Intersection of trajectories in 3D

How can i find the intersection (which is unlikely in 3D) or the closest points of trajectories in 3D?

I have discrete time series data of 3 variables for several initial conditions. I want to draw a plot of these three variables, for different initial conditions(let's say 2 at the beginning) and check if they intersect? (or kind of intersect)

How can I do this using MATLAB?

Thank you very much in advance.

[Walter Roberson]

Are you assuming straight line travel between the points?

[Yigit]

No, they are not straight trajectories. I am still trying to find a way.

Answer 1

[Azzi Abdelmalek]

v1=[x1 y1 z1]  % trajectory 1
v2=[x2 y2 z2]  % trajectory 2
plot3(x1,y1,z1)
hold on;plot3(x2,y2,z2,'r')
idx=find(~all(v1-v2,2)) % gives the indedx idx corresponding to exact intersection 
[c,idxc]=min(sum(abs(v1-v2),2)) % gives the closest point:index idxc

[Yigit]

Thank you very much. Yet, this doesn't work. The data at hand describes population dynamics and therefore has all zero columns for both trajectories.

[Yigit]

Hi, I have two parametric curves defined in three dimensions, which are functions of a variable n (timesteps), like so:

x1 = f1(n) y1 = f2(n) z1 = f3(n)

x2 = f4(n) y2 = f5(n) z2 = f6(n)

I need to find if they intersect or somehow gets too close and follows the same route for a certain time.