How can I create a surface plot of a function of 3 variables?

I have the following function that describes a quadric surface:

syms f(x, y, z)
f(x, y, z) = -x^2 - (y^2 / 4) + (z^2 / 4) == 1

I'm trying to understand how to plot it. I've tried a few things, like solving the equation for z, and then filling in a matrix containing z values. e.g.

syms g(x, y);
g(x, y) = solve(f(x, y, z), z);  % matrix([[-(4*x^2 + y^2 + 4)^(1/2)], [(4*x^2 + y^2 + 4)^(1/2)]])

xrange = -10:10;
yrange = -10:10;
zrange = zeros(numel(xrange), numel(yrange));
for i = 1:numel(xrange)
  for j = 1:numel(yrange)
    zrange(i, j) = g(xrange(i), yrange(j));
  end
end

Unfortunately, this code does not because z can take on multiple values for a given (x, y) value. MATLAB rightly complains:

Assignment has more non-singleton rhs dimensions than non-singleton subscripts

Any tips? Do I need to make xrange and yrange into matrix values? If so, then what should they look like? If not, then what are some other things I can look into?

Thanks.

Answer 1

[Azzi Abdelmalek]

 syms f(x, y, z)
f(x, y, z) = -x^2 - (y^2 / 4) + (z^2 / 4) == 1
syms g(x, y);
g(x, y) = solve(f(x, y, z), z);  % matrix([[-(4*x^2 + y^2 + 4)^(1/2)], [(4*x^2 + y^2 + 4)^(1/2)]])
xrange = -10:10;
yrange = -10:10;
zrange = zeros(numel(xrange), numel(yrange));
for i = 1:numel(xrange)
  for j = 1:numel(yrange)
      a=g(xrange(i), yrange(j));
    zrange1(i, j) = double(a(1));
    zrange2(i,j)=double(a(2));
  end
end
close
surf(xrange,yrange,zrange1)
hold on
surf(xrange,yrange,zrange2)

[Kamil Jiwa]

Thanks Azzi. That's helpful, but is there a way I can make it generic for other functions? For example, what if f is defined as such:

f(x, y, z) = 4*x + 7*y - 6*z - 8 == 0

In this case, z will only have 1 value at every point.

I noticed the surf() function is able to plot surfaces with multiple values at a given (x, y) value (e.g. sphere()), so this seems like a possible avenue to explore. However, I'm not clear about how the matrices for X and Y should look in that case.

Answer 2

[Walter Roberson]

I suggest you use isosurface over a meshgrid of x, y, z

[Kamil Jiwa]

Thanks. It does look promising, but I'd appreciate an example using the function the way I defined it. The MATLAB docs don't show any such examples.