Re: incremental triangulation for 2D collision detection broadphase

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Hi Samuel,

At first glance this approach seems pretty complex and expensive for a 
broad phase? I can't see how you can do this without triangulation and 
thats not a cheap operation. Even then, you have to intersect polygons 
against AABBs which is actually quite a costly operation - not that far 
away from a full narrow phase.

I would recommend sweep and prune, or multi-sweep and prune if your worlds 
are huge. We used sweep and prune in little big planet psp and it worked 
quite well.

Just my 2p :)

Cheers, Paul.

Samuel Moll <[email protected]> wrote on 03/02/2010 14:38:46:

> @Ben: Thanks for the link, but I wanted to avoid doing full Delauney
> triangulation since everything remotely Delauney-like suffices for
> me... but I can probably use some of the methods in this paper.
> @ Erwin: Thought I read somewhere that Box2D uses a hash... but the
> source code looks alot like a AABB tree ;)
> 
> 
> But I think I found something better, because I realized that I don't
> really need a triangulation, only some partition for example using
> polygons...
> 
> Okay, here's the outline to my approach:
> Every objects center is a "node", around the node is this objects
> bounding volume (I think I'll use circles).
> Then you build a graph that partitions the plane into (convex and
> concave) polygons (You could make the graph so that only triangles are
> used). On every corner of a polygon is an object, no object is on the
> inside of a polygon.
> 
> Now you test for every object which polygon its bounding volume
> intersects. Obviously it intersects at least all polygons adjacent to
> its node; if the bounding volumes are relatively tight, it should not
> intersect more than these.
> I think the average number of bounding volume tests for each object
> should be around 6.
> 
> Now all nodes move, and if the graph changes its topology, it needs to
> be repaired. This is the part where I have no concrete algorithm
> yet... but I guess I'll find one. I'm relatively sure that this step
> should be fast ;)
> 
> Then the graph is optimized: a few edges are swapped, inserted etc. to
> avoid slivers and such. This should be easy.
> 
> Greets,
> Samuel
> 
> 
> 
> On Wed, Feb 3, 2010 at 6:39 AM, Erwin Coumans <[email protected]> 
wrote:
> >
> > Hi Samuel,
> >
> > Box2d uses a dynamic AABB tree for the broadphase, based on the 
original
> > implementation from our Bullet library in 3d.
> >
> > This tree is incrementally updated, faster than sweep and prune.
> >
> > No spatial hash.
> >
> > I'm interested in your approach. How do you 'triangulate' the centers, 
and
> > compute connectivity?
> >
> > Thanks,
> > Erwin
> >
> > Feel free to forward this to the list, I cannot mail to the list 
because of
> > mail server issues.
> >
> > Sent from my iPhone
> >
> > On Feb 2, 2010, at 16:54, Samuel Moll <[email protected]> wrote:
> >
> >> Hello all,
> >>
> >> I need a broadphase collision detection algorithm for 2D rigid body
> >> physics (continuous collision detection, but that shouldn't matter 
for
> >> the broadphase...).
> >>
> >> I have objects of wildly varying sizes, lots of free space and
> >> possibly lots of clustering or even a single object very far away 
from
> >> all the others, so a Quadtree (without some strange modifications,
> >> wrapping the world came to mind) is not the best option.
> >>
> >> What I came up with is to take all the objects positions and
> >> triangulate this point set. Then for each triangle I determine which
> >> objects it overlaps and test all these objects for collision.
> >>
> >> This has a number of advantages, and I believe it could be 
competitive
> >> to sweep and prune or Quadtrees (at least in 2D, in 3D its probably
> >> not cool, but who knows?). I couldn't find anything about this 
method,
> >> but if somebody already invented it I'd appreciate some pointers.
> >>
> >> What I need now is an (efficient :D) algorithm for updating the
> >> triangulation when the points move. i.e. given a valid triangulation
> >> (no triangles overlap, triangulates the convex hull of all points) 
and
> >> movement vectors for all points, how can I "repair" the old
> >> triangulation?
> >>
> >> The first part of the problem is how to maintain fat triangles
> >> (slivers lead to poor collision rejection). I'm sure there are 
already
> >> good algorithms to incrementally maintain a good triangulation, but I
> >> couldn't find them. Also, the union of all triangles must stay 
convex.
> >>
> >> The second problem is how to detect and remove triangle overlaps that
> >> arise due to fast-moving objects. I have no idea how to do this
> >> robustly (theoretically, the points could teleport arbitrarily)
> >>
> >> I guess somebody already has solved this problem, but I could find no
> >> relevant paper...
> >>
> >> Of course I'll release the finished implementation as open source, or
> >> try to incorporate it into Box2D if they want it and if it proves
> >> faster than their existing spatial hashing ;)
> >>
> >>
> >> Sincerely,
> >> Samuel Moll
> >>
> >>
> >> 
> 
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