How to find the intersection values?

Question

GULZAR 2023-8-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2009582-how-to-find-the-intersection-values

编辑： Torsten 2023-8-17

采纳的回答： Bruno Luong

在 MATLAB Online 中打开

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 = sqrt(12);n2 = 1;

lambda = linspace(400e-3,800e-3, 100000);

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(lambda,RHS)

hold on

yline(-1);

hold off

hold on

yline(1);

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Answer 1

Bruno Luong 2023-8-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2009582-how-to-find-the-intersection-values#answer_1288782

在 MATLAB Online 中打开

d1 = 0.4;d2 = 0.6;d = d1 + d2;

n1 = sqrt(12);n2 = 1;

lambda = linspace(400e-3,800e-3, 100000);

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(lambda,RHS)

hold on

for yx = [-1 1]

yline(yx);

ys = RHS-yx;

i = find(ys(1:end-1).*ys(2:end) <= 0);

% linear interpolation

i1 = i; ss1 = ys(i1);

i2 = i1 + 1; ss2 = ys(i2);

w = ss2./(ss2-ss1);

xx = w.*lambda(i1) + (1-w).*lambda(i2);

plot(xx, yx+zeros(size(xx)), 'rx')

end

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GULZAR 2023-8-17

Thank you. And how to show the intersection points...

Torsten 2023-8-17

编辑：Torsten 2023-8-17

在 MATLAB Online 中打开

xx

at the end of the for-loop.

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Answer 2

Torsten 2023-8-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2009582-how-to-find-the-intersection-values#answer_1288777

在 MATLAB Online 中打开

format long
d1 = 0.4;d2 = 0.6;d = d1 + d2;
n1 = sqrt(12);n2 = 1;
D1 = @(lambda)(2*pi*n1*d1)./lambda;D2 = @(lambda)(2*pi*n2*d2)./lambda;
RHS = @(lambda)cos(D1(lambda)).*cos(D2(lambda)) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1(lambda)) .*sin(D2(lambda));
% Case -1
start = [0.42,0.45,0.56,0.59,0.72];
offset = -1;
rhs = @(lambda) RHS(lambda)-offset;
for i = 1:numel(start)
    sol(i) = fsolve(rhs,start(i),optimset('Display','none'));
end
sol
sol = 1×5
   0.425911883383464   0.453366368933051   0.559061333603378   0.580387744533463   0.740288322697614
% Case 1
start = [0.4,0.47,0.52,0.63,0.67];
offset = 1;
rhs = @(lambda) RHS(lambda)-offset;
for i = 1:numel(start)
    sol(i) = fsolve(rhs,start(i),optimset('Display','none'));
end
sol
sol = 1×5
   0.398347393959160   0.476820539375385   0.520624847917834   0.636196969306721   0.680659944575321