How to finde intersections ?

Hi,

I hope you are Keeping safe.

I have a code as belows

clear all
clc
close all
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
M=max(P,eta1); N=max(P,eta2);
a = -1:M;m = 0; c = eta2; b = m * a + c;
plot(a, b, '--','Color', 'black')
hold on
b = -1:N; m = 0; c = eta1; b = m * a + c;
plot(b, a, ':','Color', 'black','LineWidth',2)

eta1=min (eta1,P);  eta2=min (eta2,P);
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+eta1+1 -1 P+eta2+1])
end

g = @(a,b) a+b-P;
fimplicit(g,[0 P 0 P],'-.','Color', 'black')

f = @(a,b) log((1+alpha1*a./(1+alpha2*b))) -lambda*log((1+beta1*a./(1+beta2*b)));
fimplicit(f,[-1 P+eta1+1 -1 P+eta2+1], 'Color','green')
hold on

and want to find intersection between lines . For example consider

alpha1=beta1=1, alpha2=0.2, beta2=2, ambda=2, eta1=3, eta2=4 and P=2

Could you please give me how to find and plot the intersections points.

MAny Thanks in advance

[Nora Khaled]

Not sure your code works as you want it to ... is this the current output?

By intersection, do you mean the vertices of the triangle?

[Hossein Alishahi]

Thank you for your consideration.

It works! I mean the intersection between green line relatad on

f = @(a,b) log((1+alpha1*a./(1+alpha2*b))) -lambda*log((1+beta1*a./(1+beta2*b)));

fimplicit(f,[-1 P+eta1+1 -1 P+eta2+1], 'Color','green')

and others lines in a sepecefic x+y-p=0 ralated to

g = @(a,b) a+b-P;

fimplicit(g,[0 P 0 P],'-.','Color', 'black')

[Hossein Alishahi]

please try it !

%% Input Parameters

clear all

clc

close all

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

M=max(P,eta1); N=max(P,eta2);

a = -1:M;m = 0; c = eta2; b = m * a + c;

plot(a, b, '--','Color', 'black')

hold on

b = -1:N; m = 0; c = eta1; b = m * a + c;

plot(b, a, ':','Color', 'black','LineWidth',2)

eta1=min (eta1,P); eta2=min (eta2,P);

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+eta1+1 -1 P+eta2+1])

end

g = @(a,b) a+b-P;

fimplicit(g,[0 P 0 P],'-.','Color', 'black')

f = @(a,b) log((1+alpha1*a./(1+alpha2*b))) -lambda*log((1+beta1*a./(1+beta2*b)));

fimplicit(f,[-1 P+eta1+1 -1 P+eta2+1], 'Color','green')

hold on

grid on

%% Legend

xlabel('{\rho_{1}}');

ylabel('{\rho_{2}}');

legend('\eta_{2}','\eta_{1}','Feasible Area','{\rho_{1}}+{\rho_{2}}={\rho}','{log}({1}+({\alpha_{1}} {\rho_{1}}))/({1}+{\alpha_{2}} {\rho_{2}})={\lambda} {log}{1}+({\beta_{1}} {\rho_{1}})/({1}+{\beta_{2}} {\rho_{2}})','Location','northeast')

[Jan]

You have asked some questions aboput the same problem already. It is still not clear, which intersections your are searching for. "intersection between lines" - between which lines? You post some code, which seems to work fine. But what exactly is your question?