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How to find the intersection values of line and curve?

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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

Risposta accettata

Star Strider
Star Strider il 22 Ago 2023
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
.
  2 Commenti
GULZAR
GULZAR il 22 Ago 2023
Thank you.....One more favor for me, I need the intersection points in ascending order in array. Can you please help.....
Star Strider
Star Strider il 22 Ago 2023
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.
.

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Torsten
Torsten il 22 Ago 2023

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