Grab polar intersection point coordinates from a plot

This code that plots a certain amount of circumferences and radiuses (separated by a given angle).

I need to find all the interesection points coordinates between radius and circumferences in polar and cartesian coordinates.

I should create vectors to store all the intersection coordinates for each radius.

Have you any idea about what I can do?

clear all
close all
clc

R=50;   %circ radius
S=20;   %num circ.lines
N=16;   %num ang.lines

sect_width=2*pi/N;    
sections_angle = rad2deg(sect_width);
offset_angle=0:sect_width:2*pi-sect_width;

%------------------

r=linspace(0,R,S+1);
w=0:.01:2*pi;

figure(1)
hold on
axis equal
grid minor
% plot circumferences
for n=2:length(r)
    plot(real(r(n)*exp(1i*w)),imag(r(n)*exp(1i*w)),'k')
end
% plot radius
for n=1:length(offset_angle)
    plot(real([0 R]*exp(1i*offset_angle(n))),imag([0 R]*exp(1i*offset_angle(n))),'k', 'LineWidth',1.2)
end

Answer 1

[Star Strider]

The intersections can be calculated directly from the information provided in the code.

Creating a table of them in Cartesian and polar coordinates is then straightforward —

R=50;   %circ radius
S=20;   %num circ.lines
N=16;   %num ang.lines

sect_width=2*pi/N;    
sections_angle = rad2deg(sect_width);
offset_angle=0:sect_width:2*pi-sect_width;

%------------------

r=linspace(0,R,S+1);
w=0:.01:2*pi;

figure(1)
hold on
axis equal
grid minor
% plot circumferences
for n=2:length(r)
    plot(real(r(n)*exp(1i*w)),imag(r(n)*exp(1i*w)),'k')
end
% plot radius
for n=1:length(offset_angle)
    plot(real([0 R]*exp(1i*offset_angle(n))),imag([0 R]*exp(1i*offset_angle(n))),'k', 'LineWidth',1.2)
end

xisx = r(:)*cos(offset_angle);                                      % X-Coordinates Of Intersections
yisx = r(:)*sin(offset_angle);                                      % Y-Coordinates Of Intersections

plot(xisx, yisx, 'sg', 'MarkerSize', 3, 'MarkerFaceColor','g')      % Plot Intersections (Cartesian)
hold off

[angisx,radisx] = cart2pol(xisx, yisx);                             % Polar Coordinates Of Interseections

Intersections = table(xisx(:), yisx(:), angisx(:), radisx(:), 'VariableNames',{'X','Y','Angle','Radius'})

Intersections = 336×4 table
     X      Y    Angle    Radius
    ____    _    _____    ______

       0    0      0          0 
     2.5    0      0        2.5 
       5    0      0          5 
     7.5    0      0        7.5 
      10    0      0         10 
    12.5    0      0       12.5 
      15    0      0         15 
    17.5    0      0       17.5 
      20    0      0         20 
    22.5    0      0       22.5 
      25    0      0         25 
    27.5    0      0       27.5 
      30    0      0         30 
    32.5    0      0       32.5 
      35    0      0         35 
    37.5    0      0       37.5 

.

[Lorenzo Lellini]

Thank you! Very useful

[Star Strider]

As always, my pleasure!