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?

Answer 1

[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')