If a point lies in the vicinity of a logarithmic spiral : Not returning points near the center

Question

I have a set of data points, which I want to test if they lie on a logarithmic spiral arm for given parameters. The following program seems to work, but does not return any points close to the center of my plane, which contains all the data points. The image attached shows that my program does not seem to find any points which overlap with the spiral near the center. Here is the link : https://i.sstatic.net/SZHXv.jpg. Moreover, it seems to show two spirals in the overlapped points, which is another issue.

int main(){ 
float radial[10000]={0}, angle[10000]={0};  // my points of interest
float theta, r_sp;  // radius and the angle theta for the spiral

Construct a spiral which lies in the same plane as my sources (green in the image)

for (j=0;j<=PI*10; j++){
    theta=j*3./10;  
    r_sp=a_sp*exp(b_sp*theta);

Calculating the radial and angular components from x and y given coordinates (read from a file)

        for (m=0;m<=30;m++){
        radial[m]=pow((x_comp*x_comp+y_comp*y_comp),0.5); 
        angle[m]= atan2f(y_comp, x_comp);

Change the range from [ -pi, pi] to [0, 2*pi] consistent with "theta" of spiral

        if (angle[m] < 0.){
        angle[m]=angle[m]+PI;
    }

Check if the point (radial and angle) lies on/around the spiral. For the realistic effect, I am considering the points at a radial distance "dr=0.5" (jitter) away from the "r_sp" value of the spiral.

 if (fabs(r_sp-radial[m]) <=0.5 && fabs(theta-angle[m]) <= 1.0e-2){
     printf("%f\t%f\t%f\t%f\n",l[k],b[k],ns[k],radial[m]);
                 }
             } 
    }
return 0;
}

Answer 1

You check the conditions only for the first turn of spiral that lies in angle range 0..2*Pi. At first you have to estimate potential turn number from r = radial[m]

r=a*exp(b*t)
r/a=exp(b*t)
ln(r/a)=b*t
t = ln(r/a) / b
turnnumber = Floor(ln(r/a) / b)

Now you can use

angle[m] = YourAngleFromArctan + 2 * Pi * turnnumber

to compare