How to plot implicit function with conditions?

I need to plot a function / surface of the form f(x,y,z)=0

But, I also need to put some constraints like

-3.14< $\sqrt{x+y}$ <3.14

How can i achieve this?

Answer 1

[Torsten]

Use "fimplicit" or "fimplicit3" and select ranges for the variables:

https://de.mathworks.com/help/matlab/ref/fimplicit.html

https://de.mathworks.com/help/matlab/ref/fimplicit3.html

[Abir Ghosh]

The problem is my condion can't be expressed as ranges

how can i express -2<z+sqrt(x^2+y^2)<2 as range?

[Torsten]

And what is the function f for which you want to plot the surface f(x,y,z)=0 ?

[Torsten]

Here is an example:

fimplicit(@fun)

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

function values = fun(x,y)
  values = NaN(size(x));
  values(x+y<0) = x.^2+y.^2-1.0;
end

[Abir Ghosh]

My function is actually in cylindrical polar coordinates:

f(R,theta, z) = (tan(r+z)+tan(z-r)) - (tan(r+z)-tan(z-r))cos(theta)

and my domain for plot is

-pi<r+z<pi and -pi<z-r<pi

Answer 2

[Torsten]

Doesn't look that nice ...

fimplicit3(@fun,[-5 5 -5 5 -5 5])

function values = fun(x,y,z)
  [theta,r] = cart2pol(x,y);
  %r = sqrt(x.^2+y.^2);
  %theta = atan2(y,x);
  values = NaN(size(x));
  for i=1:numel(x)
    if abs(z(i)+r(i)) < pi && abs(z(i)-r(i)) < pi
      values(i) = (tan(z(i)+r(i))+tan(z(i)-r(i))) - (tan(z(i)+r(i))-tan(z(i)-r(i))).*cos(theta(i));
    end
  end
end