I am working with a game engine, and my task is to add code for simulating fracture of rigid meshes.

Right now I'm only working on breaking a cube.

I am using Voronoi's algorithm to make a (realistic)fractured shard and I am using the half-plane method to generate a voronoi cell.

Now the way I do this is for every seed point, I make planes that are perpendicular bisector planes(the straight black lines in the image) with rest of the seed points and I calculate the intersections of all these planes to give me distinct points(all the orange dots).

I've gotten this far.

Out of all these calculated intersection points, I only need the ones that are closest and enclosing the seed point(the points encircled in red) and I need to discard all the rest.

Information that I have :

1) Plane equations of all planes(defined by normalized normal vectors and their distance from origin)

2) Points of intersection(that I've calculated)

Can anybody help me find out how I can find the points encircled in red?

Thanks.