How to calculate the line segment?

Hi,

I am trying to draw random lines in a circle.

I need to figure out the average of the random lines, the number of intersection of lines, and the average of line segment.

I cannot figure out how to calculate the average of line segment.

The codes are as follows:

close all; clearvars; clc;

% SIMULATION DISK DIMENSIONS

xx0=0; yy0=0; % ceneter of disk

r=1; % disk radius

numbLines=4;

theta = zeros(numbLines,1);

theta(1) = 2*pi*rand();

for i = 2: numbLines

theta(i) = theta(i-1) + 20*(pi/180) - 60*(pi/180)*rand;

end

p=r*rand(numbLines,1);

q=sqrt(r.^2-p.^2);

sin_theta=sin(theta);

cos_theta=cos(theta);

xx1=xx0+p.*cos_theta+q.*sin_theta;

yy1=yy0+p.*sin_theta-q.*cos_theta;

xx2=xx0+p.*cos_theta-q.*sin_theta;

yy2=yy0+p.*sin_theta+q.*cos_theta;

%%% START Plotting %%%START

%draw circle

t=linspace(0,2*pi,300);

xp=xx0+r*cos(t); yp=yy0+r*sin(t);

plot(xp,yp,'k');

axis square; hold on;

axis tight;

xticks([]);yticks([]);

set(gca,'Visible','off');

%plot segments of Poisson line process

plot([xx1';xx2'],[yy1';yy2'],'b','LineWidth',2);

%%%END Plotting END%%%

slope = zeros(numbLines,1);

ycept = zeros(numbLines,1);

xx = [xx1'; xx2'];

yy = [yy1'; yy2'];

Total_length=[sqrt((xx1-xx2).^2+(yy1-yy2).^2)];

sumOfElements = sum(sum(Total_length));

Average_length = sumOfElements/numbLines

for ii = 1:numbLines

slope(ii,1) = (yy(2,ii)-yy(1,ii))/(xx(2,ii)-xx(1,ii));

ycept(ii,1) = -(yy(2,ii)-yy(1,ii))/(xx(2,ii)-xx(1,ii))*xx(1,ii)...

+yy(1,ii); %% Might as well use xx(2,ii) & yy(2,ii) for the y-intercept

end

x_int = []; %% X and Y intersecting points

y_int = [];

for ii = 1:numbLines-1

slope_temp = slope(ii,1); ycept_temp = ycept(ii,1);

for jj = ii+1:numbLines

xtemp = -(ycept(jj,1)-ycept_temp)/(slope(jj,1)-slope_temp);

ytemp = slope_temp*xtemp+ycept_temp;

rr_temp = xtemp^2+ytemp^2;

if rr_temp<=r %% Pick only the intersecting points that are in the circle

x_int = [x_int; xtemp];

y_int = [y_int; ytemp];

end

end

end

scatter(x_int,y_int,100,'r','*');

** Line segement indicates that the line between two intersections.

Answer 1

[Vidhi Agarwal]

Hi @HyeongJu Lee,

To calculate the average length of line segments between intersections within the circle, you can follow these steps:

• After you have calculated the intersection points of the lines within the circle, for each pair of intersections on the same line, calculate the line segment length. Sample code for the same is given below:

% Calculate line segment lengths
segment_lengths = [];
for i = 1:numbLines
    % Find intersections on the current line
    line_intersections = [];
    for j = 1:length(x_int)
        if abs(slope(i) * x_int(j) + ycept(i) - y_int(j)) < 1e-6
            line_intersections = [line_intersections; x_int(j), y_int(j)];
        end
    end
    
    % Sort intersections along the line
    line_intersections = sortrows(line_intersections);
    
    % Calculate segments between intersections
    for k = 1:size(line_intersections, 1) - 1
        seg_length = sqrt((line_intersections(k+1, 1) - line_intersections(k, 1))^2 + ...
                          (line_intersections(k+1, 2) - line_intersections(k, 2))^2);
        segment_lengths = [segment_lengths; seg_length];
    end
end

• Compute the average length of these segments.

% Average segment length
if ~isempty(segment_lengths)
    average_segment_length = mean(segment_lengths);
else
    average_segment_length = 0;
end

Hope this helps!