Intersection of two lines

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Gaetano Pavone 2021-9-21

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https://ww2.mathworks.cn/matlabcentral/answers/1457729-intersection-of-two-lines

编辑： Matt J 2021-9-21

Hi, I have four coplanar points P1, P2, P3 and P4 in 3d. I would like to calculate the intersection point among the line passing through P1 and P2 and that passing through P3 and P4.

Moreover I would like to evaluate the angle between the vector connecting such intersection and the origin with z-axis and then plot the vector.

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Matt J 2021-9-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1457729-intersection-of-two-lines#answer_792034

编辑：Matt J 2021-9-21

在 MATLAB Online 中打开

You need a least squares solution, since lines in 3D do not generally intersect. Assuming your point data are in column-vector form, this is,

c=[P2-P1,P3-P4]\(P3-P1);
P_intersection=P1+c(1)*(P2-P1)
angle=acos(P_intersection(3)/norm(P_intersection))

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Gaetano Pavone 2021-9-21

在 MATLAB Online 中打开

For

P1=[735;234;1397];
P2=[234;735;1397];
P3=[-265;234;1397];
P4=[234;-265;1397];
c=[P2-P1,P3-P4]\[-P1,P3];
P_intersection=P1+c(1)*(P2-P1);
angle=acos(P_intersection(3)/norm(P_intersection));

it doesn't give me the correct answer.

P_intersection should be [234;234;1397].

Matt J 2021-9-21

编辑：Matt J 2021-9-21

在 MATLAB Online 中打开

You seem to have had P2 and P3 interchanged.

P1=[735;234;1397];
P3=[234;735;1397];
P2=[-265;234;1397];
P4=[234;-265;1397];
c=[P2-P1,P3-P4]\(P3-P1); %edited
P_intersection=P1+c(1)*(P2-P1)
P_intersection = 3×1
         234
         234
        1397