## How to find out the cordinates of the intersection point of a line and a surface?

### Zarak Mo (view profile)

on 29 Jul 2019
Latest activity Commented on by Zarak Mo

on 30 Jul 2019

### Matt J (view profile)

Hello
I need to find out weather a line that connect to points in a 3D situation have an intersection with a surface or not, and also report the intersection point for further steps.
Imagine I have two points A and B ( which needs to be connected) a surface z.
A : x= 0.5 y=-0.5 z=-1
B : x=-0.7 y=1 z=1.5
and the surface z is:
[x, y] = meshgrid(linspace(-1, 1));
z = y.^2 + 2*x;
"The above data are just as an example"
Thanks alot for any help on my question

on 30 Jul 2019
Edited by Matt J

### Matt J (view profile)

on 30 Jul 2019

Plug the equation for the line into the equation for the surface and use fzero to find the root. This root will give the location of the intersection.
L=@(t) A+(B-A)*t; %line equation
S= @(xyz) xyz(3)-xyz(1).^2 -xyz(2).^2; %surface equation
t_intersection = fzero(@(t) S(L(t)) ,t0 )

Zarak Mo

on 30 Jul 2019
Dear Matt