How to I plot 3D level surfaces of this 4D function?

I have the following function. I wish to plot the 3D surface of the function when density equals 100000, 80000, 60000, 40000. I am unsure how to plot a function of 3 variables. Thanks

density= @(x,y,z)10.^5 -24000.*z + 10.^4.*sech((0.75.*x-1.5).^2+(y-1).^2)

Answer 1

[Walter Roberson]

Use ndgrid or meshgrid to create a 3D grid of x, y, z locations, and evaluate the function at those points . Suppose we call the result D .

Now use

arrayfun(@(LEVEL) isosurface(x, y, z, D, LEVEL), [100000, 80000, 60000, 40000]);

It is not possible to pass multiple levels to isosurface() in one call.

[Jessica Peterson]

Could you elaborate more on creating D? I am unsure how to do that.

[Walter Roberson]

density= @(x,y,z)10.^5 -24000.*z + 10.^4.*sech((0.75.*x-1.5).^2+(y-1).^2)
minx = -1; maxx = 5;
miny = -1; maxy = 5;
minz = -1; maxz = 5;
N = 50;
xv = linspace(minx, maxx, N);
yv = linspace(miny, maxy, N);
zv = linspace(minz, maxz, N);
[X, Y, Z] = meshgrid(xv, yv, zv);
D = density(X, Y, Z);
cla
arrayfun(@(LEVEL) isosurface(X, Y, Z, D, LEVEL), [100000, 80000, 60000, 40000]);
xlabel('x');
ylabel('y');
zlabel('z');
legend({'100000', '80000', '60000', '40000'})

[Jessica Peterson]

That creates a 2D plot of a rectangle. I am trying to make a 3D plot.

[Walter Roberson]

Grab the plot with your cursor and rotate it. Or give the command

view(3)