How to find intersection between lines

I have below code

%% Input Values
clear all
clc
alpha1=input('Enter positive "alpha1"?');
alpha2=input('Enter positive  "alpha2"?');
beta1=input('Enter positive  "beta1"?');
beta2=input('Enter positive  "beta2"?');
lambda=input('Enter positive  "lambda"?');
eta1=input('Enter positive  "eta1"?');
eta2=input('Enter positive  "eta2"?');
P=input('Enter positive  "P"?');
%% Feasible Area
x = -1:P;m = 0; c = eta2; y = m * x + c;
plot(x, y, 'black')
y = -1:P; m = 0; c = eta1; y = m * x + c;
plot(y, x, 'black')

eta1=min (eta1,P);  eta2=min (eta2,P);
if eta1==0 && eta2==0;
    X=[0 0 P];   Y=[0 P 0];
    fill(X,Y,[0.85 0.85 0.85]);  axis([-1 P -1 P])
end
if eta1+eta2<P
    X=[0 0 eta1  eta1];     Y=[0 eta2 eta2 0];
    fill(X,Y,[0.85 0.85 0.85]);
else
    X=[0 0 P-eta2 eta1 eta1]; Y=[0 eta2 eta2 P-eta1 0];
    fill(X,Y,[0.85 0.85 0.85]); axis([-1 P -1 P])
end

X=[0 0]; Y=[0 P];
line(X,Y,'Color','black')
hold on
line(Y,X,'Color','black')

g = @(x,y) x+y-P;
y1=fimplicit(g,[0 P 0 P])

f = @(x,y) log((1+alpha1*x./(1+alpha2*y))) -lambda*log((1+beta1*x./(1+beta2*y)));
y2=fimplicit(f,[-1 P -1 P], '-')
hold on
grid on

Where I consider alpha1=1, alpha2=0.2, beta1=1; beta2=2, lambda=2, eta1=2, eta2=3, P=1

I want to find the intersection for lines in the picture. Could you please help me!

Answer 1

[darova]

use polyxpoly

[Hossein Alishahi]

Thank you for your consideration.

It does not work for fimplicit function which has ploted the lines. Could you please give me more information in specefic codes

Best,

Hossein

[darova]

• use contour to get lines
• use polyxpoly to calculate interseciton

clc,clear

[x,y,z] = peaks(30);
[~,h] = contour(x,y,z,[0 0]);
x2 = [-2 3];
y2 = [-3 0];

h1 = get(h,'children');
x1 = get(h1(3),'xdata');            % extract 3d contour
y1 = get(h1(3),'ydata');
[xc,yc] = polyxpoly(x1,y1,x2,y2);   % find intersection
hold on
plot(x1,y1,'.r')
plot(x2,y2,'linewidth',2)
plot3(xc,yc,'or')
hold off

Answer 2

[Gautam]

Hello Hossein,

If you want to find the point of intersection of any tow lines programmatically, you can do so following the steps below:

1. Create handles to the line objects for which you want to find the intersection point, like:

line1 = line(X,Y,'Color','black');
line2 = line(Y,X,'Color','black');

2. Use the “XData” and “YData” properties of the line objects to find the point of intersection:

interX = line1.XData(line1.XData == line2.XData);>>interY = line1.YData(line1.YData == line2.YData);

3. You can show the point of intersection on the plot using

plot(interX, interY, 'rO', 'MarkerSize',6, 'MarkerFaceColor','red')

This would give you the intersection point like:

Following this, you can find the intersection etween any two lines

[Walter Roberson]

Comparing the XData and YData properties of two lines will generally not work.

X = [0 3];
Y = [1 2];
line1 = line(X,Y,'Color','black');
line2 = line(Y,X,'Color','black');

●

interX = line1.XData(line1.XData == line2.XData);
interY = line1.YData(line1.YData == line2.YData);
plot(interX, interY, 'rO', 'MarkerSize',6, 'MarkerFaceColor','red')

There is no-place that the XData from the one line happens to be exactly the XData from the other line.

The XData property does not interpolate. The result is not the same as

cla
X = 0:.1:3;
Y = linspace(1,2,numel(X));
line1 = line(X,Y,'Color','black');
line2 = line(Y,X,'Color','black');

interX = line1.XData(line1.XData == line2.XData);
interY = line1.YData(line1.YData == line2.YData);
plot(interX, interY, 'rO', 'MarkerSize',6, 'MarkerFaceColor','red')