How do I get the coordinate where an edge intersects a face using geometry nodes?

Question

Using geometry nodes, is there any way to detect where an edge intersects with a face? It's difficult for me to explain. But I drew a picture. The gray line is merely an edge, and it intersects a face of a mesh, as indicated by the gray circle. Is there a way to get the vector of that circle? I figure if I knew what that vector was, I could move other points toward or away from it. Oh, and I would really prefer it if both the mesh and the edge are of the same object. Not two different objects. One object's edges, detecting the faces of itself.

Answer 1

To solve this task you could use the node Raycast.

By subtracting the two positions of your mesh line from each other you get the direction, and starting from one of the two positions you can then send a raycast to the grid.

Something like this:

It depends on what exactly you are planning or how you want to set this up, but in that case it seemed to make sense to me to capture the hit directly on the mesh line, convert it to a point, and then move the point to the position where the grid is hit.

_{(Blender 3.2+)}

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Update

To solve your specific task and to be able to process everything in a single object, you would have to define more precisely what your plans are.

There are many possibilities here, and the structure of the solution depends primarily on the domain in which you need the information of the intersections.

However, I will try to illustrate a possible solution with the following example:

Here I use basically the same mechanism as shown in the previous example.

However, I send the raycast in the length of each edge, starting from each point, in both directions.

Thus it is possible to find also the intersections of more complex shapes (but always only maximum twice along an edge).

_{(Blender 3.2+)}