Surface and Line interaction point

Hello

I have two pints and I need to find the surface passing them and then investigate even a line that passes new points A nad B have an interaction with the surface or not?

I have to add that all my numbers are positive and I do not have a negetive integer so I can not use "fzero" function since the root of the function is where fun(x) changes sign.

I write the below code as far and have problem for the intersection part.

Thanks for any help.

%Creating surface in matlab
x=[-1;5];
y=[1;1];
[X,Y]=meshgrid(x,y);
z=[0 0; 2 2];
S=surf(X, Y, z)
hold on
stem3(x, y, z, '--*m')
% A and B cordinates
XN =[ 0.5; -0.7];
YN=[-0.5;1.5];
ZN=[-1;1.5];
hold on
scatter3(XN,YN,ZN);
A =[XN(1) YN(1) ZN(1)];
B =[XN(2) YN(2) ZN(2)];
plot3(XN,YN,ZN);
% check if the line passinng A and B has an interaction with surface "S" or not?

[KALYAN ACHARJYA]

Is this you are looking for?

[Zarak kh]

I want to find the (x,y,z) cordinates of the intersection point of the mentioned line and surface, So I will be able to add an "if" clause for the rest of the program.

Answer 1

[Jyotsna Talluri]

Hi,

As you know coordinates of the surface ,first determine the normal vector to the surface

From your code the coordinates are

 p0=[-1 1 2]; 
 p1=[5 1 2]; 
 p2=[-1 1 0]; 
 p3=[5 1 0];  
 n=cross(p0-p2,p0-p3); 

gives the normal to the plane of the surface.

The function plane_line_intersect in the below link of file exchange determines the point of intersection of surface and the line

https://www.mathworks.com/matlabcentral/fileexchange/17751-straight-line-and-plane-intersection

As argument V0 can be any point in the plane ,it can be p0,p1,p2,p3;

You declared line end points as A and B

Hence, call the function plane_line_intersect(n,V0,A,B) by passsing the arguments