Find Intersection between curves

In the intersection part

I tried many functions but still couldn't get the right value

Answer 1

[KSSV]

This should not dissappoint you.

https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

[Anfal AlShehhi]

I do have 2 functions only that vary with a range. Not helpful but thanks anyway

[KSSV]

Why not helpful?

[Anfal AlShehhi]

As my 2 curves functions have a range that changes i can't defined y1, x1, x2,y2

[KSSV]

Why not?? Copy and paste your code here....image will not help us to help you.

[Anfal AlShehhi]

clc; clear all;
% Defined values
atm=0.17                % km-1
xt=2.3;                  % target (x) in m
yt=2.3;                  % target (y) in m
p=50/100;               % percent target
vis=23;                 %Visibility in km target
er=26;                  % LRF 
dref=500;               % LRF in m
pref=85/100;            % LRF 
vis2=23;                % LRF Visbility
T=90/100;               % LRF 
sc=1;                   % LRF
 
% Range 
x=0:0.01:10;        % in km 
A= exp(-2*atm.*x)   % Attenuation func
B= ((pref/p)*((x.*x)*1000/dref*dref))*(((exp((-2*atm*dref/1000))*10^(-er/10)))/(T*sc)) % Sensi func

%Intersection point
f1 = @(x) exp(-2*atm.*x);
f2 = @(x)((pref/p)*((x.*x)*1000/dref*dref))*(((exp((-2*atm*dref/1000))*10^(-er/10)))/(T*sc)); 
f = @(x) f1(x) - f2(x);
xx = 0:0.01:10;a
t = f(xx) > 0; 

% plotting 
figure
plot(A,x.*1000,'-b')
hold on
plot(B/1000,x.*1000,'-r')
plot(x0,y0,'ro','MarkerFaceColor','g')
grid on 
xlabel("Range in km")
ylabel("Distance in km")
title("Range Preformance")
legend('Atmospheric Attenuation','Sensitivity','Intersection')
hold off

[KSSV]

You want intersection of what and what?

[Anfal AlShehhi]

When plotting eqauation A & B there is an intersect point between the 2 curves. Am trying to figure this out.

[KSSV]

clc; clear all;
% Defined values
atm=0.17 ;               % km-1
xt=2.3;                  % target (x) in m
yt=2.3;                  % target (y) in m
p=50/100;               % percent target
vis=23;                 %Visibility in km target
er=26;                  % LRF
dref=500;               % LRF in m
pref=85/100;            % LRF
vis2=23;                % LRF Visbility
T=90/100;               % LRF
sc=1;                   % LRF

% Range
x=0:0.01:10;        % in km
A= exp(-2*atm.*x) ;  % Attenuation func
B= ((pref/p)*((x.*x)*1000/dref*dref))*(((exp((-2*atm*dref/1000))*10^(-er/10)))/(T*sc)) ;% Sensi func

L1 = [x;A] ; L2 = [x;B] ;

P = InterX(L1,L2) ; 

Answer 2

[Sam Chak]

Hi @Anfal AlShehhi

I think the script shared File Exchange works. However, if you want something mathematically simple to understand, you can try fzero(). The approach is similar to what you did previously.

atm  = 0.17;        % km-1
xt   = 2.3;         % target (x) in m
yt   = 2.3;         % target (y) in m
p    = 50/100;      % percent target
vis  = 23;          % Visibility in km target
er   = 26;          % LRF 
dref = 500;         % LRF in m
pref = 85/100;      % LRF 
vis2 = 23;          % LRF Visbility
T    = 90/100;      % LRF 
sc   = 1;           % LRF
 
% Range 
x = 0:0.01:10;      % in km 
A = exp(-2*atm.*x); % Attenuation func
B = ((pref/p)*((x.*x)*1000/dref*dref))*(((exp((-2*atm*dref/1000))*10^(-er/10)))/(T*sc)); % Sensi func
% Plotting two curves initially
plot(x, A, x, B)
ylim([0 1])

% Finding the intersection point
f1 = @(x) exp(-2*atm.*x);
f2 = @(x) ((pref/p)*((x.*x)*1000/dref*dref))*(((exp((-2*atm*dref/1000))*10^(-er/10)))/(T*sc)); 
f  = @(x) f1(x) - f2(x);
x0 = 0.5;       % initial guess value (intersection is somewhere near x = 0.5)
xsol = fzero(f, x0)

xsol = 0.4621

ysol = f1(xsol)

ysol = 0.8546

% Markng the intersection point
plot(x, A, x, B), hold on
plot(xsol, ysol, 'mo', 'MarkerSize', 14), hold on
ylim([0 1])