# How to understand if a line cut a surface plot

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ENRICO FAIELLA am 30 Mär. 2023
Hi everyone:
I have a surface plot which represents a plane parallel to XY reference frame. I would like to understand if a straight line which pass through two arbitrary points intersects or not.
Is there anyone who knows how to face this kind of problem or can give me some tips?
Thanks.
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### Antworten (1)

Antoni Garcia-Herreros am 30 Mär. 2023
Bearbeitet: Antoni Garcia-Herreros am 30 Mär. 2023
If you have a plane parallel to XY reference frame (Z=a) , the line connecting the two points (p1 and p2) will cross the plane if the z component of the vector of that line (v=p2-p1) is nonzero, a.k.a not parallel to the plane.
%Orthogonal case
p1=[1 3 4];
p2=[5 6 8];
v=p2-p1;
v(3)==0 %If 0 it crosses the plane otherwise the plane and the line are parallel to each other
ans = logical
0
%Parallel case
p1=[1 3 4];
p2=[5 6 4];
v=p2-p1;
v(3)==0 %If 0 it crosses the plane otherwise the plane and the line are parallel to each other
ans = logical
1
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