but I do not get that error.

[x,y,z] = meshgrid(-4:0.1:4,-4:0.1:4,-4:0.1:4);

% w=1;

[w]=meshgrid(-4:0.1:4)

w = 81×81

-4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000

%parameter

a=25;K=0.5;K_p=0.4;K_b=0.3; V_s=0.8;K_s=0.2; gamma=6;K_bar=1.5e-4;

%Function

phi_1 = y.^3 ./ ( y.^3 + K ^3 );

phi_2 = w.^2 ./ ( K_p^2 + w.^2);

phi_3= K_p^2 ./ ( K_p^2 + w.^2);

teta = phi_1 .* phi_2 .* z;

aa = phi_3 .* ( 1 - phi_3).*x;

b = teta./(teta+K_b*(teta+aa));

Beta=(1-K_bar*(gamma*(x-y)./y).^2)./(1+(K_s./y).^2);

alpha=a*b*gamma.*(x-(1+(1/gamma).*y))/V_s;

d=alpha-Beta;

fv=isosurface(x,y,z,d,0);

fv = isosurface(d,0);

fvc = isosurface(d,'blue');

pp = patch(isosurface(x,y,z,d,-0));

isonormals(x,y,z,d,pp)

set(pp,'FaceColor','red','EdgeColor','none');

view(3);

axis tight

camlight

DGM 2021-8-18

编辑：DGM 2021-8-18

在 MATLAB Online 中打开

This should at least fix your errors.

%teta = phi_1 .* phi_2 .* z;
teta = phi_1 .* bsxfun(@times,phi_2,z);
%aa = phi_3 .* ( 1 - phi_3).*x;
aa = bsxfun(@times,phi_3 .* ( 1 - phi_3),x);

isosurface doesn't tend to give a very pretty figure for a coarse grid. In order to use surf(), you'd need to express (either literally or mathematically) the location of the isosurface as a mesh of points in x,y,z space. It might look a lot nicer than using isosurface(), but it's often a lot more complicated to accomplish.

FWIW, you can always throw extra memory at it and use a finer mesh. I don't have much memory, so I just did this:

vv = linspace(-4,4,400);
[x,y,z] = meshgrid(single(vv));
[w]=meshgrid(vv);
%parameter
a=25;K=0.5;K_p=0.4;K_b=0.3; V_s=0.8;K_s=0.2; gamma=6;K_bar=1.5e-4;
%Function
phi_1 = y.^3 ./ ( y.^3 + K ^3 );
phi_2 = w.^2 ./ ( K_p^2 + w.^2);
phi_3= K_p^2 ./ ( K_p^2 + w.^2);
teta = phi_1 .* bsxfun(@times,phi_2,z);
aa = bsxfun(@times,phi_3 .* ( 1 - phi_3),x);
clear phi_1 phi_2 phi_3 w
b = teta./(teta+K_b*(teta+aa));
Beta=(1-K_bar*(gamma*(x-y)./y).^2)./(1+(K_s./y).^2);
alpha=a*b*gamma.*(x-(1+(1/gamma).*y))/V_s;
d=alpha-Beta;
clear alpha Beta a b aa teta
pp = patch(isosurface(x,y,z,d,-0));
isonormals(x,y,z,d,pp)
set(pp,'FaceColor','red','EdgeColor','none');
view(3); 
axis tight
camlight
grid on

It's a bit better, but it's still rough. At this resolution, each one of the 3D arrays occupies about 250MB, so it gets impractical to do much more.

M 2021-8-19

Thanks Adam and DGM for your comments,

DGM, I copied your code and run it, it has an error that "out of memory"...

I did something else, solve "alpha-Beta=0" and found an equation that x is written based on y,z,w and use "surface" or "plot3" to plot it.

DGM 2021-8-19

If you're running out of memory, with that example, then you'd need to reduce the number of points to something less than 400.

If you managed to get it working with surf, then you probably don't need to bother with my example.

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Plotting a 3d figure for a function with 4 variables?

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