MATLAB: How to find the coordinate of the intersection multiple lines

intersectionlineMATLABtriangulation

Hi How to find multiple lines intersections. Example :
m=([0,1,2,3,5;9,10,12,12,10;5,0,6,4,1;5,7,4,9,1]); 
x=([m(:,1),m(:,3)]); y=([m(:,2),m(:,4)]); 
plot(x',y')

Best Answer

Interesting Friday afternoon problem!
The solution is reasonably straightforward, although not immediately obvious. The ‘Row’ designations correspond to the rows of ‘x’ and ‘y’, since that is the easiest way to refer to them. (The lines do not intersect in the original plot, so I assume the idea is to see where they would intersect if they were extended.)
First, estimate the parameters of each line: 
for k = 1:size(x,1)
    B(:,k) = [x(k,:)' ones(2,1)] \ y(k,:)';                         % Parameters
end
Then determine the intersections: 
for k1 = 1:size(B,2)
    for k2 = 1:size(B,2)
        XY(k1,k2,:) = [-B(1,[k1 k2])' [1;1]] \ B(2,[k1 k2])';       % Intersections
    end
end
X = XY(:,:,1)
Y = XY(:,:,2)
Then tabulate the intersections: 
Names = sprintfc('Row_%d',1:4);
XInt = table(X(:,1),X(:,2),X(:,3),X(:,4),'VariableNames',Names,'RowNames',Names)
YInt = table(Y(:,1),Y(:,2),Y(:,3),Y(:,4),'VariableNames',Names,'RowNames',Names)
XInt =
             Row_1     Row_2    Row_3     Row_4 
             ______    _____    ______    ______
    Row_1       NaN        9         7    5.3333
    Row_2         9      NaN       7.2     4.875
    Row_3         7      7.2       NaN    6.1667
    Row_4    5.3333    4.875    6.1667       NaN
    
YInt =
             Row_1     Row_2    Row_3     Row_4 
             ______    _____    ______    ______
    Row_1       NaN      10          8    6.3333
    Row_2        10     NaN        8.8      7.25
    Row_3         8     8.8        NaN    4.6667
    Row_4    6.3333    7.25     4.6667       NaN
And plot them: 
xv = linspace(0,15);
Ym = B(1,:)'*xv + B(2,:)';
figure
plot(xv,Ym)
ylim([0 15])
grid
legend(Names, 'Location','SE')
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