# How to find the line of intersection between the following two planes and plot the intersected line on the same two planes?

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M on 2 Feb 2023
Commented: Matt J on 15 Jul 2024 at 12:58
How to find the line of intersection between the following two planes and plot the intersected line on the same two planes?
The following points contain the following points:
The first plane:
P1 = 177668442.453315 -102576923.076923 0
P2 = -102576923.076923 177668442.453315 -102576923.076923
P3= 0 -102576923.076923 88834221.2266576
The secod Plane:
P1= 152763459.308716 -102576923.076923 0
P2= -102576923.076923 183536536.231793 -102576923.076923
P3= 0 -102576923.076923 91768268.1158967
Torsten on 2 Feb 2023
Edited: Torsten on 2 Feb 2023
Quite large, your point coordinates. You might want to scale in x,y and z direction by a factor of 1/100000000.

Matt J on 2 Feb 2023
Edited: Matt J on 2 Feb 2023
You can get the line of intersection in Dual Plucker Matrix form as follows:
A=null([[P11;P21;P31],ones(3,1)]); %plane 1
B=null([[P12;P22;P32],ones(3,1)]); %plane 2
L=A*B.' - B*A.'; %line of intersection
However, for this to work well, you must re-express your P data in larger units, as Torsten suggests.
M on 15 Jul 2024 at 11:42
Edited: M on 15 Jul 2024 at 11:43
Becase the plot box has 12 edges, but the planes only intersect 6 of them.
Regarding this, Is there a way to control the vertices? for example to have only 4 vertices in the plot? or that will affect the meaning or so ? I need the plots only for visualization purposes in my research, having 6 vertices looks weird
Matt J on 15 Jul 2024 at 12:58
You can use patch to plot whatever portion of the plane you wish.