Help with implementing viscircles

Hello, I'm wondering if there is a simple way to add a trajectory to all of my vectors in my last plot. I'm not the brightest with MATLAB and I have been trying to play around with viscircles already, I just dont know how I would implement it into my code correctly, specficially I don't exactly know how I would be able to update each circle continuously throughout all of the vectors complete motion.

For reference, I have attached what my current plot looks like, the second image shows what I am trying to achieve.

Thank you for your time and any help.

Current Plot:

What I am trying to achieve (trajectories of each line):

%%Loading 2D Line Data


clear; close all
s = load('coord.mat');

position = complex(s.coord(:,1),s.coord(:,2));
Ndata = length(position); % Number of Data Point

Ncoef = 20;



%% CFFT


tmp_coef = fft(position);

idx1 = 1:Ncoef/2;
idx2 = Ndata:-1:Ndata-Ncoef/2+1;
tmp_idx = [idx1;idx2];

k_idx = tmp_idx(:)';
Fcoef = tmp_coef(k_idx);



%% Inverse Fourier Transform and Calculation of Reproduced Coordinate Points


pos_Ncoef = zeros(Ndata,1);
pos_NcoefMatrix = zeros(Ndata,Ncoef);

for jj=1:Ndata
    pos_Ncoef(jj) = (exp(1i*2*pi*(k_idx-1)*(jj-1)/Ndata)*Fcoef)/Ndata;
    pos_NcoefMatrix(jj,:) = (exp(1i*2*pi*(k_idx-1)*(jj-1)/Ndata).*Fcoef.')/Ndata;
end
% pos_Ncoef = sum(pos_NcoefMatrix,2); % pos_Ncoef is same as this equation.



%% Drawing Reproduced Coordinate Points


figure(1)
plot(real(position),imag(position),'r');
hold on
plot(real(pos_Ncoef),imag(pos_Ncoef),'b');
hold off
axis equal
ax=gca;
xlim([-1.2 1.2])
ylim([-1.3 1.1])
legend("Origial","Fourier Series Iteration")



%% Vector Display of Each Coefficient Component


figure(2);

Rg=plot(real(position),imag(position),'LineWidth',2);
hold on
axis equal
ax=gca;

% Cumulative sum of each coefficient component is taken from the lower frequency.
pos_cumsum = cumsum(pos_NcoefMatrix,2);

x0 = real(pos_cumsum(1,1:end-1)); % origin x
y0 = imag(pos_cumsum(1,1:end-1)); % origin y
u0 = real(pos_NcoefMatrix(1,2:end)); % x elements
v0 = imag(pos_NcoefMatrix(1,2:end)); % y elements
h2=quiver(x0, y0, u0, v0,...
    'AutoScale','off',...
    'LineStyle','-',...
    'LineWidth',0.5,...
    'Color',[0 0 0],...
    'MaxHeadSize',1);



%% Moving Display of Each Coefficient Component


Z=plot(position(1),'r','LineWidth',1.5); % Reference line
legend("Origial Plot","Fourier Series Vectors","Fourier Series Plot")

for iter = 1:numel(position)-1
    xIter = real(pos_cumsum(iter,1:end-1)); % origin x
    yIter = imag(pos_cumsum(iter,1:end-1)); % origin y
    uIter = real(pos_NcoefMatrix(iter,2:end)); % x element
    vIter = imag(pos_NcoefMatrix(iter,2:end)); % y element

    zeta = [uIter vIter];
    
    h2.XData = xIter;
    h2.YData = yIter;
    h2.UData = uIter;
    h2.VData = vIter;
    
    Z.XData=real(pos_Ncoef(1:iter));
    Z.YData=imag(pos_Ncoef(1:iter));
 
drawnow
end

Answer 1

[Aashray]

Hello @Crazy duck,

According to my understanding of your question, you want to visualize the trajectory (the circular paths) of each rotating vector in the Fourier series animation. This will help to visualize how each harmonic contributes to the final path over time.

To achieve this, we can add a circular trail to every vector using MATLAB plotting functions. We can precompute the circle points using “sin” and “cos” and use the “plot” function to draw each circle in real time. Also one enhancement is storing the plot handles in “gobjects” so that they get updated efficiently within the loop.

You may refer to the code below for more clarity:

%% Load 2D Line Data 
clear; close all 
s = load('coord.mat'); 
position = complex(s.coord(:,1), s.coord(:,2)); 
Ndata = length(position); % Number of Data Points 
Ncoef = 20; 

%% FFT and Extract Coefficients 
tmp_coef = fft(position); 
idx1 = 1:Ncoef/2; 
idx2 = Ndata:-1:Ndata-Ncoef/2+1; 
tmp_idx = [idx1;idx2]; 
k_idx = tmp_idx(:)'; 
Fcoef = tmp_coef(k_idx); 

%% Precompute Points from Inverse FFT 
pos_Ncoef = zeros(Ndata,1); 
pos_NcoefMatrix = zeros(Ndata, Ncoef); 
for jj = 1:Ndata 
    pos_Ncoef(jj) = (exp(1i*2*pi*(k_idx-1)*(jj-1)/Ndata) * Fcoef) / Ndata; 
    pos_NcoefMatrix(jj,:) = (exp(1i*2*pi*(k_idx-1)*(jj-1)/Ndata) .* Fcoef.') / Ndata; 
end 

pos_cumsum = cumsum(pos_NcoefMatrix, 2); 

%% Set Up Plot with Initial Vectors 
figure(2); clf  
plot(real(position), imag(position), 'k', 'LineWidth', 1.5); hold on  
axis equal 
xlim([-2 2]); ylim([-2 2]);  
legend("Original Plot", "Fourier Series Vectors", "Fourier Series Plot"); 

% Initial vector display 
x0 = real(pos_cumsum(1,1:end-1)); 
y0 = imag(pos_cumsum(1,1:end-1)); 
u0 = real(pos_NcoefMatrix(1,2:end)); 
v0 = imag(pos_NcoefMatrix(1,2:end)); 

h2 = quiver(x0, y0, u0, v0, ... 
    'AutoScale', 'off', ... 
    'LineStyle', '-', ... 
    'LineWidth', 0.5, ... 
    'Color', [0 0 0], ... 
    'MaxHeadSize', 1); 

Z = plot(real(pos_Ncoef(1)), imag(pos_Ncoef(1)), 'r', 'LineWidth', 1.5); 

%% Add Initial Trajectory Circles <-- NEW BLOCK 
theta = linspace(0, 2*pi, 100); 
numCircles = Ncoef - 1; 
circleHandles = gobjects(numCircles, 1); 

for k = 1:numCircles 
    radius = abs(pos_NcoefMatrix(1,k+1)); 
    cx = real(pos_cumsum(1,k)); 
    cy = imag(pos_cumsum(1,k)); 
    xCirc = radius * cos(theta) + cx; 
    yCirc = radius * sin(theta) + cy; 
    circleHandles(k) = plot(xCirc, yCirc, '-', 'Color', [0.2 0.8 0.2]); % greenish 
end 

%% Animate Vectors and Circles <-- MODIFIED BLOCK 
for iter = 1:Ndata 
    xIter = real(pos_cumsum(iter,1:end-1)); 
    yIter = imag(pos_cumsum(iter,1:end-1)); 
    uIter = real(pos_NcoefMatrix(iter,2:end)); 
    vIter = imag(pos_NcoefMatrix(iter,2:end)); 
    
    h2.XData = xIter; 
    h2.YData = yIter; 
    h2.UData = uIter; 
    h2.VData = vIter; 
    
    Z.XData = real(pos_Ncoef(1:iter)); 
    Z.YData = imag(pos_Ncoef(1:iter)); 
    
    %% <-- NEW: Update each circle's position 
    for k = 1:numCircles 
        radius = abs(pos_NcoefMatrix(iter,k+1)); 
        cx = xIter(k); 
        cy = yIter(k); 
        xCirc = radius * cos(theta) + cx; 
        yCirc = radius * sin(theta) + cy; 
        circleHandles(k).XData = xCirc; 
        circleHandles(k).YData = yCirc; 
    end 
    
    drawnow 
end 

I have marked the modified parts for better understanding.

Finally, the desired plot is obtained.

I am also attaching documentation links of the functions used:

1. “plot” : https://www.mathworks.com/help/matlab/ref/plot.html
2. “gobjects”: https://www.mathworks.com/help/matlab/ref/gobjects.html
3. “drawnow” : https://www.mathworks.com/help/matlab/ref/drawnow.html