Graphing a hypersurface from two inequalities

I am trying to graph a hypersurface with inputs in mu_i, alpha_i, b_i space.

I tried to do this with a for loop but I am just getting what looks like a stack of 2D surfaces, which I don't think is correct.

Looking at a slice of this, varying only X (mu_i) and Y (alpha_i) I am getting a curved cone-like area, so I am expecting something like a curved 3D cone shape.

%% initializing constants
g = 2.5;
muj=18.5;
aj=7.6;
bj=23.3;

%% define range of alpha, bi and mui values
Z=linspace(bj,100); %bi
Y=linspace(aj,100); %alpha_i
X=linspace(0,muj); %mu_i


%% Making a Matrix of mu_i and alpha_i and b_i values
[m,a,b] = meshgrid(X,Y,Z);


%% Defining the two inequalities I want to graph the intersection of as a
%hypersurface
Sij= ((1/2).*b.*bj.^(-1).*(b+(-1).*g+(-1).*m).^(-1).*(bj+(-1).*g+(-1).*muj).*(g+muj).^(-1).*(g+m+muj).^(-1).*(2.*g+m+muj).*(g+2.*muj))<(a.^(-1).*aj);

Sji= (a.^(-1).*aj)<(2.*b.*bj.^(-1).*(b+(-1).*g+(-1).*m).^(-1).*(g+m).*(g+2.*m).^(-1).*(bj+(-1).*g+(-1).*muj).*(g+m+muj).*(2.*g+m+muj).^(-1)); 

    feas = Sij.*Sji;
    feas(feas==0) = NaN;

%% Graphing

fig1=figure();
hold on

    for i =1:100 % not sure if this is right?
    surf(m(:,:,i),a(:,:,i),b(:,:,i),feas(:,:,i),'DisplayName','Feasibility','EdgeColor', 'none', 'FaceColor','k','FaceAlpha',1)
    end   
    
xlabel('\mu_i , mortality sp i','FontSize',14)
ylabel('\alpha_i , senstivity sp i','FontSize',14)
zlabel('b_i, birth sp i','FontSize', 14)

Thank you, I would appreciate any tips.

I will attach the code varying only two of the variables here.

%% initializing constants
meshsize = .01;
g = 2.5;
muj=18.5;
aj=7.6;
bj=23.3;
bi=23.3;


%% define range of alpha and mu values
alphai=aj:meshsize:100;
mui=0:meshsize/4.995:muj;



%% Making a Matrix of mu_i and alpha_i values
[m,a] = meshgrid(mui,alphai);


%% Defining the inequalities I want to graph the intersection of 
Sij= ((1/2).*bi.*bj.^(-1).*(bi+(-1).*g+(-1).*m).^(-1).*(bj+(-1).*g+(-1).*muj).*(g+muj).^(-1).*(g+m+muj).^(-1).*(2.*g+m+muj).*(g+2.*muj))<(a.^(-1).*aj);

Sji= (a.^(-1).*aj)<(2.*bi.*bj.^(-1).*(bi+(-1).*g+(-1).*m).^(-1).*(g+m).*(g+2.*m).^(-1).*(bj+(-1).*g+(-1).*muj).*(g+m+muj).*(2.*g+m+muj).^(-1)); 

feas = Sij.*Sji;
feas(feas==0) = NaN;


%% Graphing
fig1=figure();

      surf(m,a,feas,'DisplayName','Feasibility','EdgeColor', 'none', 'FaceColor','k','FaceAlpha',1)

xlabel('\mu_i , mortality sp i','FontSize',14)
ylabel('\alpha_i , senstivity sp i','FontSize',14)

Answer 1

[Ishu]

Hi Ursula,

I understand that you are trying to plot a hypersurface using "surf" function.

In your code you are using "hold on" before ant of the surface was plotted. In this case "hold on" by default assumes 2D axes and adjusts the surfaces according to that adn because of this you are getting a 2D plot instead of 3D plot.

You can change your code according to this:

fig1=figure();
    for i =1:100 % not sure if this is right?
    surf(m(:,:,i),a(:,:,i),b(:,:,i),feas(:,:,i),'DisplayName','Feasibility','EdgeColor', 'none', 'FaceColor','k','FaceAlpha',1)
    hold on %shift hold on here
    end   
    
xlabel('\mu_i , mortality sp i','FontSize',14)
ylabel('\alpha_i , senstivity sp i','FontSize',14)
zlabel('b_i, birth sp i','FontSize', 14)

And as "surf" can only create a 3D surface plot, if you want to visualize more than 3D data, you can use "griddatan" to fit a hypersurface in 3D.

For more information on "griddatan: you can refer this documentation:

https://www.mathworks.com/help/matlab/ref/griddatan.html

Hope it helps.