How to find the point of intersection of a line and a curve?

Hi, I wrote a code to plot few straight lines and a and a curve made of scattered points. The data set and the code is as follows.

 for n=1:1:33
    xn=[Transects(n,1) Transects(n,3)];  
    yn=[Transects(n,2) Transects(n,4)];
plot (xn,yn,'*')
hold on
line (xn,yn)
hold on
end
k=1;
for i=1:2:2146
    xi=Shorelines(i,1);  
    yi=Shorelines(i,2);
    xj=Shorelines(i+1,1);
    yj=Shorelines(i+1,2);
    a1=[xi,xj];
    b1=[yi,yj];
    Interm(k,1)= xi;
    Interm(k,2)= yi;
    Interm(k,3)= xj;
    Interm(k,4)= yj;
    k=k+1;
end
for r=1:1:1073
    xn1=[Interm(r,1) Interm(r,3)];  
    yn1=[Interm(r,2) Interm(r,4)];
    plot(Interm(r,1),Interm(r,2),'.');
    plot(Interm(r,3),Interm(r,4),'.');
    hold on
    if r<1073 
        xn2=[Interm(r,3) Interm(r+1,1)];  
        yn2=[Interm(r,4) Interm(r+1,2)];
        line (xn2,yn2);
    end
 line (xn1,yn1)
    hold on  
end
grid on
title('Finding Intersections of Functions')
xlabel('Easting')
ylabel('Northing')

Now I would like to find the point of intersection of the two lines. Any help would be appreciated. Thanks

Answer 1

[John BG]

Hi Venkata

this is John BG [e-mail]

In order to simplify the acquisition of data from the .csv files you have supplied I've had to modify Shoreline.csv removing all non-figures cells.

Please find attached copy of this script along with the .csv files I used, and an early version of Mr Douglas Schwarz function intersections.m needed again to readily get the intersecting points of the doubled seashore with each segment.

Updates on intersections.m can be downloaded from

https://uk.mathworks.com/matlabcentral/fileexchange/11837-fast-and-robust-curve-intersections?s_tid=srchtitle

So,

the start point is

.

1.-

Acquiring data

clear all;close all;clc

Transects=csvread('Transects.csv')
Shorelines=csvread('Shoreline.csv')
dc=3                                                   % amount decimals precision

.

2.-

Getting the points of each Transects segment

L={}
for n=1:1:33
    xn=[Transects(n,1) Transects(n,3)];	
    yn=[Transects(n,2) Transects(n,4)];
plot(xn,yn,'*')
hold on
hl=plot(xn,yn,'b-')

3.-

Capturing segment points needed to get to intersections

kx=10^-dc*floor(linspace(10^dc*xn(1,1),...
                         10^dc*xn(1,2),...
                  max(abs(10^dc*xn(1,1)-10^dc*xn(1,2)),abs(10^dc*yn(1,1)-10^dc*yn(1,2)))));

ky=10^-dc*floor(linspace(10^dc*yn(1,1),...
                         10^dc*yn(1,2),...
                  max(abs(10^dc*xn(1,1)-10^dc*xn(1,2)),abs(10^dc*yn(1,1)-10^dc*yn(1,2)))));
pkxy=[kx' ky'];
L=[L pkxy];

plot(kx,ky,'r*');   % just checking

% hl=line(xn,yn)   % I like plot
% hl.XData           % neither handles to plot or line returns contain more than the tip points
% hl.YData

end

.

4.-

Acquiring the cutting line, the Seashore-like line

k=1;                                                                    

for i=1:2:2146
    xi=Shorelines(i,1);	
    yi=Shorelines(i,2);
    xj=Shorelines(i+1,1);
    yj=Shorelines(i+1,2);
    a1=[xi,xj];
    b1=[yi,yj];
    Interm(k,1)= xi;
    Interm(k,2)= yi;
    Interm(k,3)= xj;
    Interm(k,4)= yj;
    k=k+1;
end

L2=[0 0];
for r=1:1:1073                                                      % plotting Shoreline along with a segment to disregard.
    xn1=[Interm(r,1) Interm(r,3)];	
    yn1=[Interm(r,2) Interm(r,4)];
    plot(Interm(r,1),Interm(r,2),'.');
    plot(Interm(r,3),Interm(r,4),'.');
    hold on
    if r<1073 
        xn2=[Interm(r,3) Interm(r+1,1)];	
        yn2=[Interm(r,4) Interm(r+1,2)];
        line(xn2,yn2);
    end
%  line(xn1,yn1)
 plot(xn1(1),yn1(1),'g*')  %  just checking
 L2=[L2;xn1(1) yn1(1)];
    hold on  
end
L2(1,:)=[];                                                            

.

Now L2 contains all points of the sea shore line.

5.-

There are 33 Transect segments, let's find the intersecting points of each Transect segment with the sea shore

L2nx=L2(:,1);
L2ny=L2(:,2);
Xp1=[0 0];
Xp2=[0 0];
for k=1:1:size(L,2)
    L1=L{k};
    L1nx=L1(:,1);
    L1ny=L1(:,2);
    [x0n,y0n]=intersections(L2nx,L2ny,[L1nx(1) L1nx(end)],[L1ny(1) L1ny(end)]);
    x0n=x0n';y0n=y0n';
    % expecting 1 and only 1 intersection point from each segment on seashore line, otherwise cell required.
    plot(x0n(1),y0n(1),'bd')
    plot(x0n(2),y0n(2),'yd')
    Xp1=[Xp;x0n(1) y0n(1)];   % yellow intersections curved sea shore
    Xp2=[Xp;x0n(2) y0n(2)];   % blue intersections, approximation of sea shore with additional straight segment.
end
Xp(1,:)=[];Xp2(1,:)=[];       % some habits die hard

.

The variables

Xp1 Xp2

.

Contain the sought intersections.

Comment: there's a short lines crossing, points Xp1 Xp2, on the left hand side of the sea shore.

Since you define the seashore line with both a detailed contour and segments approximation, there's need to know if you want to discard one of them, or it's ok as it is now.

Venkata

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

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thanks in advance for time and attention

John BG

[e-mail]