How to check if two convex polyhedrons intersect with each other in Three.js?

Question

I'm working on a problem that need to randomly generate and put convex polyhedrons into a cube/cylinder container at randomly chosen points without overlapping. I'm using three.js to get a graphic output.

A demo.

While putting a polyhedron, how to check whether it intersects with other polyhedrons?

The convex polyhedron involved is simply tetrahedron or hexahedron and is constructed using THREE.ConvexGeometry. As I need a precise check, bounding box is not enough, I just use it to make sure two polyhedrons are not intersected.

I've done a lot research and found many complicated theories and methods, what I need is to get a Boolean result that tells if there exists an intersection between two convex polyhedrons. SAT (Separating Axis Theorem) in 3D is good enough, but Three.js doesn't seem to be capable of doing this. Can anyone tell me how to do this kind of check in a simple way or just explain how to do it with SAT in 3D?

Answer 1

You can take a look at http://www.realtimerendering.com/intersections.html . Even though the site is from 2011 the intersection algorithms have not changed in the last years. From the demo it seems that once the polyhedrons are placed in the cube, they don't move. So the SAT algorithm would not be the best solution as it is used for moving polyhedra.

Answer 2

The Gilbert–Johnson–Keerthi is a powerful algorithm that allow to measure distance and check for intersection between convex polyhedrons. Still I believe that it is better to use on simple polyhedron otherwise the computation in the support function might take some time. A possible drawback is that you need to have functions able to measure the distance between a point and another point/segment/triangle, I do not know if some are available in three.js.

http://en.wikipedia.org/wiki/Gilbert%E2%80%93Johnson%E2%80%93Keerthi_distance_algorithm