I want to animate 3D vectors

Hello,

I want to demosntrate how changing every single angle would affect the areas. I did some search about Sliders. But it seems hard to build this on MATLAB. Any ideas?

I'm also open to use other online solutions or softwares.

Answer 1

[Altaïr]

Hey @Bilge Kaan Atay,

To create an animated visualization of 3D vectors and explore how varying angles influence operating zones, you can leverage MATLAB’s programmatic app-building capabilities. You’ll find a comprehensive list of relevant functions by running:

web(fullfile(docroot, 'matlab/referencelist.html?type=function&s_tid=CRUX_topnav&category=develop-apps-programmatically'))

Below is a complete implementation of the app. It includes sliders for adjusting the characteristic angle, forward and reverse angle limits, and dynamically updates the 3D plot accordingly:

function animate_operating_zones
    % Initial angle values
    charAngle = 30;
    fwdMin = 10;
    fwdMax = 40;
    revMin = 15;
    revMax = 45;

    % Create GUI figure
    f = figure('Name', 'Operating Zones on Sphere', 'Position', [100 100 1000 600]);

    % Axes for 3D plot
    ax = axes('Parent', f, 'Position', [0.35 0.1 0.6 0.8]);
    axis equal
    hold on
    grid on
    view(3)
    xlabel('X'); ylabel('Y'); zlabel('Z');

    % Create slider structure
    angles = struct();
    labels = struct(); % for value text labels

    % Slider: Characteristic Angle
    uicontrol(f, 'Style', 'text', 'String', 'Characteristic Angle', 'Position', [20 520 200 20]);
    uicontrol(f, 'Style', 'text', 'String', '0', 'Position', [20 500 30 20]);
    angles.char = uicontrol(f, 'Style', 'slider', 'Min', 0, 'Max', 360, 'Value', charAngle, ...
        'Position', [50 500 200 20], 'Callback', @(src,~) update());
    uicontrol(f, 'Style', 'text', 'String', '360', 'Position', [250 500 30 20]);
    labels.char = uicontrol(f, 'Style', 'text', 'String', num2str(charAngle), 'Position', [280 500 40 20]);

    % Slider: Min Forward
    uicontrol(f, 'Style', 'text', 'String', 'Min Forward Angle', 'Position', [20 460 200 20]);
    uicontrol(f, 'Style', 'text', 'String', '0', 'Position', [20 440 30 20]);
    angles.fwdMin = uicontrol(f, 'Style', 'slider', 'Min', 0, 'Max', 90, 'Value', fwdMin, ...
        'Position', [50 440 200 20], 'Callback', @(src,~) update());
    uicontrol(f, 'Style', 'text', 'String', '90', 'Position', [250 440 30 20]);
    labels.fwdMin = uicontrol(f, 'Style', 'text', 'String', num2str(fwdMin), 'Position', [280 440 40 20]);

    % Slider: Max Forward
    uicontrol(f, 'Style', 'text', 'String', 'Max Forward Angle', 'Position', [20 400 200 20]);
    uicontrol(f, 'Style', 'text', 'String', '0', 'Position', [20 380 30 20]);
    angles.fwdMax = uicontrol(f, 'Style', 'slider', 'Min', 0, 'Max', 90, 'Value', fwdMax, ...
        'Position', [50 380 200 20], 'Callback', @(src,~) update());
    uicontrol(f, 'Style', 'text', 'String', '90', 'Position', [250 380 30 20]);
    labels.fwdMax = uicontrol(f, 'Style', 'text', 'String', num2str(fwdMax), 'Position', [280 380 40 20]);

    % Slider: Min Reverse
    uicontrol(f, 'Style', 'text', 'String', 'Min Reverse Angle', 'Position', [20 340 200 20]);
    uicontrol(f, 'Style', 'text', 'String', '0', 'Position', [20 320 30 20]);
    angles.revMin = uicontrol(f, 'Style', 'slider', 'Min', 0, 'Max', 90, 'Value', revMin, ...
        'Position', [50 320 200 20], 'Callback', @(src,~) update());
    uicontrol(f, 'Style', 'text', 'String', '90', 'Position', [250 320 30 20]);
    labels.revMin = uicontrol(f, 'Style', 'text', 'String', num2str(revMin), 'Position', [280 320 40 20]);

    % Slider: Max Reverse
    uicontrol(f, 'Style', 'text', 'String', 'Max Reverse Angle', 'Position', [20 280 200 20]);
    uicontrol(f, 'Style', 'text', 'String', '0', 'Position', [20 260 30 20]);
    angles.revMax = uicontrol(f, 'Style', 'slider', 'Min', 0, 'Max', 90, 'Value', revMax, ...
        'Position', [50 260 200 20], 'Callback', @(src,~) update());
    uicontrol(f, 'Style', 'text', 'String', '90', 'Position', [250 260 30 20]);
    labels.revMax = uicontrol(f, 'Style', 'text', 'String', num2str(revMax), 'Position', [280 260 40 20]);

    % Update function
    function update()
        cla(ax);
        [X, Y, Z] = sphere(100);
        surf(ax, 0.1*X, 0.1*Y, 0.1*Z, 'FaceAlpha', 0.8, 'EdgeColor', 'none');
        axis(ax, [-1 1 -1 1 -1 1]);
        xlabel('X'); ylabel('Y'); zlabel('Z');
        hold on

        % Get current angles
        ca = angles.char.Value;
        fmin = angles.fwdMin.Value;
        fmax = angles.fwdMax.Value;
        rmin = angles.revMin.Value;
        rmax = angles.revMax.Value;

        % Update value displays
        labels.char.String = sprintf('%.1f', ca);
        labels.fwdMin.String = sprintf('%.1f', fmin);
        labels.fwdMax.String = sprintf('%.1f', fmax);
        labels.revMin.String = sprintf('%.1f', rmin);
        labels.revMax.String = sprintf('%.1f', rmax);

        % Directions
        zt_axis = [0 1 0];  % Zero torque axis = y-axis
        mt_dir = rotate_vector([0 0 1], zt_axis, deg2rad(ca)); % Max torque
        mt_dir = mt_dir / norm(mt_dir);

        % Plot vectors
        quiver3(0, 0, 0, mt_dir(1), mt_dir(2), mt_dir(3), 'r', 'LineWidth', 2, 'MaxHeadSize', 1);
        text(mt_dir(1), mt_dir(2), mt_dir(3), 'Max Torque', 'Color', 'r');

        quiver3(0, 0, 0, zt_axis(1), zt_axis(2), zt_axis(3), 'b', 'LineWidth', 2, 'MaxHeadSize', 1);
        text(zt_axis(1), zt_axis(2), zt_axis(3), 'Zero Torque', 'Color', 'b');

        negZ = [0 0 1];
        quiver3(0, 0, 0, negZ(1), negZ(2), negZ(3), 'k', 'LineWidth', 2, 'MaxHeadSize', 1);
        text(negZ(1), negZ(2), negZ(3), '-U_0', 'Color', 'k', 'VerticalAlignment', 'top');

        % Plot sectors
        plot_sector(mt_dir, zt_axis, -fmin, fmax, [0 1 0]);       % Forward (green)
        plot_sector(-mt_dir, zt_axis, rmin, -rmax, [1 0.5 0]);    % Reverse (orange)
    end

    % Initial draw
    update();
end

function v_rot = rotate_vector(v, axis, angle)
    axis = axis / norm(axis);
    v_rot = v*cos(angle) + cross(axis, v)*sin(angle) + axis*dot(axis, v)*(1 - cos(angle));
end

function plot_sector(mt_dir, zt_dir, minAngle, maxAngle, color)
    N = 50;
    u = mt_dir / norm(mt_dir);
    v = zt_dir - dot(zt_dir, u)*u;
    if norm(v) < 1e-6
        v = null(u(:).');
        v = v(:,1);
    end
    v = v / norm(v);

    theta = deg2rad(linspace(minAngle, maxAngle, N));
    arc = zeros(N, 3);
    for i = 1:N
        arc(i, :) = cos(theta(i))*u + sin(theta(i))*v;
        arc(i, :) = arc(i, :) / norm(arc(i, :));
    end

    fill3([0; arc(:,1)], [0; arc(:,2)], [0; arc(:,3)], color, ...
        'FaceAlpha', 0.4, 'EdgeColor', 'none');
end

This example creates an interactive MATLAB GUI using uicontrol elements to build sliders that adjust five angle parameters, enabling real-time updates of a 3D visualization. The app uses quiver3 and fill3 to plot vectors and angular zones on a sphere, with the axes object providing full 3D customization including labels, grid, and camera view. As users manipulate the sliders, the update() function dynamically redraws the scene: a unit sphere is rendered, and vectors representing maximum and zero torque directions are plotted. Colored sectors for forward and reverse operating zones are drawn using the plot_sector function, while vector orientations are computed using Rodrigues’ rotation formula implemented in the rotate_vector function. This setup is particularly effective for visualizing torque directions and understanding angular effects interactively.

Here's what the resulting app looks like:

To learn more about the functions used, you can access their documentation directly:

• uicontrol

    web(fullfile(docroot, 'matlab/ref/uicontrol.html'))

• fill3

    web(fullfile(docroot, 'matlab/ref/fill3.html'))

• quiver3

    web(fullfile(docroot, 'matlab/ref/quiver3.html'))