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

beginendMATLABplotplottingspiralstartturns

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;

Best Answer

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
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