Fourier Circle Art

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Kaustubh
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Fourier Circle Art
on 1 Nov 2024
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Cite your audio source here (if applicable):
% Audio Source
% Zeta - Vincent Rubinetti
drawframe(1);
Write your drawframe function below
function drawframe(f)
    persistent drawpath;
    
    % Define the points as a complex array
    path = [345-63i,314-63i,284-64i,256-66i,250-90i,242-118i,234-149i,226-182i,217-216i,209-249i,201-281i,193-310i,187-334i,177-373i,166-409i,155-438i,142-459i,124-471i,94-467i,82-442i,90-420i,102-392i,116-361i,131-330i,143-302i,151-284i,160-264i,170-237i,181-205i,193-171i,205-137i,215-104i,225-75i,223-63i,200-63i,151-64i,113-71i,82-89i,58-112i,39-135i,25-152i,4-153i,4-137i,15-118i,36-88i,65-48i,96-21i,125-7i,147-2i,169-1i,200-1i,230-1i,261-1i,291-1i,322-1i,352-1i,383-1i,413-1i,444-1i,474-1i,505-1i,535-1i,563-2i,579-28i,563-55i,535-62i,505-63i,474-63i,444-63i,413-64i,403-73i,400-90i,393-129i,384-189i,380-231i,380-262i,382-286i,386-306i,391-328i,401-361i,411-392i,419-416i,421-440i,402-466i,367-471i,352-457i,342-434i,334-394i,332-358i,333-320i,335-287i,337-265i,339-242i,345-212i,351-182i,357-152i,363-122i,369-92i,376-62i];
    
    % Number of points
    N = numel(path);
    
    % Compute the Discrete Fourier Transform (DFT)
    F = fft(path) / N;
    
    % Prepare time values to interpolate the points smoothly
    t = linspace(0,1,96);
    
    % Number of Fourier terms to include in reconstruction
    num_terms = 24;
    
    % precompute and save the reconstructed path 
    if f == 1
        drawpath = zeros(size(t));
        for k=1:96
            % Reset for each time point
            current_point = F(mod(0,N) + 1) * exp(2*pi*1i*0*t(k));
            
            % Plot each Fourier component as a rotating circle
            for n = -num_terms:num_terms
            
                if n==0
                    continue
                end
                % Get the index in the DFT result
                idx = mod(n,N) + 1;
                
                % Calculate the contribution of the current frequency
                term = F(idx) * exp(2*pi*1i*n*t(k));
                
                % Update the current point for this Fourier component
                current_point = current_point + term;
            
            end
            
            % Store the point in the reconstruction for visualization
            drawpath(k) = current_point;
        
        end
    end
    
    
    % Create a figure for visualization
    figure("Color",'k',Position=[0,0,600,600])
    hold on;
    
    % Reset for each time point
    current_point = F(mod(0,N) + 1) * exp(2*pi*1i*0*t(f));
    
    % Plot each Fourier component as a rotating circle
    for n = -num_terms:num_terms
    
        if n==0
            continue
        end
        % Get the index in the DFT result
        idx = mod(n,N) + 1;
        
        % Calculate the contribution of the current frequency
        term = F(idx) * exp(2*pi*1i*n*t(f));
        
        % Update the current point for this Fourier component
        current_point = current_point + term;
        
        % Draw the circle
        theta = linspace(0,2*pi,100);
        circle = abs(F(idx)) * exp(1i*theta) + current_point - term;
        plot(real(circle),imag(circle),Color='#679baa', LineWidth=2);
    
        vlen = abs(term);
        
        % Draw the vector
        plot([real(current_point - term),real(current_point)],...
             [imag(current_point - term),imag(current_point)],'w',LineWidth=0.1+vlen/50);
    
    end
    
    
    % Plot the reconstructed shape as it forms
    % And create the fading trail
    for k=1:96
        start = k-1;
        if start == 0
            start = 96;
        end
        opacity = 1-mod(f+96-k,96)/128;
        plot(real([drawpath(start) drawpath(k)]),imag([drawpath(start) drawpath(k)]),Color=opacity*[1 1 0],LineWidth=2);
    end
    
    xlim([-150,750]);
    ylim([-650,250]);
    hold off;
    axis off;
end
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