How to check 2D rectangle and 3D rectangular prism intersect with each other?

When there are 2D rectangle and 3D rectangular prism with their own orientations, how can I check if they intersect with each other in 3D space? I have 4 points for the rectangle and 8 points for the prism. Is there a built-in function I can use in MATLAB for this purpose? Two suitable rectangle and rectangular prism points are given as .mat file.

[KSSV]

Share the points....lets give a try.

[Berk]

I add them into the post.

Answer 1

[Matt J]

You can use intersectionHull() in this File Exchange submission,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or-in-equalities

load('rectangle.mat')
load('prism.mat')

S=intersectionHull('vert',prism,'vert',rectangle);

For the data you provided, there is indeed an intersection whose vertices are,

>> S.vert

ans =

  649.7498  426.2143  507.2920
  647.0217  430.5573  507.3727
  655.9783  432.4427  512.9273
  653.2502  436.7857  513.0080

[Berk]

Hello, thanks for help. Nevertheless, I can't use it in Simulink because it says "Function cellfun is not supported for code generation."

Actually, I don't need the intersection area, I just need to know if they intersect with each other. Maybe cellfun part might be used for finding intersection area and we can exclude that part..

[Matt J]

If the sides of the prism and rectangle are always parallel/perpendicular to one another, there may be simpler ways.

Answer 2

[Bruno Luong]

Quick and dirty code

load('prism.mat')
load('rectangle.mat')

% Normalize the coordinates
M = prism;
minM = min(M,[],1);
maxM = max(M,[],1);
dM = max(maxM-minM);
cfun = @(xyz) (xyz-(minM+maxM)/2)./dM;
M = [cfun(prism); -cfun(rectangle)]';
% Solve for common point
b = [0; 0; 0; 1; 1];
A = [M;
     ones(1,8)  zeros(1,4);
     zeros(1,8) ones(1,4)];
w = lsqnonneg(A,b);
% Check if solution exists
if norm(A*w-b,inf)<1e-10
    fprintf('intersected\n')
else
    fprintf('not intersected\n')
end