MATLAB: Plotting an Archimedean Spiral

archimedean spiralarchimedesequationgraphmathematicsplotplotting

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?

Best Answer

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)]
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