How to set a specific distance between new point and previous calculated points?

Hello, I try to generate a set of points using the fermat spiral equations teta(i)=2*pi*(phi^-2)*i; r(i)=a*i^b These points represent heliostats and I would like to avoid overlapping or collision so my question is i would like to ensure a certain euclidien distance between new point (xi,yi) and previous calculated points. Looking for your reply.

[Torsten]

Distance along the spiral or euclidean distance ?

[zouhir zeroual]

euclidean distance would be better

Answer 1

[Ameer Hamza]

The following code will generate a spiral, while ensuring that distance between consecutive point is greater then a threshold

phi = 2;
a = 1;
b = 1;

threshold = 0.1;

totalPoints = 1000;

i = zeros(1, totalPoints);
r = zeros(1, totalPoints);
theta = zeros(1, totalPoints);
di = 0.01;

count = 1;
failCounter = 1;
while count < totalPoints
  testPoint = i(count)+failCounter*di;
  thetaTestPoint = 2*pi/phi^2*testPoint;
  rTestPoint = a*testPoint.^b;

    [xTestPoint, yTestPoint] = pol2cart(thetaTestPoint, rTestPoint);
    [x, y] = pol2cart(theta(count), r(count));
    distance = norm([xTestPoint, yTestPoint] - [x, y]);

    if distance > threshold
        count = count + 1;
        i(count) = testPoint;
        r(count) = rTestPoint;
        theta(count) = thetaTestPoint;
        failCounter = 0;
    end

    failCounter = failCounter + 1;
end

polarplot(theta, r)

It will generate totalPoints number of points, which are at least threshold distance apart.

[zouhir zeroual]

I appreciate your immense effort, but Sir Hamza the final pattern should look like that (image attached),in fact these are the value i should work with a=2; b=0.5; phi = (sqrt(5)+1)/2; and thanks again

Answer 2

[ritika malik]

r = zeros(25,1);
c= 20;
theta = zeros(25,1);
for i = 1:25
    r(i) = c*sqrt(i);
theta(i) = i*137.508;
end
theta = deg2rad(theta);

 [M,N]= size(f);
  x = r.*cos(theta);
 y = r.*sin(theta);

 b = zeros(M,N);
 for i  = 1:25
   b(round(M/2+x(i)) , round(N/2+y(i))) = 1;
 end
 figure();imagesc(abs(b));colormap('gray')