// Copyright 2006 Google Inc. All Rights Reserved. #include "s2polygonbuilder.h" #include "s2.h" #include using std::min; using std::max; using std::swap; using std::reverse; #include "hash.h" #include using std::setprecision; #include using std::ostream; using std::cout; using std::endl; #include using std::map; using std::multimap; #include using std::set; using std::multiset; #include using std::vector; #include "base/logging.h" #include "base/macros.h" #include "s2.h" #include "s2cellid.h" #include "s2polygon.h" #include "util/math/matrix3x3-inl.h" void S2PolygonBuilderOptions::set_undirected_edges(bool undirected_edges) { undirected_edges_ = undirected_edges; } void S2PolygonBuilderOptions::set_xor_edges(bool xor_edges) { xor_edges_ = xor_edges; } void S2PolygonBuilderOptions::set_validate(bool validate) { validate_ = validate; } void S2PolygonBuilderOptions::set_vertex_merge_radius(S1Angle const& angle) { vertex_merge_radius_ = angle; } void S2PolygonBuilderOptions::set_edge_splice_fraction(double fraction) { CHECK(fraction < sqrt(3.) / 2); edge_splice_fraction_ = fraction; } S2PolygonBuilder::S2PolygonBuilder(S2PolygonBuilderOptions const& options) : options_(options), edges_(new EdgeSet) { } S2PolygonBuilder::~S2PolygonBuilder() { } bool S2PolygonBuilder::HasEdge(S2Point const& v0, S2Point const& v1) { EdgeSet::const_iterator candidates = edges_->find(v0); return (candidates != edges_->end() && candidates->second.find(v1) != candidates->second.end()); } bool S2PolygonBuilder::AddEdge(S2Point const& v0, S2Point const& v1) { // If xor_edges is true, we look for an existing edge in the opposite // direction. We either delete that edge or insert a new one. if (v0 == v1) return false; if (options_.xor_edges() && HasEdge(v1, v0)) { EraseEdge(v1, v0); return false; } if (edges_->find(v0) == edges_->end()) starting_vertices_.push_back(v0); (*edges_)[v0].insert(v1); if (options_.undirected_edges()) { if (edges_->find(v1) == edges_->end()) starting_vertices_.push_back(v1); (*edges_)[v1].insert(v0); } return true; } void S2PolygonBuilder::AddLoop(S2Loop const* loop) { int sign = loop->sign(); for (int i = loop->num_vertices(); i > 0; --i) { // Vertex indices need to be in the range [0, 2*num_vertices()-1]. AddEdge(loop->vertex(i), loop->vertex(i + sign)); } } void S2PolygonBuilder::AddPolygon(S2Polygon const* polygon) { for (int i = 0; i < polygon->num_loops(); ++i) { AddLoop(polygon->loop(i)); } } void S2PolygonBuilder::EraseEdge(S2Point const& v0, S2Point const& v1) { // Note that there may be more than one copy of an edge if we are not XORing // them, so a VertexSet is a multiset. VertexSet* vset = &(*edges_)[v0]; DCHECK(vset->find(v1) != vset->end()); vset->erase(vset->find(v1)); if (vset->empty()) edges_->erase(v0); if (options_.undirected_edges()) { vset = &(*edges_)[v1]; DCHECK(vset->find(v0) != vset->end()); vset->erase(vset->find(v0)); if (vset->empty()) edges_->erase(v1); } } void S2PolygonBuilder::set_debug_matrix(Matrix3x3_d const& m) { debug_matrix_.reset(new Matrix3x3_d(m)); } void S2PolygonBuilder::DumpVertex(S2Point const& v) const { if (debug_matrix_.get()) { // For orthonormal matrices, Inverse() == Transpose(). cout << S2LatLng(debug_matrix_->Transpose() * v); } else { cout << setprecision(17) << v << setprecision(6); } } void S2PolygonBuilder::DumpEdges(S2Point const& v0) const { DumpVertex(v0); cout << ":\n"; EdgeSet::const_iterator candidates = edges_->find(v0); if (candidates != edges_->end()) { VertexSet const& vset = candidates->second; for (VertexSet::const_iterator i = vset.begin(); i != vset.end(); ++i) { cout << " "; DumpVertex(*i); cout << "\n"; } } } void S2PolygonBuilder::Dump() const { for (EdgeSet::const_iterator i = edges_->begin(); i != edges_->end(); ++i) { DumpEdges(i->first); } } void S2PolygonBuilder::EraseLoop(S2Point const* v, int n) { for (int i = n - 1, j = 0; j < n; i = j++) { EraseEdge(v[i], v[j]); } } void S2PolygonBuilder::RejectLoop(S2Point const* v, int n, EdgeList* unused_edges) { for (int i = n - 1, j = 0; j < n; i = j++) { unused_edges->push_back(make_pair(v[i], v[j])); } } S2Loop* S2PolygonBuilder::AssembleLoop(S2Point const& v0, S2Point const& v1, EdgeList* unused_edges) { // We start at the given edge and assemble a loop taking left turns // whenever possible. We stop the loop as soon as we encounter any // vertex that we have seen before *except* for the first vertex (v0). // This ensures that only CCW loops are constructed when possible. vector path; // The path so far. hash_map index; // Maps a vertex to its index in "path". path.push_back(v0); path.push_back(v1); index[v1] = 1; while (path.size() >= 2) { // Note that "v0" and "v1" become invalid if "path" is modified. S2Point const& v0 = path.end()[-2]; S2Point const& v1 = path.end()[-1]; S2Point v2; bool v2_found = false; EdgeSet::const_iterator candidates = edges_->find(v1); if (candidates != edges_->end()) { VertexSet const& vset = candidates->second; for (VertexSet::const_iterator i = vset.begin(); i != vset.end(); ++i) { // We prefer the leftmost outgoing edge, ignoring any reverse edges. if (*i == v0) continue; if (!v2_found || S2::OrderedCCW(v0, v2, *i, v1)) { v2 = *i; } v2_found = true; } } if (!v2_found) { // We've hit a dead end. Remove this edge and backtrack. unused_edges->push_back(make_pair(v0, v1)); EraseEdge(v0, v1); index.erase(v1); path.pop_back(); } else if (index.insert(make_pair(v2, path.size())).second) { // This is the first time we've visited this vertex. path.push_back(v2); } else { // We've completed a loop. Throw away any initial vertices that // are not part of the loop. path.erase(path.begin(), path.begin() + index[v2]); // In the case of undirected edges, we may have assembled a clockwise // loop while trying to assemble a CCW loop. To fix this, we assemble // a new loop starting with an arbitrary edge in the reverse direction. // This is guaranteed to assemble a loop that is interior to the previous // one and will therefore eventually terminate. S2Loop* loop = new S2Loop(path); if (options_.validate() && !loop->IsValid()) { // We've constructed a loop that crosses itself, which can only // happen if there is bad input data. Throw away the whole loop. RejectLoop(&path[0], path.size(), unused_edges); EraseLoop(&path[0], path.size()); delete loop; return NULL; } if (options_.undirected_edges() && !loop->IsNormalized()) { scoped_ptr deleter(loop); // XXX for debugging return AssembleLoop(path[1], path[0], unused_edges); } return loop; } } return NULL; } class S2PolygonBuilder::PointIndex { // A PointIndex is a cheap spatial index to help us find mergeable // vertices. Given a set of points, it can efficiently find all of the // points within a given search radius of an arbitrary query location. // It is essentially just a hash map from cell ids at a given fixed level to // the set of points contained by that cell id. // // This class is not suitable for general use because it only supports // fixed-radius queries and has various special-purpose operations to avoid // the need for additional data structures. private: typedef multimap Map; Map map_; double vertex_radius_; double edge_fraction_; int level_; vector ids_; // Allocated here for efficiency. public: PointIndex(double vertex_radius, double edge_fraction) : vertex_radius_(vertex_radius), edge_fraction_(edge_fraction), // We compute an S2CellId level such that the vertex neighbors at that // level of any point A are a covering for spherical cap (i.e. "disc") // of the given search radius centered at A. This requires that the // minimum cell width at that level must be twice the search radius. level_(min(S2::kMinWidth.GetMaxLevel(2 * vertex_radius), S2CellId::kMaxLevel - 1)) { // We insert a sentinel so that we don't need to test for map_.end(). map_.insert(make_pair(S2CellId::Sentinel(), S2Point())); } void Insert(S2Point const& p) { S2CellId::FromPoint(p).AppendVertexNeighbors(level_, &ids_); for (int i = ids_.size(); --i >= 0; ) { map_.insert(make_pair(ids_[i], p)); } ids_.clear(); } void Erase(S2Point const& p) { S2CellId::FromPoint(p).AppendVertexNeighbors(level_, &ids_); for (int i = ids_.size(); --i >= 0; ) { Map::iterator j = map_.lower_bound(ids_[i]); for (; j->second != p; ++j) { DCHECK_EQ(ids_[i], j->first); } map_.erase(j); } ids_.clear(); } void QueryCap(S2Point const& axis, vector* output) { // Return the set the points whose distance to "axis" is less than // vertex_radius_. output->clear(); S2CellId id = S2CellId::FromPoint(axis).parent(level_); for (Map::const_iterator i = map_.lower_bound(id); i->first == id; ++i) { S2Point const& p = i->second; if (axis.Angle(p) < vertex_radius_) { output->push_back(p); } } } bool FindNearbyPoint(S2Point const& v0, S2Point const& v1, S2Point* nearby) { // Return a point whose distance from the edge (v0,v1) is less than // vertex_radius_, and which is not equal to v0 or v1. The current // implementation returns the closest such point. // // Strategy: we compute a very cheap covering by approximating the edge as // two spherical caps, one around each endpoint, and then computing a // 4-cell covering of each one. We could improve the quality of the // covering by using some intermediate points along the edge as well. double length = v0.Angle(v1); S2Point normal = S2::RobustCrossProd(v0, v1); int level = min(level_, S2::kMinWidth.GetMaxLevel(length)); S2CellId::FromPoint(v0).AppendVertexNeighbors(level, &ids_); S2CellId::FromPoint(v1).AppendVertexNeighbors(level, &ids_); // Sort the cell ids so that we can skip duplicates in the loop below. sort(ids_.begin(), ids_.end()); double best_dist = 2 * vertex_radius_; for (int i = ids_.size(); --i >= 0; ) { if (i > 0 && ids_[i-1] == ids_[i]) continue; // Skip duplicates. S2CellId const& max_id = ids_[i].range_max(); for (Map::const_iterator j = map_.lower_bound(ids_[i].range_min()); j->first <= max_id; ++j) { S2Point const& p = j->second; if (p == v0 || p == v1) continue; double dist = S2EdgeUtil::GetDistance(p, v0, v1, normal).radians(); if (dist < best_dist) { best_dist = dist; *nearby = p; } } } ids_.clear(); return (best_dist < edge_fraction_ * vertex_radius_); } private: DISALLOW_EVIL_CONSTRUCTORS(PointIndex); }; void S2PolygonBuilder::BuildMergeMap(PointIndex* index, MergeMap* merge_map) { // The overall strategy is to start from each vertex and grow a maximal // cluster of mergeable vertices. In graph theoretic terms, we find the // connected components of the undirected graph whose edges connect pairs of // vertices that are separated by at most vertex_merge_radius(). // // We then choose a single representative vertex for each cluster, and // update "merge_map" appropriately. We choose an arbitrary existing // vertex rather than computing the centroid of all the vertices to avoid // creating new vertex pairs that need to be merged. (We guarantee that all // vertex pairs are separated by at least the merge radius in the output.) // First, we build the set of all the distinct vertices in the input. // We need to include the source and destination of every edge. hash_set vertices; for (EdgeSet::const_iterator i = edges_->begin(); i != edges_->end(); ++i) { vertices.insert(i->first); VertexSet const& vset = i->second; for (VertexSet::const_iterator j = vset.begin(); j != vset.end(); ++j) vertices.insert(*j); } // Build a spatial index containing all the distinct vertices. for (hash_set::const_iterator i = vertices.begin(); i != vertices.end(); ++i) { index->Insert(*i); } // Next, we loop through all the vertices and attempt to grow a maximial // mergeable group starting from each vertex. vector frontier, mergeable; for (hash_set::const_iterator vstart = vertices.begin(); vstart != vertices.end(); ++vstart) { // Skip any vertices that have already been merged with another vertex. if (merge_map->find(*vstart) != merge_map->end()) continue; // Grow a maximal mergeable component starting from "vstart", the // canonical representative of the mergeable group. frontier.push_back(*vstart); while (!frontier.empty()) { index->QueryCap(frontier.back(), &mergeable); frontier.pop_back(); // Do this before entering the loop below. for (int j = mergeable.size(); --j >= 0; ) { S2Point const& v1 = mergeable[j]; if (v1 != *vstart) { // Erase from the index any vertices that will be merged. This // ensures that we won't try to merge the same vertex twice. index->Erase(v1); frontier.push_back(v1); (*merge_map)[v1] = *vstart; } } } } } void S2PolygonBuilder::MoveVertices(MergeMap const& merge_map) { if (merge_map.empty()) return; // We need to copy the set of edges affected by the move, since // edges_ could be reallocated when we start modifying it. vector > edges; for (EdgeSet::const_iterator i = edges_->begin(); i != edges_->end(); ++i) { S2Point const& v0 = i->first; VertexSet const& vset = i->second; for (VertexSet::const_iterator j = vset.begin(); j != vset.end(); ++j) { S2Point const& v1 = *j; if (merge_map.find(v0) != merge_map.end() || merge_map.find(v1) != merge_map.end()) { // We only need to modify one copy of each undirected edge. if (!options_.undirected_edges() || v0 < v1) { edges.push_back(make_pair(v0, v1)); } } } } // Now erase all the old edges, and add all the new edges. This will // automatically take care of any XORing that needs to be done, because // EraseEdge also erases the sibling of undirected edges. for (size_t i = 0; i < edges.size(); ++i) { S2Point v0 = edges[i].first; S2Point v1 = edges[i].second; EraseEdge(v0, v1); MergeMap::const_iterator new0 = merge_map.find(v0); if (new0 != merge_map.end()) v0 = new0->second; MergeMap::const_iterator new1 = merge_map.find(v1); if (new1 != merge_map.end()) v1 = new1->second; AddEdge(v0, v1); } } void S2PolygonBuilder::SpliceEdges(PointIndex* index) { // We keep a stack of unprocessed edges. Initially all edges are // pushed onto the stack. vector > edges; for (EdgeSet::const_iterator i = edges_->begin(); i != edges_->end(); ++i) { S2Point const& v0 = i->first; VertexSet const& vset = i->second; for (VertexSet::const_iterator j = vset.begin(); j != vset.end(); ++j) { S2Point const& v1 = *j; // We only need to modify one copy of each undirected edge. if (!options_.undirected_edges() || v0 < v1) { edges.push_back(make_pair(v0, v1)); } } } // For each edge, we check whether there are any nearby vertices that should // be spliced into it. If there are, we choose one such vertex, split // the edge into two pieces, and iterate on each piece. while (!edges.empty()) { S2Point v0 = edges.back().first; S2Point v1 = edges.back().second; edges.pop_back(); // Do this before pushing new edges. // If we are xoring, edges may be erased before we get to them. if (options_.xor_edges() && !HasEdge(v0, v1)) continue; S2Point vmid; if (!index->FindNearbyPoint(v0, v1, &vmid)) continue; EraseEdge(v0, v1); if (AddEdge(v0, vmid)) edges.push_back(make_pair(v0, vmid)); if (AddEdge(vmid, v1)) edges.push_back(make_pair(vmid, v1)); } } bool S2PolygonBuilder::AssembleLoops(vector* loops, EdgeList* unused_edges) { if (options_.vertex_merge_radius().radians() > 0) { PointIndex index(options_.vertex_merge_radius().radians(), options_.edge_splice_fraction()); MergeMap merge_map; BuildMergeMap(&index, &merge_map); MoveVertices(merge_map); if (options_.edge_splice_fraction() > 0) { SpliceEdges(&index); } } EdgeList dummy_unused_edges; if (unused_edges == NULL) unused_edges = &dummy_unused_edges; // We repeatedly choose an edge and attempt to assemble a loop // starting from that edge. (This is always possible unless the // input includes extra edges that are not part of any loop.) To // maintain a consistent scanning order over edges_ between // different machine architectures (e.g. 'clovertown' vs. 'opteron'), // we follow the order they were added to the builder. unused_edges->clear(); for (size_t i = 0; i < starting_vertices_.size(); ) { S2Point const& v0 = starting_vertices_[i]; EdgeSet::const_iterator candidates = edges_->find(v0); if (candidates == edges_->end()) { ++i; continue; } // NOTE(user): If we have such two S2Points a, b that: // // a.x = b.x, a.y = b.y and // -- a.z = b.z if CPU is Intel // -- a.z <> b.z if CPU is AMD // // then the order of points picked up as v1 on the following line // can be inconsistent between different machine architectures. // // As of b/3088321 and of cl/17847332, it's not clear if such // input really exists in our input and probably it's O.K. not to // address it in favor of the speed. S2Point const& v1 = *(candidates->second.begin()); S2Loop* loop = AssembleLoop(v0, v1, unused_edges); if (loop != NULL) { loops->push_back(loop); EraseLoop(&loop->vertex(0), loop->num_vertices()); } } return unused_edges->empty(); } bool S2PolygonBuilder::AssemblePolygon(S2Polygon* polygon, EdgeList* unused_edges) { vector loops; bool success = AssembleLoops(&loops, unused_edges); // If edges are undirected, then all loops are already CCW. Otherwise we // need to make sure the loops are normalized. if (!options_.undirected_edges()) { for (size_t i = 0; i < loops.size(); ++i) { loops[i]->Normalize(); } } if (options_.validate() && !S2Polygon::IsValid(loops)) { if (unused_edges != NULL) { for (size_t i = 0; i < loops.size(); ++i) { RejectLoop(&loops[i]->vertex(0), loops[i]->num_vertices(), unused_edges); } } for (size_t i = 0; i < loops.size(); ++i) { delete loops[i]; } loops.clear(); return false; } polygon->Init(&loops); return success; }