Determine the intersection coordinates between a 3D object and an infinite plane

Hi! I would like to know if there is a way to determine the intersection coordinates between a reported 3D geometry (tube) and an infinite plane. That is, determine the coordinates where the red line is in the image.

NODES = importdata("NODES.mat");
FACES = importdata("FACES.mat");

P = [24.3377 -21.8635 81.9835];
plane = [0.1385	0.0645	0.9883];
a = plane(1); 
b = plane(2); 
c = plane(3);
d = dot(plane,P);

figure
plot3(P(:,1),P(:,2),P(:,3),'k.','Markersize',20);
hold on
% plot3(NODES(:,1),NODES(:,2),NODES(:,3),'b.','Markersize',3)
trimesh(FACES(:,:),NODES(:,1),NODES(:,2),NODES(:,3),'EdgeColor','k','Linewidth',0.1,'Facecolor','b','FaceAlpha',.4)
f_1 = fimplicit3(@(x,y,z) a*x+b*y+z*c-d);
hold off
axis equal
zlim([70 90])

Answer 1

[Bruno Luong]

Mesh your plane then use this

https://www.mathworks.com/matlabcentral/fileexchange/49160-fast-mesh-mesh-intersection-using-ray-tri-intersection-with-octree-spatial-partitioning

[Alberto Acri]

Hi @Bruno Luong! Thanks for the link. How can I create the mesh of my plane?

[Bruno Luong]

Similar to Matt's answer to another thread from you, just replace circle by square

[Alberto Acri]

Yes, using the code that Matt J provided me I created a mesh of the circle (the circle is also fine as geometry).

To use the code in the link I would need the nodes and faces of the circle. I have the nodes (the V matrix). How can I recover the faces?

load V
V=num2cell(V,1);
[x,y,z]=deal(V{:});
trisurf(delaunay(x,y), x,y,z)

[Bruno Luong]

The face is

delaunay(x,y)