How to define plane in 3d cube. Intersection point of segment with plane in 3d cube

Hello!

I am trying to find intersection point with any planes of cube.

I wrote function of plane_line_intersect using this https://www.mathworks.com/matlabcentral/fileexchange/17751-straight-line-and-plane-intersection

And using this function I was able to find intersection point. But before it I need to identify with which plane my segment will be intersected

And also I wrote function which will first check all planes for intersection and then I will call function plane_line_intersect

I am confused about how to write and organize all plane coordinates (p0, p1, p2, p3) of each plane in one function check_planes Should it be after I have attached picture and my code.

Thank you in advance for any help

Here is my code

function [I] = check_planes(x0,x1)
% Plane1 of cube
p0 = [0 3 3];
p1 = [0 0 3];
p2 = [0 3 0];
p3 = [0 0 0];
% Plane 2 of cube
p0 = [0 0 3];
p1 = [3 0 3];
p2 = [0 0 0];
p3 = [3 0 0];
% Plane 3 of cube
p0 = [3 0 3];
p1 = [3 3 3];
p2 = [3 0 0];
p3 = [3 3 0];
% Plane 4 of cube
p0 = [3 3 3];
p1 = [0 3 3];
p2 = [3 3 0];
p3 = [0 3 0];
% Plane 5 of cube
p0 = [0 3 0];
p1 = [3 3 0];
p2 = [0 0 0];
p3 = [3 0 0];
% Plane 6 of cube
p0 = [0 3 3];
p1 = [3 3 3];
p2 = [0 0 3];
p3 = [3 0 3];

for i=1:6
    [I, check] = plane_line_intersect(p0, p1, p2, p3, V0, x0, x1);
    if check == 1
        return
    end
end
end

[Matt J]

If you are doing this for the purposes of tomographic forward projection, it's a bad idea to do it in Matlab. There are publicly available, well-optimized forward projector libraries that will do it, e.g.

https://github.com/CERN/TIGRE

Answer 1

[KSSV]

You define p0, p1, p2 and p3 as matrix arrays.

function [I] = check_planes(x0,x1)
p0 = zeros(1,3,6) ; 
p1 = zeros(1,3,6) ; 
p2 = zeros(1,3,6) ; 
p3 = zeros(1,3,6) ; 
% Plane1 of cube
p0(1,:,1) = [0 3 3];
p1(1,:,1) = [0 0 3];
p2(1,:,1) = [0 3 0];
p3(1,:,1) = [0 0 0];
% Plane 2 of cube
p0(1,:,2) = [0 0 3];
p1(1,:,2) = [3 0 3];
p2(1,:,2) = [0 0 0];
p3(1,:,2) = [3 0 0];
% Plane 3 of cube
p0(1,:,3) = [3 0 3];
p1(1,:,3) = [3 3 3];
p2(1,:,3) = [3 0 0];
p3(1,:,3) = [3 3 0];
% Plane 4 of cube
p0(1,:,4) = [3 3 3];
p1(1,:,4) = [0 3 3];
p2(1,:,4) = [3 3 0];
p3(1,:,4) = [0 3 0];
% Plane 5 of cube
p0(1,:,5) = [0 3 0];
p1(1,:,5) = [3 3 0];
p2(1,:,5) = [0 0 0];
p3(1,:,5) = [3 0 0];
% Plane 6 of cube
p0(1,:,6) = [0 3 3];
p1(1,:,6) = [3 3 3];
p2(1,:,6) = [0 0 3];
p3(1,:,6) = [3 0 3];

for i=1:6
    [I, check] = plane_line_intersect(p0(1,:,i), p1(1,:,i), p2(1,:,i), p3(1,:,i), V0, x0, x1);
    if check == 1
        fprintf('%d plane\n',i)
        return
    end
end
end

[Aknur]

@KSSV thank you for your help.

It works

Answer 2

[Matt J]

Use intersectionHull() and addBounds from this FEX download:

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

lb=[0 0 0]; %upper and lower bounds of cube
ub=[1 1 1];

Pt1=-[0.5 0.5 0.5];   %line segment end points
Pt2=+[2 2 2];

[A,b] =addBounds([],[],[],[],lb,ub);

S=intersectionHull('vert',[Pt1;Pt2],...
                   'lcon', A,b );  %intersection of line segment and cube

>> S.vert

ans =

0 0.0000 0.0000

1.0000 1.0000 1.0000