Plot figure for f(y,z)=0

Hi, I have two functions f and g.

and ; I want to plot f-g=0 (or f=g) in a yz plane of 3D plot. I can solve it and write y as a function of z and then plot it; but I want to know how I can plot f-g=0 directly.

Answer 1

[John D'Errico]

Simple enough. Define the two functions. Then subtract them, and plot using fimplicit.

f = @(z) 0.07*z.^2./(0.09 + z.^2);
g = @(y,z) 0.003 + 0.01*42./((y - z).^2 + 42);

fminusg = @(y,z) f(z) - g(y,z);

fimplicit(fminusg)
xlabel y
ylabel z
grid on

It can be a bit simpler if you want to use syms, because then you don't need to define f and g as explicit functions of the to variables.

syms y z
f = 0.07*z.^2./(0.09 + z.^2);
g = 0.003 + 0.01*42./((y - z).^2 + 42);

fminusg = f - g;

fimplicit(fminusg,[-20,20 -.15 .15])
xlabel y
ylabel z
grid on

You can choose a different domain for y and z (in the call to fimplicit) if you wish to expand it. You can see I did that in the second figure.

[Behi]

Many thanks for the answer. I have Matlab 2015 and fimplicit is not defined. Is there any other functions to use instead for this version of Matlab?

[Walter Roberson]

sol = solve(fminusg, z, 'maxdegree', 4);
Y = linspace(-20,20);
Z = double(subs(sol, Y)).';
plot(Y, Z)

Your version is old enough that you do not have symbolic fplot() either, which would have simplified the code.

The solution is the roots of a polynomial of degree 4.