Intersection of two lines
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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.
采纳的回答
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))
6 个评论
Gaetano Pavone
2021-9-21
编辑：Gaetano Pavone
2021-9-21
I don't see anything new in the phrasing of the post that would change my answer. Did you try it?
You seem to have added that your 4 points are ideally coplanar, but that simply isn't a reliable assumption, in general. If P1...P4 were generated by floating point calculations, they will contain floating point errors that effectively render the points non-coplanar. It doesn't matter, though. My solution should work whether the data is ideally coplanar or not.
Gaetano Pavone
2021-9-21
Matt J
2021-9-21
You can use the line() command to plot the vector. If you want the vector to appear as an arrow, you can use
or other similar File Exchange offerings.
Gaetano Pavone
2021-9-21
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)
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