How to plot 3d version of rose plot?

I have a data.mat file where the first column represents indices, the second column contains force values in the x-direction, the third column contains force values in the y-direction, and the fourth column contains force values in the z-direction. I need to create a 3D rose plot similar to the one shown in the attached file 3dplot.png.

for 2D i can make the rose plot as shown below:

load('data.mat'); 
force_x = data(:, 2); % Force in x-direction
force_z = data(:, 4); % Force in z-direction
x = force_x;
z = force_z;
theta_rad = atan2(z, x);
theta_deg = rad2deg(theta_rad);
theta_deg = mod(theta_deg, 360);
disp('Theta');
disp(theta_deg);
figure;
rose(theta_rad);

Answer 1

[Abhas]

Hi @Sahil Wani,

To create a 3D rose plot in MATLAB, you need to calculate spherical coordinates and create a custom visualization. You can follow the below steps to generate a 3D rose plot:

1. Convert the Cartesian force components into spherical coordinates.
2. Generate a 2D histogram to represent angular distributions.
3. Visualize the distribution by drawing patches in 3D space.
4. Apply colors to the patches based on the normalized count within each bin.
5. Ensure the color scale aligns with your example (ranging from 0.05 to 0.40).

Below is the MATLAB code to guide you in creating this visualization:

% Load the data
load('data.mat');

% Extract force components
force_x = data(:, 2);
force_y = data(:, 3);
force_z = data(:, 4);

% Calculate spherical coordinates
r = sqrt(force_x.^2 + force_y.^2 + force_z.^2);
theta = atan2(force_y, force_x);
phi = acos(force_z ./ r);

[X,Y,Z] = sphere(50);

figure('Color', 'white');
hold on;

% Number of bins for discretization
n_theta = 20; 
n_phi = 10;   

% Create histogram bins
theta_edges = linspace(-pi, pi, n_theta+1);
phi_edges = linspace(0, pi, n_phi+1);

N = histcounts2(theta, phi, theta_edges, phi_edges);
N = N / max(N(:)); 

% Create the 3D rose plot
for i = 1:n_theta
    for j = 1:n_phi
        if N(i,j) > 0
            % Calculate center points of each bin
            theta_center = (theta_edges(i) + theta_edges(i+1))/2;
            phi_center = (phi_edges(j) + phi_edges(j+1))/2;
            
            % Calculate the vertices for this patch
            dtheta = (theta_edges(i+1) - theta_edges(i));
            dphi = (phi_edges(j+1) - phi_edges(j));
            
            % Create patch vertices
            theta_patch = [theta_center-dtheta/2, theta_center+dtheta/2, ...
                         theta_center+dtheta/2, theta_center-dtheta/2];
            phi_patch = [phi_center-dphi/2, phi_center-dphi/2, ...
                        phi_center+dphi/2, phi_center+dphi/2];
           
            scale = N(i,j);  
            [x, y, z] = sph2cart(theta_patch, pi/2-phi_patch, scale);
           
            patch(x, y, z, scale, 'EdgeColor', 'none');
        end
    end
end

% Customize the plot
colormap(jet);
colorbar;
caxis([0 0.4]);  % Match the color scale in your example
axis equal;
grid on;
xlabel('X');
ylabel('Y');
zlabel('Z');
view(45, 30);  % Adjust view angle

title('3D Force Distribution Rose Plot');

You may refer to the below MathWorks documentation links to know more about the spherical co-ordinates conversion:

1. https://www.mathworks.com/help/matlab/ref/atan2.html
2. https://www.mathworks.com/help/matlab/ref/acos.html
3. https://www.mathworks.com/help/matlab/ref/histcounts2.html
4. https://www.mathworks.com/help/matlab/ref/sph2cart.html

I hope this helps!