Finding the intersection points between two curves

Question

raha ahmadi 2021-7-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/889367-finding-the-intersection-points-between-two-curves

评论： Star Strider 2021-8-7

采纳的回答： Star Strider

I need to find the intersection points of this equation:

this is my code. I dont know what is the best way . Also when I plot in terms of

I have some periods but when I plot in terms of β I have only one period. How I can plot it in terms of beta but with nulti perids?

many thanks in advance

h=20;

K=13.6;

l=1148e-6;

g1=fplot(@(beta)tan(beta*l));

hold on

g2=fplot(@(beta)2*h*beta*K/(K^2*beta^2-h^2));

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

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Answer 1

Star Strider 2021-7-30

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/889367-finding-the-intersection-points-between-two-curves#answer_757592

Several options —

h=20;

K=13.6;

l=1148e-6;

f1 = @(beta)tan(beta*l);

f2 = @(beta)2*h*beta*K./(K^2*beta.^2-h^2);

figure

g1 = fplot(f1);

hold on

g2 = fplot(f2);

g3 = fplot(@(beta) f2(beta)-f1(beta), '--'); % Use 'fsolve' On 'g3' To Find The Intersections

Another option:

format long
Xint = interp1(g3.YData, g3.XData, 0)
Xint = 
     0

.

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Star Strider 2021-7-31

My pleasure!

If you want to calculate those roots —

h=20;

K=13.6;

l=1148e-6;

g1=fplot(@(betaL)tan(betaL));

hold on

g2=fplot(@(betaL)2*h.*betaL/l*K./(h^2-K^2.*betaL/l.^2));

hold on

f3 = @(betaL) (tan(betaL)) - (2*h.*betaL/l*K./(h^2-K^2.*betaL/l.^2));

g3 = fplot(f3, [-1 1]*20, ':');

zxi = find(diff(sign(g3.YData)));

for k = 1:numel(zxi)

idxrng = (-1:1)+zxi(k); % Index Range For Interpolation

xv(k,:) = interp1(g3.YData(idxrng), g3.XData(idxrng), 0);

yv(k,:) = interp1(g3.XData, g3.YData, xv(k));

end

plot(xv(abs(yv)<1), zeros(size(xv(abs(yv)<1))), 'xr')

hold off

Intersections = table(xv(abs(yv)<1),yv(abs(yv)<1), 'VariableNames',{'x','y'})

Intersections = 14×2 table

x y _______ ___________ -18.853 3.747e-16 -15.711 -1.4554e-15 -12.569 9.7145e-17 -9.428 2.498e-16 -6.2861 6.5919e-17 -3.1452 7.4593e-17 0 0 0 0 3.1386 -1.8735e-16 6.2802 3.1225e-16 9.4214 -9.1593e-16 12.563 -9.5063e-16 15.704 -5.1348e-16 18.846 -8.3267e-16

.

Star Strider 2021-8-7

There is nothing to fix.

Look at the results:

x=[-1000,1000]
x = 1×2
       -1000        1000
y=sin (x)
y = 1×2
   -0.8269    0.8269
roots(y)
ans = 1

so, plotting ‘y’ using polyval:

xv = linspace(-10,10);

pv = polyval(y, xv);

figure

plot(xv, pv)

grid

The reason is readily apparent! The ‘y’ vector corresponds to:

This is a linear relationship with one zero-crossing (root) at

.

However,

x = -1000:1000;
y = sin (x);
roots(y)
ans = 
   1.1126 + 0.0000i
  -0.7096 + 0.7046i
  -0.7096 - 0.7046i
  -0.7074 + 0.7068i
  -0.7074 - 0.7068i
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  -0.7051 - 0.7091i
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  -0.7029 - 0.7113i
  -0.7140 + 0.7001i
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  -0.7007 + 0.7135i
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   0.9993 + 0.0380i
   0.9993 - 0.0380i
   0.1401 + 0.9901i
   0.1401 - 0.9901i
  -0.1416 + 0.9899i
  -0.1416 - 0.9899i
   0.1370 + 0.9906i
   0.1370 - 0.9906i
  -0.1385 + 0.9904i
  -0.1385 - 0.9904i
  -0.9891 + 0.1470i
  -0.9891 - 0.1470i
   0.9976 + 0.0696i
   0.9976 - 0.0696i
   0.1339 + 0.9910i
   0.1339 - 0.9910i
   0.1308 + 0.9914i
   0.1308 - 0.9914i
  -0.1353 + 0.9908i
  -0.1353 - 0.9908i
  -0.9896 + 0.1439i
  -0.9896 - 0.1439i
  -0.9900 + 0.1408i
  -0.9900 - 0.1408i
  -0.1322 + 0.9912i
  -0.1322 - 0.9912i
   0.1277 + 0.9918i
   0.1277 - 0.9918i
  -0.9905 + 0.1377i
  -0.9905 - 0.1377i
  -0.1291 + 0.9916i
  -0.1291 - 0.9916i
  -0.9909 + 0.1346i
  -0.9909 - 0.1346i
   0.1246 + 0.9922i
   0.1246 - 0.9922i
  -0.1260 + 0.9920i
  -0.1260 - 0.9920i
  -0.1229 + 0.9924i
  -0.1229 - 0.9924i
  -0.9913 + 0.1315i
  -0.9913 - 0.1315i
  -0.9917 + 0.1284i
  -0.9917 - 0.1284i
   0.1214 + 0.9926i
   0.1214 - 0.9926i
   0.1183 + 0.9930i
   0.1183 - 0.9930i
   0.1152 + 0.9933i
   0.1152 - 0.9933i
  -0.1198 + 0.9928i
  -0.1198 - 0.9928i
  -0.1167 + 0.9932i
  -0.1167 - 0.9932i
  -0.1135 + 0.9935i
  -0.1135 - 0.9935i
   0.9994 + 0.0348i
   0.9994 - 0.0348i
   0.1121 + 0.9937i
   0.1121 - 0.9937i
   0.1090 + 0.9940i
   0.1090 - 0.9940i
   0.1058 + 0.9944i
   0.1058 - 0.9944i
  -0.1104 + 0.9939i
  -0.1104 - 0.9939i
   0.1027 + 0.9947i
   0.1027 - 0.9947i
  -0.1073 + 0.9942i
  -0.1073 - 0.9942i
  -0.1042 + 0.9946i
  -0.1042 - 0.9946i
  -0.1010 + 0.9949i
  -0.1010 - 0.9949i
  -0.9921 + 0.1253i
  -0.9921 - 0.1253i
  -0.9925 + 0.1222i
  -0.9925 - 0.1222i
  -0.9929 + 0.1190i
  -0.9929 - 0.1190i
  -0.9933 + 0.1159i
  -0.9933 - 0.1159i
  -0.0979 + 0.9952i
  -0.0979 - 0.9952i
  -0.9936 + 0.1128i
  -0.9936 - 0.1128i
  -0.9940 + 0.1097i
  -0.9940 - 0.1097i
  -0.9943 + 0.1066i
  -0.9943 - 0.1066i
  -0.9946 + 0.1034i
  -0.9946 - 0.1034i
   0.0996 + 0.9950i
   0.0996 - 0.9950i
   0.0965 + 0.9953i
   0.0965 - 0.9953i
   0.0933 + 0.9956i
   0.0933 - 0.9956i
  -0.0917 + 0.9958i
  -0.0917 - 0.9958i
  -0.0948 + 0.9955i
  -0.0948 - 0.9955i
  -0.9950 + 0.1003i
  -0.9950 - 0.1003i
  -0.9953 + 0.0972i
  -0.9953 - 0.0972i
   0.0902 + 0.9959i
   0.0902 - 0.9959i
  -0.0885 + 0.9961i
  -0.0885 - 0.9961i
   0.0871 + 0.9962i
   0.0871 - 0.9962i
   0.0777 + 0.9970i
   0.0777 - 0.9970i
   0.0808 + 0.9967i
   0.0808 - 0.9967i
   0.0840 + 0.9965i
   0.0840 - 0.9965i
  -0.9956 + 0.0941i
  -0.9956 - 0.0941i
  -0.9959 + 0.0909i
  -0.9959 - 0.0909i
  -0.9961 + 0.0878i
  -0.9961 - 0.0878i
  -1.0000 + 0.0000i
  -0.9964 + 0.0847i
  -0.9964 - 0.0847i
  -0.9967 + 0.0816i
  -0.9967 - 0.0816i
  -0.9999 + 0.0126i
  -0.9999 - 0.0126i
  -1.0000 + 0.0094i
  -1.0000 - 0.0094i
  -1.0000 + 0.0031i
  -1.0000 - 0.0031i
  -0.9982 + 0.0596i
  -0.9982 - 0.0596i
  -0.9978 + 0.0659i
  -0.9978 - 0.0659i
  -0.9974 + 0.0722i
  -0.9974 - 0.0722i
  -0.9980 + 0.0628i
  -0.9980 - 0.0628i
  -1.0000 + 0.0063i
  -1.0000 - 0.0063i
  -0.9976 + 0.0690i
  -0.9976 - 0.0690i
  -0.9969 + 0.0784i
  -0.9969 - 0.0784i
  -0.9972 + 0.0753i
  -0.9972 - 0.0753i
  -0.9984 + 0.0565i
  -0.9984 - 0.0565i
  -0.9999 + 0.0157i
  -0.9999 - 0.0157i
  -0.9992 + 0.0408i
  -0.9992 - 0.0408i
  -0.9990 + 0.0439i
  -0.9990 - 0.0439i
  -0.9993 + 0.0377i
  -0.9993 - 0.0377i
  -0.9986 + 0.0534i
  -0.9986 - 0.0534i
  -0.9994 + 0.0345i
  -0.9994 - 0.0345i
  -0.9989 + 0.0471i
  -0.9989 - 0.0471i
  -0.9995 + 0.0314i
  -0.9995 - 0.0314i
  -0.9987 + 0.0502i
  -0.9987 - 0.0502i
  -0.9996 + 0.0283i
  -0.9996 - 0.0283i
  -0.9997 + 0.0251i
  -0.9997 - 0.0251i
  -0.9998 + 0.0188i
  -0.9998 - 0.0188i
  -0.9998 + 0.0220i
  -0.9998 - 0.0220i
   0.0746 + 0.9972i
   0.0746 - 0.9972i
   0.0714 + 0.9974i
   0.0714 - 0.9974i
   0.0683 + 0.9977i
   0.0683 - 0.9977i
   0.0652 + 0.9979i
   0.0652 - 0.9979i
  -0.0854 + 0.9963i
  -0.0854 - 0.9963i
  -0.0823 + 0.9966i
  -0.0823 - 0.9966i
  -0.0792 + 0.9969i
  -0.0792 - 0.9969i
  -0.0760 + 0.9971i
  -0.0760 - 0.9971i
  -0.0698 + 0.9976i
  -0.0698 - 0.9976i
  -0.0729 + 0.9973i
  -0.0729 - 0.9973i
   0.0620 + 0.9981i
   0.0620 - 0.9981i
   0.0589 + 0.9983i
   0.0589 - 0.9983i
  -0.0666 + 0.9978i
  -0.0666 - 0.9978i
  -0.0635 + 0.9980i
  -0.0635 - 0.9980i
   0.0495 + 0.9988i
   0.0495 - 0.9988i
   0.0526 + 0.9986i
   0.0526 - 0.9986i
   0.0464 + 0.9989i
   0.0464 - 0.9989i
   0.0432 + 0.9991i
   0.0432 - 0.9991i
   0.0558 + 0.9984i
   0.0558 - 0.9984i
   0.0401 + 0.9992i
   0.0401 - 0.9992i
  -0.0604 + 0.9982i
  -0.0604 - 0.9982i
  -0.0541 + 0.9985i
  -0.0541 - 0.9985i
  -0.0572 + 0.9984i
  -0.0572 - 0.9984i
  -0.0510 + 0.9987i
  -0.0510 - 0.9987i
  -0.0478 + 0.9989i
  -0.0478 - 0.9989i
  -0.0415 + 0.9991i
  -0.0415 - 0.9991i
  -0.0447 + 0.9990i
  -0.0447 - 0.9990i
   0.0369 + 0.9993i
   0.0369 - 0.9993i
  -0.0384 + 0.9993i
  -0.0384 - 0.9993i
   0.0338 + 0.9994i
   0.0338 - 0.9994i
  -0.0353 + 0.9994i
  -0.0353 - 0.9994i
  -0.0259 + 0.9997i
  -0.0259 - 0.9997i
  -0.0290 + 0.9996i
  -0.0290 - 0.9996i
  -0.0227 + 0.9997i
  -0.0227 - 0.9997i
  -0.0321 + 0.9995i
  -0.0321 - 0.9995i
   0.0307 + 0.9995i
   0.0307 - 0.9995i
   0.0212 + 0.9998i
   0.0212 - 0.9998i
   0.0181 + 0.9998i
   0.0181 - 0.9998i
   0.0244 + 0.9997i
   0.0244 - 0.9997i
   0.0150 + 0.9999i
   0.0150 - 0.9999i
   0.0024 + 1.0000i
   0.0024 - 1.0000i
  -0.0007 + 1.0000i
  -0.0007 - 1.0000i
  -0.0196 + 0.9998i
  -0.0196 - 0.9998i
   0.0275 + 0.9996i
   0.0275 - 0.9996i
   0.0087 + 1.0000i
   0.0087 - 1.0000i
   0.0055 + 1.0000i
   0.0055 - 1.0000i
  -0.0102 + 0.9999i
  -0.0102 - 0.9999i
  -0.0039 + 1.0000i
  -0.0039 - 1.0000i
  -0.0070 + 1.0000i
  -0.0070 - 1.0000i
  -0.0133 + 0.9999i
  -0.0133 - 0.9999i
  -0.0164 + 0.9999i
  -0.0164 - 0.9999i
   0.0118 + 0.9999i
   0.0118 - 0.9999i
   0.8988 + 0.0000i

Except for the first element (1.1126), the absolute values of all the others are uniformly 1.

This time, ‘y’ corresponds to:

syms x

yp = vpa(poly2sym(y,x),5)

yp =

figure

fplot(yp, [-1000, 1000])

grid

axis([-pi pi -5 5])

The vertical dashed lines indicate singularities

.

The sin function has an infiinty of roots, those being

radians, where n is an integer. It is necessary to use a zero-finding algorithm (such as fzero or fsolve) or interpolation (interp1) to locate them, not the roots function.

.

raha ahmadi 2021-8-7

your answer is perfect. I m really appresiate.

hope you all the best

Star Strider 2021-8-7

Thank you!

As always, my pleasure!

.

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Answer 2

darova 2021-7-30

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/889367-finding-the-intersection-points-between-two-curves#answer_757557

I'd try fsolve for solving

Read help carefully:

fplot(f,[0 10])

1 个评论
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raha ahmadi 2021-7-30

编辑：raha ahmadi 2021-7-30

Dear darova

Thank you for your help, I read fsolve but I think it solves a system of nonlinear equations. I used fzero instead but I only got one answer I need solve it in some periods and get more roots

Best regards

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