Plotting an Archimedean Spiral

r = 12.5; %outer radius
a = 0;    %inner radius
b = 0.01; %incerement per rev

n = (r - a)./(b); %number  of revolutions

th = 2*n*pi;      %angle

Th = linspace(0,th,1250*720);  
x = (a + b.*Th).*cos(Th);
y = (a + b.*Th).*sin(Th);

plot(x,y)

The code executes well r, a, n and b are correct. Th and th both are also correct, but the problem which arises is in the values of x and y.

outer value or last value (desired) should be 12.5, but after execution it gives 78.53 and same corresponds to y.

what can be the solutions of this problem?

[KALYAN ACHARJYA]

Is your plot not an Archimedean Spiral? or ??

[Rajbir Singh]

yes its an archimedean spiral

[KALYAN ACHARJYA]

Then what is the problem?

[Rajbir Singh]

Sir,

The output which i am getting is an Archimedean Spiral, thats fine. But the problem arises with the output values x and y.

According to the software that i am using r, a, n, b, th and Th values are correct.

My desired outer radius for archemedean spiral is 12.5 but it gives 78.53

[Rajbir Singh]

How can i change the rotation (clockwise or anti-cloclwise) of Archimedean Spiral?

Answer 1

[Jos (10584)]

In the computation of x and y you wrongly multiply b with Th. You should multipy by Th / (2*pi):

r = 12.5; %outer radius
a = 0;    %inner radius
b = 0.5; %incerement per rev % Jos: changed to see the spiral!!
n = (r - a)./(b); %number  of revolutions
th = 2*n*pi;      %angle  
Th = linspace(0,th,1250*720);  
x = (a + b.*Th/(2*pi)).*cos(Th);
y = (a + b.*Th/(2*pi)).*sin(Th);
% better:
% i = linspace(0,n,1250*720)
% x = (a+b*i).* cos(2*pi*i)
plot(x,y)
[x(end) y(end)]

[Rajbir Singh]

It works, thanks a lot Sir.

[Rajbir Singh]

How can i change the rotation (clockwise or anti-cloclwise) of Archimedean Spiral?

[Jos (10584)]

hint: use a minus sign :-)

[Rajbir Singh]

It works, thanks once again. :)

[Leroy Tyrone]

@ Jos Is it possible to return which revolution in 'n' that each value in 'Th' belongs to? Alnd also to plot the points as equidistant by assigning a variable 's' as arc length?