How to find the intersection values of line and curve?

How to find the intersection values of line(black) and the curve(blue)

clc 
close all 
d1 = 0.4;d2 = 0.6;d = d1 + d2; n1 = 3.46;n2 = 1.5; 
lambda = linspace(400e-3,800e-3, 100000); w=2*pi./lambda; 
D1 = (2*pi*n1*d1)./lambda;D2 = (2*pi*n2*d2)./lambda; 
RHS = cos(D1).*cos(D2) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1) .*sin(D2); 
plot(w,RHS) 
hold on 
yline(-1); hold off 
hold on 
yline(1); hold off

Answer 1

[Star Strider]

Try this —

% clc 
% close all 
d1 = 0.4;d2 = 0.6;d = d1 + d2; n1 = 3.46;n2 = 1.5; 
lambda = linspace(400e-3,800e-3, 100000); w=2*pi./lambda; 
D1 = (2*pi*n1*d1)./lambda;D2 = (2*pi*n2*d2)./lambda; 
RHS = cos(D1).*cos(D2) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1) .*sin(D2); 

yl = [-1 1];
for k = 1:numel(yl)
    [xi{k},yi{k}] = intsx(w, RHS, yl(k));
end

figure
plot(w,RHS) 
hold on 

for k = 1:numel(yl)
    plot(xi{k}, yi{k}, 'rs')
end

yline(-1)
yline(1)
hold off

function [xi,yi] = intsx(x,y,c)                                 % Simple Intersection Function
% ARGUMENTS: (x,y): Vectors, c: Constant
    zci = find(diff(sign(y-c)));
    for k = 1:numel(zci)
        idxrng = max(1,zci(k)-1) : min(numel(x),zci(k)+1);
        xi(k,:) = interp1(y(idxrng)-c,x(idxrng),0);
        yi(k,:) = interp1(x(idxrng), y(idxrng), xi(k));
    end
end

.

[GULZAR]

Thank you.....One more favor for me, I need the intersection points in ascending order in array. Can you please help.....

[Star Strider]

As always, my pleasure!

They already are for each line value (-1,+1) intersection.

To get them all in one array, concatenate them and sort it by the ‘x’ value:

% clc 
% close all 
d1 = 0.4;d2 = 0.6;d = d1 + d2; n1 = 3.46;n2 = 1.5; 
lambda = linspace(400e-3,800e-3, 100000); w=2*pi./lambda; 
D1 = (2*pi*n1*d1)./lambda;D2 = (2*pi*n2*d2)./lambda; 
RHS = cos(D1).*cos(D2) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1) .*sin(D2); 

yl = [-1 1];
for k = 1:numel(yl)
    [xi,yi] = intsx(w, RHS, yl(k));
    xv{k,:} = xi;
    yv{k,:} = yi;
end

Intersections = array2table(sortrows(cell2mat([xv yv]),1), 'VariableNames',{'x','y'})

Intersections = 12×2 table
      x       y 
    ______    __

    7.9193     1
    8.5627     1
    9.4017    -1
    9.8854    -1
    10.831     1
    11.153     1
    12.033    -1
    12.734    -1
    13.695     1
    13.825     1
    14.811    -1
    15.423    -1

figure
plot(w,RHS) 
hold on 

for k = 1:numel(yl)
    plot(xv{k}, yv{k}, 'rs')
end

yline(-1)
yline(1)
hold off

function [xi,yi] = intsx(x,y,c)                                 % Simple Intersection Function
% ARGUMENTS: (x,y): Vectors, c: Constant
    zci = find(diff(sign(y-c)));
    for k = 1:numel(zci)
        idxrng = max(1,zci(k)-1) : min(numel(x),zci(k)+1);
        xi(k,:) = interp1(y(idxrng)-c,x(idxrng),0);
        yi(k,:) = interp1(x(idxrng), y(idxrng), xi(k));
    end
end

The relevant previous function is interp1, and the relevant new functions are cell2mat, sortrows, and array2table.

.

Answer 2

[Torsten]

https://uk.mathworks.com/matlabcentral/answers/2009582-how-to-find-the-intersection-values?s_tid=srchtitle