How to understand if a line cut a surface plot

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.

Answer 1

[Antoni Garcia-Herreros]

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