Unable to get the correct 3-D Helix plot using the parameters

Iam trying to plot a 3-D Helix using the below parameters. Iam supposed to get the below helix:

But, the helix iam getting is not as expected.

Parameters:

p=0.199; Pitch distance

a=0.02999500; Radius of the helis wire

b=0.191; Radius of the helix

n = 5; is the number of turns.

δ =atan(p/(2*pi*b));

x’ = b + a cos(Ө)

y’ = -a sin(Ө) sin(δ)

x =x’ sin(ф)+y’ cos(ф);

y =-x’ cos(ф)+y’ sin(ф);

z =p*ф/(2*pi)+a*sin(Ө)*cos(δ);

This is the plot Iam getting:

This is the code I have done so far. Any help would be appreciated! Thanks.

% Define the parameters
p = 0.199;  % Pitch distance
a = 0.02999500;  % Radius of the helix wire
b = 0.191;  % Radius of the helix
n = 5;  % Number of turns
delta = atan(p/(2*pi*b));  % Angle delta

% Define the color map
colormap([0 0 1; 1 1 0; 0 1 0]);  % Shades of blue, yellow, and green

% Define the range of angles for phi and theta
phi = linspace(0, 2*pi, 100);
theta = linspace(0, 2*pi*n, 1000);

% Initialize the arrays for x, y, and z coordinates
x = zeros(length(phi), length(theta));
y = zeros(length(phi), length(theta));
z = zeros(length(phi), length(theta));

% Compute the x, y, and z coordinates for each point in the grid
for i = 1:length(phi)
    for j = 1:length(theta)
        x_prime = b + a*cos(theta(j));
        y_prime = -a*sin(phi(i))*sin(theta(j))*sin(delta);
        x(i,j) = x_prime*sin(phi(i)) + y_prime*cos(phi(i));
        y(i,j) = -x_prime*cos(phi(i)) + y_prime*sin(phi(i));
        z(i,j) = p*theta(j)/(2*pi) + a*sin(theta(j))*cos(delta);
    end
end

% Create the 3D plot
surf(x, y, z);
axis equal;
colormap('default');
colorbar;
xlabel('x');
ylabel('y');
zlabel('z');
title('Helix with Shades of Blue, Yellow, and Green Colors');

[Mathieu NOE]

Funny

the same exact helix problem was already answered here

Creating a 3d Helix Spiral with Surf command - MATLAB Answers - MATLAB Central (mathworks.com)

Answer 1

[VBBV]

% Define the parameters
p = 0.199;  % Pitch distance
a = 0.02999500;  % Radius of the helix wire
b = 0.191;  % Radius of the helix
n = 5;  % Number of turns
delta = atan(p/(2*pi*b));  % Angle delta

% Define the color map
colormap([0 0 1; 1 1 0; 0 1 0]);  % Shades of blue, yellow, and green

% Define the range of angles for phi and theta
phi = linspace(0, 2*pi*n, 100);
theta = linspace(0, 2*pi*n, 1000);

% Initialize the arrays for x, y, and z coordinates
x = zeros(length(phi), length(theta));
y = zeros(length(phi), length(theta));
z = zeros(length(phi), length(theta));

% Compute the x, y, and z coordinates for each point in the grid
for i = 1:length(phi)
    for j = 1:length(theta)
        x_prime = b + a*cos(theta(j));
        y_prime = -a*sin(theta(j))*sin(delta);
        x(i,j) = x_prime*sin(phi(i)) + y_prime*cos(phi(i));
        y(i,j) = -x_prime*cos(phi(i)) + y_prime*sin(phi(i));
        z(i,j) = p*phi(i)/(2*pi) + a*sin(theta(j))*cos(delta);
    end
end

% Create the 3D plot
mesh(x, y, z);
axis equal;
colormap('default');
colorbar;
xlabel('x');
ylabel('y');
zlabel('z');
title('Helix with Shades of Blue, Yellow, and Green Colors');

[R Vaidehi]

Thanks for this!