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