Re: [Algorithms] incremental triangulation for 2D collision detection broadphase

 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Ben Sunshine-Hill - 2010-02-03 02:01:32 ```On Tue, Feb 2, 2010 at 7:54 PM, Samuel Moll wrote: > 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? Take a look at "Voronoi Diagrams of Moving Points", link below. Remember that the Voronoi tessellation is the dual of the Delaunay triangulation, which in general tends not to produce many slivers. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.8944 Ben ```

 [Algorithms] incremental triangulation for 2D collision detection broadphase From: Samuel Moll - 2010-02-03 00:54:12 ```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 ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Ben Sunshine-Hill - 2010-02-03 02:01:32 ```On Tue, Feb 2, 2010 at 7:54 PM, Samuel Moll wrote: > 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? Take a look at "Voronoi Diagrams of Moving Points", link below. Remember that the Voronoi tessellation is the dual of the Delaunay triangulation, which in general tends not to produce many slivers. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.8944 Ben ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Samuel Moll - 2010-02-03 14:38:54 ```@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 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 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 >> >> >> ------------------------------------------------------------------------------ >> The Planet: dedicated and managed hosting, cloud storage, colocation >> Stay online with enterprise data centers and the best network in the >> business >> Choose flexible plans and management services without long-term contracts >> Personal 24x7 support from experience hosting pros just a phone call away. >> http://p.sf.net/sfu/theplanet-com >> _______________________________________________ >> GDAlgorithms-list mailing list >> GDAlgorithms-list@... >> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list >> Archives: >> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list > ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Paul_F - 2010-02-05 16:42:14 ```-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA256 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 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 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 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 > >> > >> > >> > - ------------------------------------------------------------------------------ > >> The Planet: dedicated and managed hosting, cloud storage, colocation > >> Stay online with enterprise data centers and the best network in the > >> business > >> Choose flexible plans and management services without long-term contracts > >> Personal 24x7 support from experience hosting pros just a phone call away. > >> http://p.sf.net/sfu/theplanet-com > >> _______________________________________________ > >> GDAlgorithms-list mailing list > >> GDAlgorithms-list@... > >> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > >> Archives: > >> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list > > > > - ------------------------------------------------------------------------------ > The Planet: dedicated and managed hosting, cloud storage, colocation > Stay online with enterprise data centers and the best network in the business > Choose flexible plans and management services without long-term contracts > Personal 24x7 support from experience hosting pros just a phone call away. > http://p.sf.net/sfu/theplanet-com > _______________________________________________ > GDAlgorithms-list mailing list > GDAlgorithms-list@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list ********************************************************************** This email and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. If you have received this email in error please notify postmaster@... This footnote also confirms that this email message has been checked for all known viruses. Sony Computer Entertainment Europe Limited Registered Office: 10 Great Marlborough Street, London W1F 7LP, United Kingdom Registered in England: 3277793 ********************************************************************** P Please consider the environment before printing this e-mail -----BEGIN PGP SIGNATURE----- Version: PGP Universal 2.9.1 (Build 287) Charset: US-ASCII wsBVAwUBS2xEHXajGqjtoMHxAQi/iQf+LA826T+HJfDyYpXe89DM3tx1H9bBBbME ND94GJj6Gbd93YNNgfXfYQV1kkyKKE+jyRG0IrQmrd3UaKIb2176hHkRfeDtmuJQ LH9W45L9ePp9kLYqadveQv0CKME8Vy9Bg9MlmTtDYp56eLUa7A0uUHVFmRaJmExK AgmZLio9fiuR14bUqHXXik50Wk7kwXcOt0sWQqSO0HPmXyLFGgCRiNF1TSzxjPZA hK7dbKzoS772s6UyT6QHqeD3B5XE6J4cJCY0utNNxMeNCcVUaP0CcS+5//IlfGZn ZcFZOvLJGoY2Mt9h1JDFWY3blmWLla+7mrGWWAag7aqCdtg2U02pYQ== =pGyB -----END PGP SIGNATURE----- ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Samuel Moll - 2010-02-08 04:47:57 ```> 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. The triangulation is maintained incrementally -- normally it doesn't change, so it only needs to be checked if it is still valid every frame. If it changes, it only needs to be recalculated partially. This is an O(n+something for the changed part) 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. Using circles makes it a bit cheaper (that's one of the reasons why I want to use circles as bounding volumes), it's something like 6 line-circle intersection tests per object on average. But yes, the cost per object is quite high compared to other methods. > 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. I guess by multi-sweep you mean doing the sweeping on more than one axis? How do you combine the results of the sweeps, for example for 100x100 objects arranged in a grid? My motivation for trying this is that all broad phase algorithms I know of are far away from a O(n) running time and have other limitations. The triangulation method doesn't have any limitations on object sizes or distribution and should have an expected O(n) running time (and memory requirement) if neighborhood relations between objects don't change too much in one frame. Maybe the cost per object is too high to be competitive with other methods like SnP. But for a very high number of objects it will definitely be better. In any case it is worth trying out... Greets, Samuel ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Paul_F - 2010-02-08 09:48:57 ```-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA256 > The triangulation is maintained incrementally -- normally it doesn't > change, so it only needs to be checked if it is still valid every > frame. If it changes, it only needs to be recalculated partially. This > is an O(n+something for the changed part) operation. I thought triangulation was a O(n^2) problem at least? (looks it up on wikipedia) ahh, i see there is talk of triangulating a simple polygon in O(n), but i'm not sure a connected graph of all objects constitutes a simple polygon? > Using circles makes it a bit cheaper (that's one of the reasons why I > want to use circles as bounding volumes), it's something like 6 The trouble with circles is that they don't fit the kind of triangles that a convex decomposition algorithm spits out very well, since they can be long and thin. We used AABBs in the end. > I guess by multi-sweep you mean doing the sweeping on more than one > axis? How do you combine the results of the sweeps, for example for > 100x100 objects arranged in a grid? Multi-sweep is where you divide your (huge) world up into a small number of chunks (rectangles in 2d) and then do regular sweep and prune in each chunk. This gets around the clustering problem where far away objects can cause a lot of clustered entries on one axis. We just used regular SAP for the record :) > My motivation for trying this is that all broad phase algorithms I > know of are far away from a O(n) running time and have other The most important thing to keep in mind is that a good broad-phase algorithm should do zero work when nothing moves in the world. > Maybe the cost per object is too high to be competitive with other > methods like SnP. But for a very high number of objects it will > definitely be better. In any case it is worth trying out... Are all your objects always moving in your world? How many objects are you talking about? Cheers, Paul. ********************************************************************** This email and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. If you have received this email in error please notify postmaster@... This footnote also confirms that this email message has been checked for all known viruses. Sony Computer Entertainment Europe Limited Registered Office: 10 Great Marlborough Street, London W1F 7LP, United Kingdom Registered in England: 3277793 ********************************************************************** P Please consider the environment before printing this e-mail -----BEGIN PGP SIGNATURE----- Version: PGP Universal 2.9.1 (Build 287) Charset: US-ASCII wsBVAwUBS2/eAHajGqjtoMHxAQjybQf/UrQsqYNvEQN82/slrWd8LwdOQchc2X4v GlwZ8lfHhMH7JB0uFnRPmgyd/pvIlj/q8JFi0SL+m0wrQNemw9Y0DvVhj3FNyk6M ezSqU5MvjVc6H6+Bp3ZGXDOWyCpgYW5FBENI8OKHkirv2YgC3Lk4iYAxIx/HPQPo 6zIbXpL1eBIM53BrcYR1WHHU57NwqHxHOZjjM6KYIt+M/vzX/fi0UFiKN4lhFkNf fOKhgdWgUsmCIFDUV/j3z+CnsCMfFSqgevSd2sDy78O5dx7rZrs+nBaSvsN31+AN IoyQVqD/RAdoXGNfGR1GxQcoGIDOU92fjijoBYOGgA/DQUzkC4lomw== =pibX -----END PGP SIGNATURE----- ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Simon Fenney - 2010-02-08 11:00:12 ```Paul_Firth@... wrote: > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA256 > >> The triangulation is maintained incrementally -- normally it doesn't >> change, so it only needs to be checked if it is still valid every >> frame. If it changes, it only needs to be recalculated partially. >> This is an O(n+something for the changed part) operation. > > I thought triangulation was a O(n^2) problem at least? (looks it up on > wikipedia) ahh, i see there is talk of triangulating a simple polygon > in O(n), but i'm not sure a connected graph of all objects > constitutes a simple polygon? Drifting a bit OT, but from what I've read, the O(n) triangulation algorithm of simple polygons is said to be very complicated. Although wikipedia does have a link to a claimed simple, linear time, triangulation algorithm, until I someone posts a copy of the paper that is in English, I'll take it with a grain of salt. :) FWIW, there are O(n log* n) algorithms (the star is important) which are fairly simple to implement and are pretty much indistinguishable from O(n). Again, apologies for going a little OT. Simon ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Samuel Moll - 2010-02-08 17:03:33 ```> I thought triangulation was a O(n^2) problem at least? (looks it up on > wikipedia) ahh, i see there is talk of triangulating a simple polygon in > O(n), but i'm not sure a connected graph of all objects constitutes a > simple polygon? You can do Delaunay-Triangulation in O(n*logn), but the point is that I need to maintain a triangulation of moving points -- that's entirely different from constructing one from scratch. > The most important thing to keep in mind is that a good broad-phase > algorithm should do zero work when nothing moves in the world. > Are all your objects always moving in your world? How many objects are you > talking about? I should have mentioned that I'm writing a 2D space shooter, so all the objects are moving all the time. And I'll have like 200 objects or so. Samuel ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Paul_F - 2010-02-09 09:34:58 ```-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA256 > I should have mentioned that I'm writing a 2D space shooter, so all > the objects are moving all the time. And I'll have like 200 objects or > so. Ahhh, ok - are you on a platform with reasonably quick memory (good caches etc)? Have you tried just gridding up your world (screen?) using a quite large cell size and do a simple bounding volume check in each cell location? The advantage of the grid is that you don't need to do any work until objects move from one cell into another. Of course if your objects are all wildly different sizes this can get tricky - there are hierarchical grid methods to cope with this but they have their own limitations... Cheers, Paul. ********************************************************************** This email and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. If you have received this email in error please notify postmaster@... This footnote also confirms that this email message has been checked for all known viruses. Sony Computer Entertainment Europe Limited Registered Office: 10 Great Marlborough Street, London W1F 7LP, United Kingdom Registered in England: 3277793 ********************************************************************** P Please consider the environment before printing this e-mail -----BEGIN PGP SIGNATURE----- Version: PGP Universal 2.9.1 (Build 287) Charset: US-ASCII wsBVAwUBS3EsOXajGqjtoMHxAQg4Fwf/RaCRsxE3qeBXKLjeVULeDqeVF0nQTZlB ZHeSkQvQ+OLgjdJpVyZsCvCAnrU7zOBS+Zu+6MzDUSi1yRZMver7Nhzfz17d7fLk tI6QLDkKzntTIMVhXjpMfxWqkLuHYElYfYzPbUQDSkLk1nhfg64alPQeFVse2huq lPUwrdbL7VMNGXIcMlGScXK8xcVu1MADhZVg+2gfMUOxZrx4gv/F6qIaVVaXF3gE dcGiSuccFinF1pq5GT5ax3/aoK3i3AREkaz6ktXjTI4AvC/1iCBF5WzPqAwUpQUo 5gOTOw3IijTM31cqU1nx3fa9h79rPx91KVnd7DjJAL3G6lneZ+jEtg== =tWrz -----END PGP SIGNATURE----- ```
 Re: [Algorithms] incremental triangulation for 2D collision detection broadphase From: Sebastian Sylvan - 2010-02-09 18:37:46 Attachments: Message as HTML ```On Tue, Feb 9, 2010 at 9:35 AM, wrote: > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA256 > > > I should have mentioned that I'm writing a 2D space shooter, so all > > the objects are moving all the time. And I'll have like 200 objects or > > so. > > Ahhh, ok - are you on a platform with reasonably quick memory (good caches > etc)? Have you tried just gridding up your world (screen?) using a quite > large cell size and do a simple bounding volume check in each cell > location? > Or even use a fairly small cell size (the size of the largest objects), and store cells with objects in them in a hashmap from the cell coordinate to a list of objects. That way you can have an infinite grid and you only need storage proportional to the number of non-empty cells for the grid itself. Of course a simple BV hierarchy (e.g. AABB-tree, BIH, etc.) works too, since you can usually adjust it to remain valid without doing a full re-insert each frame. I suspect that a simple SaP will outdo all of these though. It's just that much simpler. -- Sebastian Sylvan ```