How can I plot a boundary between real and imaginary solutions in a 3D graph?

Hi everyone,

I have a function of three variables and I would like to plot a 3D graph where you can see the boundary (a surface or any shape) that separates the real and imaginary solutions of the function for a certain input. How can I do it?

So far, I have the following code:

fun = @(psi,theta,x)sqrt(-1.0./((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0)).^2.*((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0)).^2+1.0).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(9.0./5.0e1)-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).*(9.0./5.0e1)-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2.*(9.0./5.0e1)+((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).*(9.0./5.0e1))./((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0))-1.0./5.0)+(((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0)).*(sin(theta).*(1.0e1./9.0)-cos(theta).*sin(psi).*(1.0e1./9.0)+sqrt(-1.0./((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0)).^2.*((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0)).^2+1.0)-1.0e1./9.0).*(9.0./5.0e1))./((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-sqrt((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).^2+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2).*(sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2-((sin(theta).*(-1.0./5.0)+cos(theta).*sin(psi).*(1.0./5.0)+1.0./5.0).^2.*(2.5e1./9.0)+(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0).^2.*(2.5e1./9.0)+(cos(psi).*(3.0./2.0e1)-3.0./2.0e1).^2.*(2.5e1./9.0)).*(x+cos(theta).*(1.0./5.0)+sin(psi).*sin(theta).*(1.0./5.0)-1.0./5.0));
% Input values:

psi = linspace(-pi/6,pi/6,50); theta = linspace(-pi/6,pi/6,50);x = linspace(0,0.5,50);
[PSI,THETA,X] = meshgrid(psi,theta,x);

% Solution for a certain input:

solution = fun(PSI,THETA,X);

% Obtain only the coordinates of real solutions and assign value
% "0" to imaginary solutions and value "1" to real ones.

coord_1 = []; 
coord_2 = [];
coord_3 = [];

l = 1;
for i=1:length(psi)
    for j=1:length(theta)
        for k=1:length(x)
            if imag(solution(i,j,k)) == 0 
               solution(i,j,k) = 1;
               coord_1(l) = PSI(i,j,k); 
               coord_2(l) = THETA(i,j,k);
               coord_3(l) = X(i,j,k);
               l=l+1;
            else
               solution(i,j,k) = 0; 
            end
        end
    end
end

scatter3(coord_1',coord_2',coord_3',2);

By boundary I mean something similar to plot only the outer points (connected each other) of the scatter3 graph.

Thank you in advance.

Answer 1

[Vimal Rathod]

Hi,

If you just want to connect points you could use the surf function on the x,y,z values obtained at the end. If you want to create just a boundary ignoring the inner points you could use the boundary function.

Hope this helps!

[Paul]

Hi Vimal,

Thanks for your answer. I wonder if there is an "optimal way" (without checking all the coordinates) to find the x,y,z values corresponding to the boundary. Because, without these values I can not use surf or boundary functions.