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Can anyone tell me how to use GEOS/C++ to efficiently find all point pairs in a dataset closer than a threshold distance d?

I suspect this might involve quadtrees or rtrees but not quite sure how to query them.

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What algorithms have you tried so far? – R.K. Oct 7 '12 at 6:15
up vote 5 down vote accepted

Ok, got this working - and feel like putting the long answer here, as it has a lot of useful GEOS example bits in it. Here we go.


  • I haven't compiled this - I stripped out a load of project specific stuff and replaced it with a simple Point class which probably needs a copy/assignment operator. But it worked before I did that.
  • I'm not sure this counts as clustering, as a long line of points each pair of which is closer than tolerance would count as a cluster (fine for my purposes). Complexity is O(n log n) as long as your clusters don't get too big, I think. tolerance is defined as a square around each point, not a circle
  • It uses the C interface to GEOS which is meant to be stable, hence use of boost::pool to manage memory of things I'm leaving GEOS with pointers to
  • for some reason stackoverflow won't format this correctly, sorry!

    void my_geos_message_handler(const char *fmt, ...)
        #ifdef DEBUG
            va_list args;
            va_start( args, fmt );
            vprintf( fmt, args );
            va_end( args );
            printf( "\n" );
    struct Point
        double x,y;
        Point(double x,double y) : x(x),y(y) {}

typedef vector<Point> Cluster; typedef vector<Cluster > ClusterList; class ClusterFinder { public: ClusterFinder() { initGEOS(&my_geos_message_handler,&my_geos_message_handler); tree = GEOSSTRtree_create(10); } ~ClusterFinder() { GEOSSTRtree_destroy(tree); finishGEOS(); } void add(const Point &p) { ClusterFinderNode *n = new (node_pool.malloc()) ClusterFinderNode(p); const double x = p.x; const double y = p.y; GEOSCoordSequence* coords = GEOSCoordSeq_create(1,2); GEOSCoordSeq_setX(coords,0,x); GEOSCoordSeq_setY(coords,0,y); GEOSGeometry * point = GEOSGeom_createPoint(coords); //point assumes ownership of coords GEOSSTRtree_insert(tree,point,(void*)n); //tree assumes ownership of point } ClusterList get_clusters(double tolerance) { ClusterFinderData data(tolerance,tree); GEOSSTRtree_iterate(tree,&try_to_find_cluster_starting_from_node,&data); return data.clusters; } private: struct ClusterFinderNode { Point point; bool visited; ClusterFinderNode(const Point &p) :point(p),visited(false) {} }; GEOSSTRtree* tree; boost::object_pool<ClusterFinderNode> node_pool; struct ClusterFinderData { ClusterList clusters; vector<ClusterFinderNode*> searchqueue; double tolerance; GEOSSTRtree *tree; ClusterFinderData(double t,GEOSSTRtree* tree):tolerance(t),tree(tree) { clusters.reserve(100); searchqueue.reserve(100); } }; static void add_node_to_queue(void* vp_node,void* vp_clusterfinderdata) { ClusterFinderNode * const node = (ClusterFinderNode*) vp_node; ClusterFinderData * const cfd = (ClusterFinderData*) vp_clusterfinderdata; if (!node->visited) { cfd->searchqueue.push_back(node); } } static void check_node_for_neighbours(ClusterFinderNode *node,ClusterFinderData* cfd) { //mark visited and add to end of list node->visited = true; cfd->clusters.back().push_back(node->point); //add all neighbours within tolerance to search queue const double x = node->point.x; const double y = node->point.y; const double buffer = cfd->tolerance; GEOSCoordSequence* buffer_coords = GEOSCoordSeq_create(2,2); GEOSCoordSeq_setX(buffer_coords,0,x-buffer); GEOSCoordSeq_setY(buffer_coords,0,y-buffer); GEOSCoordSeq_setX(buffer_coords,1,x+buffer); GEOSCoordSeq_setY(buffer_coords,1,y+buffer); GEOSGeometry *line = GEOSGeom_createLineString(buffer_coords); //line takes ownership of buffer_coords GEOSGeometry *envelope = GEOSEnvelope(line); GEOSSTRtree_query(cfd->tree,envelope,&add_node_to_queue,(void*)cfd); GEOSGeom_destroy(line); GEOSGeom_destroy(envelope); } static void try_to_find_cluster_starting_from_node(void* vp_node,void* vp_clusterfinderdata) { ClusterFinderNode * const initial_node = (ClusterFinderNode*) vp_node; ClusterFinderData * const cfd = (ClusterFinderData*) vp_clusterfinderdata; if (initial_node->visited) return; //node was already discovered when starting from another node //push back new empty cluster vector cfd->clusters.push_back(Cluster()); //initialize exploration queue assert(cfd->searchqueue.size()==0); cfd->searchqueue.push_back(initial_node); //explore node to fill cluster vector while (cfd->searchqueue.size()>0) { ClusterFinderNode* node_to_search_next = cfd->searchqueue.back(); cfd->searchqueue.pop_back(); check_node_for_neighbours(node_to_search_next,cfd); } //all found nodes will now be on end of cfd->clusters //remove cluster vector if no neighbours found Cluster &latest_cluster = cfd->clusters.back(); if (latest_cluster.size() <= 1) { //should be a vector containing only the starting point //should never be size 0 assert(latest_cluster.size()==1 && latest_cluster[0] == initial_node->point); cfd->clusters.pop_back(); } } }; int main() { ClusterFinder cf; cf.add(Point(1,2)); cf.add(Point(3,4)); cf.add(Point(3.05,4)); //etc ClusterList clusters = cf.get_clusters(0.1); return 0; }
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