Broad-phase collision detection methods?

Question

I'm building a 2D physics engine and I want to add broad-phase collision detection, though I only know of 2 or 3 types:

• Check everything against everything else (O(n^2) complexity)
• Sweep and Prune (sort and sweep)
• something about Binary Space Partition (not sure how to do this)

But surely there's more options right? what are they? And can either a basic description of each be provided or links to descriptions?

I've seen this but I'm asking for a list of algorithms available, not the best one for my needs.

In this case, "Broad phase collision detection" is a method used by physics engines to determine which bodies in their simulation are close enough to warrant further investigation and possibly collision resolution.

Answer 1

The best approach depends on the specific use, but the bottom line is that you want to subdivide your world space such that (a) every body is in exactly one subdivision, (b) every subdivision is large enough that a a body in a particular subdivision can only collide with bodies in that same subdivision or an adjacent subdivision, and (c) the number of bodies in a particular subdivision is as small as possible.

How you do that depends on how many bodies you have, how they're moving, what your performance requirements are, and how much time you want to spend on your engine. If you're talking about bodies moving around in a largely open space, the simplest technique would be divide the world into a grid where each cell is larger than your largest object, and track the list of objects in each cell. If you're building something on the scale of a classic arcade game, this solution may well suffice.

If you're dealing with bodies moving in a larger open world, a simple grid will become overwhelming pretty quickly, and you'll probably want some sort of a tree-based structure like quadtrees, as Arriu suggests.

If you're talking about moving bodies around within bounded spaces instead of open spaces, then you may consider a BSP tree; the tree partitions the world into 'space you can walk in' and 'walls', and clipping a body into the tree determines whether it's in a legal position. Depending on the world geometry, you can also use a BSP for your broad-phase detection of collisions between bodies in the world.

Another option for bodies moving in bounded space would be a portal engine; if your world can consist of convex polygonal regions where each side of the polygon is either a solid wall or a 'portal' to another concave space, you can easily determine whether a body is within a region with a point-in-polygon test and simplify collision detection by only looking at bodies in the same region or connected regions.

Answer 2

An alternative to QuadTrees or BSPTrees are SphereTrees (CircleTrees in 2D, the implementation would be more or less the same). The advantage that SphereTrees have are that they handle large loads of dynamic objects very well. If you're objects are constantly moving, BSPTrees and QuadTrees are much slower in their updates than a Sphere/Circle Tree would be.

If you have a good mix of static and dynamic objects, a reasonably good solution is to use a QuadTree/BSPTree for the statics and a Sphere/Cicle Tree for the dynamic objects. Just remember that for any given object, you would need to check it against both trees.