How to find the point of intersection of two level curves?

Question

Gyan Swarup Nag 2021-3-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/759469-how-to-find-the-point-of-intersection-of-two-level-curves

回答： darova 2021-3-2

采纳的回答： darova

在 MATLAB Online 中打开

I have two functions $z1 = (1-2.2*x-0.1*y).*(2-2.3*x-0.1*y)-(1-x+y).*(1-x+y);

z2 = (2-x-2*y).*(-1+.1*x-4*y)-(1+.2*x+.1*y).*(1+.2*x+.1*y)$

I want to find the point of intersection of the level curves of the two functions. Can anyone help in this regard?

I have implimented a code which I am attaching below but in that code I could not get all the points

clc; clear all
  [x,y] = meshgrid(-3:0.01:3,-3:0.01:3);
  z1 = (1-2.2*x-0.1*y).*(2-2.3*x-0.1*y)-(1-x+y).*(1-x+y); 
  z2 = (2-x-2*y).*(-1+.1*x-4*y)-(1+.2*x+.1*y).*(1+.2*x+.1*y);
  % Calculate the coordinates of the contour lines
    % (here, just the contour line at z = 0)
    C1 = contourcs(x(1,:),y(:,1),z1,[0 0]);
    C2 = contourcs(x(1,:),y(:,1),z2,[0 0]);
    % Use polyxpoly to find intersections
    for ic = 1:length(C1)
        [xint1{ic}, yint1{ic}] = polyxpoly(C1(ic).X, C1(ic).Y, C2(ic).X, C2(ic).Y);
    end
    xint1 = cat(1, xint1{:});
    yint1 = cat(1, yint1{:});
    % Plot the results
    figure;
    contour(x,y,z1,[0 0]);
    hold on;
    contour(x,y,z2,[0 0]);
    plot(xint1, yint1, 'r*');

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Gyan Swarup Nag 2021-3-1

[x,y] = meshgrid(-3:0.01:3,-3:0.01:3);

z1 = (1-2.2*x-0.1*y).*(2-2.3*x-0.1*y)-(1-x+y).*(1-x+y);

z2 = (2-x-2*y).*(-1+.1*x-4*y)-(1+.2*x+.1*y).*(1+.2*x+.1*y);

[C1,h] = contour(x,y,z1,[0 0],'*k')

hold on

[C2,h]= contour(x,y,z2,[0,0]);

contourTable1 = getContourLineCoordinates(C1)

contourTable2 = getContourLineCoordinates(C2)

[xi,yi] = intersections(contourTable1.X,contourTable1.Y,contourTable2.X,contourTable2.Y)

plot(xi, yi, 'ko')

This code is working

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Answer 1

darova 2021-3-2

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/759469-how-to-find-the-point-of-intersection-of-two-level-curves#answer_637306

在 MATLAB Online 中打开

You need double for loop

k = 0;
for ic = 1:length(C1)
    for jc = 1:length(C2)
        k = k + 1;
        [xint1{k}, yint1{k}] = polyxpoly(C1(ic).X, C1(ic).Y, C2(jc).X, C2(jc).Y);
    end
end

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Answer 2

KSSV 2021-3-1

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/759469-how-to-find-the-point-of-intersection-of-two-level-curves#answer_636274

The best function for you:

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

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Gyan Swarup Nag 2021-3-1

The link you provides discuss about a function which is dependint on one variable but in my case the functions are depending on two variables. I could not understand how to use this function.

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