How i can make an animation mp4 for the graph?

I have found a point 'P(x,y)' connecting 3 points A(6,9),B(20,38),C(49,25) such that the total length PA+PB+PC is minimum by the code

M=500;%we take a fixed value of M
x=6:.01:49; % p is the domain of x
y=9:.01:38; % q is the domain of y
for i=1:length(x)
    for j=1:length(y)
        L=sqrt((x(i)-6)^2+(y(j)-9)^2)+sqrt((x(i)-20)^2+(y(j)-38)^2)+sqrt((x(i)-49)^2+(y(j)-25)^2);
        if L<M
            M=L;
            a=x(i);
            b=y(j);
           
        end
        
    end
    
end

[a,b]

P(x,y)=(23.1200 29.5000)

Then draw the figure of point P joint three point A,B,C

x = [6 20 49];
y = [9 38 25];
x0 = 23.1200;
y0 = 29.5000;
figure('color','white');
hold on;
for ipt = 1:length(x)
    plot([x(ipt) x0],[y(ipt) y0],'color',[0 0 1]);
    myChar = char(64+ipt);
    text(x(ipt)+0.5,y(ipt)+0.75,myChar);
end
plot(x,y,'P','markerfacecolor','k','markeredgecolor','none', ...
    'markersize',4);
plot(x0,y0,'P','markerfacecolor','k','markeredgecolor','none', ...
    'markersize',4);
text(x0+0.5,y0+0.75,'P');
xlabel('x');
ylabel('y');

How i can make an animation mp4 of the graph for different value of p ?

Thank you.

Answer 1

[Deepak]

Hi @jakaria babar,

To animate the optimization of point (P(x, y)) minimizing (PA + PB + PC), we can use “VideoWriter” function to capture frames during each iteration.

Initialize a “VideoWriter” to create an MP4 file, and as the loops iterate over (x) and (y), plot the position of (P) and its connections to (A), (B), and (C). Use “getframe” to capture these plots and write them to the video using “writeVideo” function. Adjust the step size of (x) and (y) to balance smoothness and speed, creating an animation that visually demonstrates path of (P) to the optimal position.

Below is the MATLAB code to achieve the same:

% Initialize parameters
M = 500; % Initial large value for minimum length
x = 6:1:49; % Coarser domain for x
y = 9:1:38; % Coarser domain for y

% Create a video writer object
v = VideoWriter('minimization_animation.mp4', 'MPEG-4');
v.FrameRate = 5; % Lower frame rate
open(v);

% Initialize figure
figure('color', 'white');
hold on;
xlabel('x');
ylabel('y');
xlim([5, 50]);
ylim([8, 40]);

% Plot fixed points A, B, C
fixedX = [6, 20, 49];
fixedY = [9, 38, 25];
plot(fixedX, fixedY, 'ko', 'MarkerFaceColor', 'r');

% Annotate points A, B, C
text(fixedX(1)+0.5, fixedY(1)+0.75, 'A');
text(fixedX(2)+0.5, fixedY(2)+0.75, 'B');
text(fixedX(3)+0.5, fixedY(3)+0.75, 'C');

% Iterate over x and y to find minimum path and create animation
for i = 1:length(x)
    for j = 1:length(y)
        % Calculate total length
        L = sqrt((x(i)-6)^2 + (y(j)-9)^2) + ...
            sqrt((x(i)-20)^2 + (y(j)-38)^2) + ...
            sqrt((x(i)-49)^2 + (y(j)-25)^2);
        
        % Check if this is the minimum length so far
        if L < M
            M = L;
            a = x(i);
            b = y(j);
        end
        
        % Plot the current position of P and connecting lines
        plot([fixedX a], [fixedY b], '-b');
        plot(a, b, 'ko', 'MarkerFaceColor', 'k');
        text(a+0.5, b+0.75, 'P');
        
        % Capture the frame every nth iteration
        if mod(i*j, 5) == 0 % Capture every 5th frame
            frame = getframe(gcf);
            writeVideo(v, frame);
        end
        
        % Clear the plot for the next frame, keeping the fixed points
        clf;
        hold on;
        plot(fixedX, fixedY, 'ko', 'MarkerFaceColor', 'r');
        text(fixedX(1)+0.5, fixedY(1)+0.75, 'A');
        text(fixedX(2)+0.5, fixedY(2)+0.75, 'B');
        text(fixedX(3)+0.5, fixedY(3)+0.75, 'C');
        xlabel('x');
        ylabel('y');
        xlim([5, 50]);
        ylim([8, 40]);
    end
end

% Close the video
close(v);
disp(['Minimum length found at P(', num2str(a), ',', num2str(b), ') with length ', num2str(M)]);

Please find attached the documentation of functions used for reference:

VideoWriter: www.mathworks.com/help/matlab/ref/videowriter.html

getframe: www.mathworks.com/help/matlab/ref/getframe.html

writeVideo: www.mathworks.com/help/matlab/ref/videowriter.writevideo.html

I hope this assists in resolving the issue.