Calculating the trajectories of several helixes running along the surface of the same cylinder

I'm attempting to write script that plots the trajectories of several helixes that run along the surface of a cylinder

I want to plot 34 helixes that start from equally distant points on the circumfrence of a circle.

Here is what I have:

% Set the number of points and the radius of the circle

num_points = 34;

radius_circle = 0.5;

% Create an array of angles equally spaced around the circle

angles = linspace(0, 2*pi, num_points+1);

angles = angles(1:end-1);

% Calculate the x and y coordinates for the points on the circle

x_circle = radius_circle * cos(angles);

y_circle = radius_circle * sin(angles);

% Display the coordinates

disp('Coordinates:');

disp([x_circle', y_circle']);

figure(1);hold on;clf

dia = 1;

pitch = 10;

height = 20;

for i=1:num_points

syms t

radius = dia/2;

x = x_circle(i) + radius*sin(t);

y = y_circle(i) + radius*cos(t);

z = t/(2*pi)*pitch;

tmax = 2*pi*height/pitch;

fplot3(x, y, z, [0 tmax], 'LineWidth', 2)

hold on

end

The helixes do not run along the same cylinder for some reason..

Answer 1

[Pseudoscientist]

solved

% Set the number of helixes to plot

N = 35;

% Set the radius and pitch of the helixes

radius = 1;

pitch = 0.2;

% Set the number of points to plot on each helix

num_points = 100;

% Initialize a matrix to hold the coordinates of the helixes

helix_coords = zeros(num_points, 3, N);

% Loop through each helix

for i = 1:N

% Set the phase offset for this helix

phase_offset = (i-1)*2*pi/N;

% Generate the x, y, and z coordinates for this helix

x = radius*cos((1:num_points)*2*pi/num_points + phase_offset);

y = radius*sin((1:num_points)*2*pi/num_points + phase_offset);

z = pitch*(1:num_points);

% Store the coordinates in the matrix

helix_coords(:,:,i) = [x', y', z'];

end

% Plot the helixes

plot3(squeeze(helix_coords(:,1,:)), squeeze(helix_coords(:,2,:)), squeeze(helix_coords(:,3,:)))