Plotting a spiral in MATLAB knowing the start and end points and number of turns?

I found a code and was able to modify it into the following code to creaet a spiral that starts at the point I want it to but I can't seem to get it to end where I want it to and have the desired numer of turns.

t = 1:5000;
u = .0265;
r0 = 10;
r = r0 +u*t;

omega = .005;
phi0 = 3*pi/2;
phi = -omega*t+phi0;
x = r .* cos(phi);
y = r .* sin(phi);
plot(x,y)
grid on;

[Jacob Shulman]

where do you want it to stop? you'll have to just figure out the value of t at that point. currently you have 5000 values of t. To shorten the spiral, shorten the array t.

Answer 1

[Jos (10584)]

This does the job (for an integer number of turns)

% given values
pos = [8 4 ;    % startpoint
       2 7 ] ;  % endpoint
nturns = 3 ;    % number of turns (integer value)

% engine
dp = diff(pos,1,1) ;
R = hypot(dp(1), dp(2)) ;
phi0 = atan2(dp(2), dp(1)) ;

phi = linspace(0, nturns*2*pi, 10000) ; % 10000 = resolution
r = linspace(0, R, numel(phi)) ;
x = pos(1,1) + r .* cos(phi + phi0) ;
y = pos(1,2) + r  .* sin(phi + phi0) ;

plot(x,y,'b-',pos(:,1),pos(:,2),'ro-') ; % nturns crossings, including end point

[madhan ravi]

+1 for hypot

[Alec Lothian]

Ok this works for the start, end, and number of turns. I forgot to say the spiral needs to be centered at the origin like a pancake solenoid shape. How can I modify this to do that?

[Image Analyst]

Set the start point to 0,0. Note, having it end where you want and having a specified number of turns might be not both achievable at the same time.

[Alec Lothian]

I don't want it to start at the origin though. I just want the center of the spiral there with the starting and end point in relation to that.

[Jos (10584)]

Subtracting the means:

x = x - mean(x)
y = y - mean(y)

will center the spiral given all points. And:

x = x - dp(1)/2
y = y - dp(2)/2

will center the spiral relative to the two points

[Alec Lothian]

Awesome. Thanks guys

[km meenu]

I have a code of galaxy model and spiral line code how i draw the spiral line in the spiral arms of the galaxy