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

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

Answer 1

[Matt J]

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 kh]

Dear Matt

Thanks for your answer.

I just have some questions about your answer:

1- You use handle function "@", I have searched about it, is it correct to say this function help us not to define the varibale "t" for example for matlab?

2- Would you please explane surface equation? how you write your code like this from the original equation?

3- and I have to define a range for "t0" where the equation chnaged the sign, so what is the best way to do it?

Thanks again for your answer and help. it wsa very useful.