How I can find intersection point of direction vector and one of the given plane of 3d cube

Hello everyone! Kindly ask help. How I can find intersection point of direction vector and given planes of cube. I have X0, Y0, Z0 and X, Y, Z and planes. (X0 =1.5; Y0 =1.5; Z0 =3.0; X = 1.5; Y = 3.0;Z = 0.699097;)

planes(:,:,1) = [0 3 3; 0 0 3; 0 3 0; 0 0 0; 0 0 0];
planes(:,:,2) = [0 0 3; 3 0 3; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,3) = [3 0 3; 3 3 3; 3 0 0; 3 3 0; 3 0 0];
planes(:,:,4) = [3 3 3; 0 3 3; 3 3 0; 0 3 0; 0 3 3];
planes(:,:,5) = [0 3 0; 3 3 0; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,6) = [0 3 3; 3 3 3; 0 0 3; 3 0 3; 0 0 3];
location_plane = 6;

Here is my function. I want to define coordinates of intersection point I1, I2, I3 and p is with which location plane intersect. Much appreciate any help

function [p, I1, I2, I3 ] = planeLocation5(X, Y, Z)
X = 1.5;      
Y = 3.0;
Z = 0.699097;
planes(:,:,1) = [0 3 3; 0 0 3; 0 3 0; 0 0 0; 0 0 0];
planes(:,:,2) = [0 0 3; 3 0 3; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,3) = [3 0 3; 3 3 3; 3 0 0; 3 3 0; 3 0 0];
planes(:,:,4) = [3 3 3; 0 3 3; 3 3 0; 0 3 0; 0 3 3];
planes(:,:,5) = [0 3 0; 3 3 0; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,6) = [0 3 3; 3 3 3; 0 0 3; 3 0 3; 0 0 3];
location_plane = 6;
for jj=1:6
    plane = planes(:,:,j);

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

[Matt J]

Back-up copy of original question:

Hello everyone! Kindly ask help. How I can find intersection point of direction vector and given planes of cube. I have X0, Y0, Z0 and X, Y, Z and planes. (X0 =1.5; Y0 =1.5; Z0 =3.0; X = 1.5; Y = 3.0;Z = 0.699097;)

planes(:,:,1) = [0 3 3; 0 0 3; 0 3 0; 0 0 0; 0 0 0];
planes(:,:,2) = [0 0 3; 3 0 3; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,3) = [3 0 3; 3 3 3; 3 0 0; 3 3 0; 3 0 0];
planes(:,:,4) = [3 3 3; 0 3 3; 3 3 0; 0 3 0; 0 3 3];
planes(:,:,5) = [0 3 0; 3 3 0; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,6) = [0 3 3; 3 3 3; 0 0 3; 3 0 3; 0 0 3];
location_plane = 6;

Here is my function. I want to define coordinates of intersection point I1, I2, I3 and p is with which location plane intersect. Much appreciate any help

function [p, I1, I2, I3 ] = planeLocation5(X, Y, Z)
X = 1.5;      
Y = 3.0;
Z = 0.699097;
planes(:,:,1) = [0 3 3; 0 0 3; 0 3 0; 0 0 0; 0 0 0];
planes(:,:,2) = [0 0 3; 3 0 3; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,3) = [3 0 3; 3 3 3; 3 0 0; 3 3 0; 3 0 0];
planes(:,:,4) = [3 3 3; 0 3 3; 3 3 0; 0 3 0; 0 3 3];
planes(:,:,5) = [0 3 0; 3 3 0; 0 0 0; 3 0 0; 0 0 0];
planes(:,:,6) = [0 3 3; 3 3 3; 0 0 3; 3 0 3; 0 0 3];
location_plane = 6;
for jj=1:6
    plane = planes(:,:,j);

Answer 1

[Matt J]

Fairly eay to do to do with this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra

However, in your list of the 6 cube faces, you've given each face 5 corners instead of 4, which doesn't seem right. So, I didn't use that description below.

X0 =1.5; Y0 =1.5; Z0 =3.0; X = 1.5; Y = 3.0;Z = 0.699097;

[p, I ] = planeLocation([X,Y,Z],[X0,Y0,Z0])

p =

5

6

I =

1.5000 3.0000 0.6991

1.5000 1.5000 3.0000

function [p, I ] = planeLocation(XYZ,XYZ0)
    
    
    
    [A,b]=addBounds([],[],[],[],[0,0,0],[3,3,3]); % equations for cube faces
    
    
    [~,~,Aeq,beq]=vert2lcon([XYZ;XYZ0]); %equations for line
    
    S=intersectionHull('lcon',A,b,'lcon',[],[],Aeq,beq); %compute intersections
    
    if isempty(S.vert)
        warning 'No intersections'
        p=[]; I=[]; return
    end
    
    I=S.vert; %intersection points
    
    %%Compute which faces intersection points belong to
    Ab=[A,b];
    ab=[S.lcon{1:2}];
    [~,p]=ismembertol(ab,Ab,1e-8,'ByRows',1,'DataScale',1);

end

[Aknur]

Hello, Dear @Matt J thank you for your time and help. Wow your code looks great. Thank you so much. I am trying to understand and apply it. I got this error "Out of memory. The likely cause is an infinite recursion within the program." Kindly ask if you know how I can fix it

I have used 5 'corner' - they are 4 corners and one point which is lying on that each plane. I tried to find intersection using dot function using normal of each plane and point which is lying on the plane.

[Matt J]

I got this error "Out of memory. The likely cause is an infinite recursion within the program." Kindly ask if you know how I can fix it

I don't know what you might have done to produce that. When I run with the input data you supplied us, I get the output shown above.

Answer 2

[Sulaymon Eshkabilov]

Have reviewed this solution: https://www.mathworks.com/matlabcentral/answers/93623-how-do-i-plot-the-line-of-intersection-between-two-surfaces

[Aknur]

Dear, @Sulaymon Eshkabilov thank you for your response and for your time. I am a little bit dot understand exactly how to work in Matlab, and still new in it

I am checking your suggestion. I could not understand. If I am undestand right is not exactly what I need.

I have tried another one example/solution

https://www.mathworks.com/matlabcentral/fileexchange/103835-plane-and-lie-intersection

But in this example they consider only two planes. In my case I need to check all planes. Because then I will rotate and continue to do the same steps for the next vectors, etc