Line pathway using intersection points

clear all
Window=10
square=[0 0; 0 Window; Window 0; Window Window];% Box coordinates
N=5;
% Coordinates of segments endpoints
X1=rand(N,1)*(10+0.1)+0.1;
X2=rand(N,1)*(10+0.1)+0.1;
Y1=rand(N,1)*(10+0.1)+0.1;
Y2=rand(N,1)*(10+0.1)+0.1;
A = [X1(:), X2(:)]; B =[Y1(:), Y2(:)];

% Find the intersection between segments
% Here i use the intersection function by Douglas M. Schwarz
ABx=[X1(:), X2(:)];
reshape(ABx,1,[]);
transpose(ABx);
ABx.';
ABx(:);
ABx=reshape(ABx.',1,[]);
ABy=[Y1(:), Y2(:)];
reshape(ABy,1,[]);
transpose(ABy);
ABy.';
ABy(:);
ABy=reshape(ABy.',1,[]);
pos         = 3:3:((((length(ABy))/2)-1)*3);
[r,c]       = size(ABy);
add         = numel(pos);           
Xnew        = NaN(r,c+add);    
Ynew        = NaN(r,c+add);    
idx         = setdiff(1:c+add,pos); 
Xnew(1,idx) = ABx;
Ynew(1,idx) = ABy;

Inter=intersections(Xnew,Ynew);% This gives the intersection points

figure, plot(A.',B.','LineWidth', 0.75)
grid on
axis square
axis([0 Window 0 Window])

I have segments as shown above. For each segment, i have the coordinates of endpoints. Now, I want to determine the pathways that connect both sides of the box, and remove the unconnected segments. So far, i have been able to find the intersections betweeen segments, and will appreciate any help finding the pathways.

[darova]

How would you know the order of connections?

[Tchilabalo]

By sorting the intersections in increasing order of x and y.

[darova]

SO what is the question? You have all points. Why don't just use plot()?

Answer 1

[darova]

Simple example

n = 5;
x1 = rand(n,2);
y1 = rand(n,2);
x2 = rand(n,2);
y2 = rand(n,2);
k = 0;
    % loop through all segment to find all intersections
for i = 1:n
    for j = 1:n
        [xc,yc] = polyxpoly(x1(i,:),y1(i,:),x2(j,:),y2(j,:));
        if ~isempty(xc)
            k = k+1;
            x(k) = xc;
            y(k) = yc;
        end
    end
end
[~, ix] = sort(x);
plot(x(ix),y(ix),'o-k','linewidth',2)
hold on
plot(x1',y1','r',x2',y2','b')
hold off

[Tchilabalo]

Thanks Darova for your answer.

[darova]

Accept the answer if it helped