How to plot a 3D surface with a circle in it?

Question

I have a rational polynomial function. I find zeros of numerator and denominator of it. Now I want to draw this function and I do it with meshgrid and mesh command in matlab. How can I draw a circle in this shape? I add my result figure at first and second figure is an image that I want to be like that( draw red circle).

Answer 1

Create x and y for your circle:

r = 1;
theta = 0:0.1:2*pi;
x = r*cos(theta);
y = r*sin(theta);

Get the value of your function at the x and y's and plot a line in 3D with the values:

z = f(x,y);
plot3(x,y,z);

The final result may have some artefacts where the line crosses in and out of the surface. If you are not so concerned about the accuracy in the plot add a very small value to z to "lift" it above the surface.