How to determine if a 3D line segment intersects a side of a 3D rectangular prism?

Hello,

I am trying to find a way to determine if a line segment drawn between two points in 3D space will intersect another 3D body (retangular prism) that is defined by regions using (x, y, z) vertices.

Is there a way to do this in Matlab?

Answer 1

[Matt J]

You can use intersectionHull() in this FEX download,

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

[MS]

Hi Matt,

Thanks for your suggestion. So in this case, V holds the vertices of the rectangular prism and Aeq holds the (x,y,z) values for the two endpoints of the line segment? What is the role of beq? I noticed in the 'lcon2vert' function, beq is referred to as equality data.

[Matt J]

No, you can specify both the line segment and the prism in terms of vertices if you wish, for example,

    Vprism=dec2bin(0:2^3-1,2)-'0'+1   %vertices of prism

    Vline=[0,0,0;3 3 3];               %vertices of line segment
    
    I=intersectionHull('vert',Vprism,'vert',Vline);  %compute intersection
    

>> I.vert

ans =

1.0000 1.0000 1.0000

2.0000 2.0000 2.0000

Answer 2

[Matt J]

You can also use Siddon's algorithm

https://aapm.onlinelibrary.wiley.com/doi/epdf/10.1118/1.595739

which will compute the intersection between a ray and many prisms.