Use a heap to store traversable polygons for pathfinding

modules/navigation/nav_map.cpp

@@ -221,27 +221,27 @@ Vector<Vector3> NavMap::get_path(Vector3 p_origin, Vector3 p_destination, bool p
 
 	// List of all reachable navigation polys.
 	LocalVector<gd::NavigationPoly> navigation_polys;
-	navigation_polys.reserve(polygons.size() * 0.75);
+	navigation_polys.resize(polygons.size() + link_polygons.size());
 
-	// Add the start polygon to the reachable navigation polygons.
-	gd::NavigationPoly begin_navigation_poly = gd::NavigationPoly(begin_poly);
-	begin_navigation_poly.self_id = 0;
+	// Initialize the matching navigation polygon.
+	gd::NavigationPoly &begin_navigation_poly = navigation_polys[begin_poly->id];
+	begin_navigation_poly.poly = begin_poly;
 	begin_navigation_poly.entry = begin_point;
 	begin_navigation_poly.back_navigation_edge_pathway_start = begin_point;
 	begin_navigation_poly.back_navigation_edge_pathway_end = begin_point;
-	navigation_polys.push_back(begin_navigation_poly);
 
-	// List of polygon IDs to visit.
-	List<uint32_t> to_visit;
-	to_visit.push_back(0);
+	// Heap of polygons to travel next.
+	gd::Heap<gd::NavigationPoly *, gd::NavPolyTravelCostGreaterThan, gd::NavPolyHeapIndexer>
+			traversable_polys;
+	traversable_polys.reserve(polygons.size() * 0.25);
 
 	// This is an implementation of the A* algorithm.
-	int least_cost_id = 0;
+	int least_cost_id = begin_poly->id;
 	int prev_least_cost_id = -1;
 	bool found_route = false;
 
 	const gd::Polygon *reachable_end = nullptr;
-	real_t reachable_d = FLT_MAX;
+	real_t distance_to_reachable_end = FLT_MAX;
 	bool is_reachable = true;
 
 	while (true) {
@@ -260,51 +260,57 @@ Vector<Vector3> NavMap::get_path(Vector3 p_origin, Vector3 p_destination, bool p
 				real_t poly_enter_cost = 0.0;
 				real_t poly_travel_cost = least_cost_poly.poly->owner->get_travel_cost();
 
-				if (prev_least_cost_id != -1 && (navigation_polys[prev_least_cost_id].poly->owner->get_self() != least_cost_poly.poly->owner->get_self())) {
+				if (prev_least_cost_id != -1 && navigation_polys[prev_least_cost_id].poly->owner->get_self() != least_cost_poly.poly->owner->get_self()) {
 					poly_enter_cost = least_cost_poly.poly->owner->get_enter_cost();
 				}
 				prev_least_cost_id = least_cost_id;
 
 				Vector3 pathway[2] = { connection.pathway_start, connection.pathway_end };
 				const Vector3 new_entry = Geometry3D::get_closest_point_to_segment(least_cost_poly.entry, pathway);
-				const real_t new_distance = (least_cost_poly.entry.distance_to(new_entry) * poly_travel_cost) + poly_enter_cost + least_cost_poly.traveled_distance;
-
-				int64_t already_visited_polygon_index = navigation_polys.find(gd::NavigationPoly(connection.polygon));
-
-				if (already_visited_polygon_index != -1) {
-					// Polygon already visited, check if we can reduce the travel cost.
-					gd::NavigationPoly &avp = navigation_polys[already_visited_polygon_index];
-					if (new_distance < avp.traveled_distance) {
-						avp.back_navigation_poly_id = least_cost_id;
-						avp.back_navigation_edge = connection.edge;
-						avp.back_navigation_edge_pathway_start = connection.pathway_start;
-						avp.back_navigation_edge_pathway_end = connection.pathway_end;
-						avp.traveled_distance = new_distance;
-						avp.entry = new_entry;
+				const real_t new_traveled_distance = least_cost_poly.entry.distance_to(new_entry) * poly_travel_cost + poly_enter_cost + least_cost_poly.traveled_distance;
+
+				// Check if the neighbor polygon has already been processed.
+				gd::NavigationPoly &neighbor_poly = navigation_polys[connection.polygon->id];
+				if (neighbor_poly.poly != nullptr) {
+					// If the neighbor polygon hasn't been traversed yet and the new path leading to
+					// it is shorter, update the polygon.
+					if (neighbor_poly.traversable_poly_index < traversable_polys.size() &&
+							new_traveled_distance < neighbor_poly.traveled_distance) {
+						neighbor_poly.back_navigation_poly_id = least_cost_id;
+						neighbor_poly.back_navigation_edge = connection.edge;
+						neighbor_poly.back_navigation_edge_pathway_start = connection.pathway_start;
+						neighbor_poly.back_navigation_edge_pathway_end = connection.pathway_end;
+						neighbor_poly.traveled_distance = new_traveled_distance;
+						neighbor_poly.distance_to_destination =
+								new_entry.distance_to(end_point) *
+								neighbor_poly.poly->owner->get_travel_cost();
+						neighbor_poly.entry = new_entry;
+
+						// Update the priority of the polygon in the heap.
+						traversable_polys.shift(neighbor_poly.traversable_poly_index);
 					}
 				} else {
-					// Add the neighbor polygon to the reachable ones.
-					gd::NavigationPoly new_navigation_poly = gd::NavigationPoly(connection.polygon);
-					new_navigation_poly.self_id = navigation_polys.size();
-					new_navigation_poly.back_navigation_poly_id = least_cost_id;
-					new_navigation_poly.back_navigation_edge = connection.edge;
-					new_navigation_poly.back_navigation_edge_pathway_start = connection.pathway_start;
-					new_navigation_poly.back_navigation_edge_pathway_end = connection.pathway_end;
-					new_navigation_poly.traveled_distance = new_distance;
-					new_navigation_poly.entry = new_entry;
-					navigation_polys.push_back(new_navigation_poly);
-
-					// Add the neighbor polygon to the polygons to visit.
-					to_visit.push_back(navigation_polys.size() - 1);
+					// Initialize the matching navigation polygon.
+					neighbor_poly.poly = connection.polygon;
+					neighbor_poly.back_navigation_poly_id = least_cost_id;
+					neighbor_poly.back_navigation_edge = connection.edge;
+					neighbor_poly.back_navigation_edge_pathway_start = connection.pathway_start;
+					neighbor_poly.back_navigation_edge_pathway_end = connection.pathway_end;
+					neighbor_poly.traveled_distance = new_traveled_distance;
+					neighbor_poly.distance_to_destination =
+							new_entry.distance_to(end_point) *
+							neighbor_poly.poly->owner->get_travel_cost();
+					neighbor_poly.entry = new_entry;
+
+					// Add the polygon to the heap of polygons to traverse next.
+					traversable_polys.push(&neighbor_poly);
 				}
 			}
 		}
 
-		// Removes the least cost polygon from the list of polygons to visit so we can advance.
-		to_visit.erase(least_cost_id);
-
-		// When the list of polygons to visit is empty at this point it means the End Polygon is not reachable
-		if (to_visit.size() == 0) {
+		// When the heap of traversable polygons is empty at this point it means the end polygon is
+		// unreachable.
+		if (traversable_polys.is_empty()) {
 			// Thus use the further reachable polygon
 			ERR_BREAK_MSG(is_reachable == false, "It's not expect to not find the most reachable polygons");
 			is_reachable = false;
@@ -366,13 +372,12 @@ Vector<Vector3> NavMap::get_path(Vector3 p_origin, Vector3 p_destination, bool p
 				return path;
 			}
 
-			// Reset open and navigation_polys
-			gd::NavigationPoly np = navigation_polys[0];
-			navigation_polys.clear();
-			navigation_polys.push_back(np);
-			to_visit.clear();
-			to_visit.push_back(0);
-			least_cost_id = 0;
+			for (gd::NavigationPoly &nav_poly : navigation_polys) {
+				nav_poly.poly = nullptr;
+			}
+			navigation_polys[begin_poly->id].poly = begin_poly;
+
+			least_cost_id = begin_poly->id;
 			prev_least_cost_id = -1;
 
 			reachable_end = nullptr;
@@ -380,26 +385,14 @@ Vector<Vector3> NavMap::get_path(Vector3 p_origin, Vector3 p_destination, bool p
 			continue;
 		}
 
-		// Find the polygon with the minimum cost from the list of polygons to visit.
-		least_cost_id = -1;
-		real_t least_cost = FLT_MAX;
-		for (List<uint32_t>::Element *element = to_visit.front(); element != nullptr; element = element->next()) {
-			gd::NavigationPoly *np = &navigation_polys[element->get()];
-			real_t cost = np->traveled_distance;
-			cost += (np->entry.distance_to(end_point) * np->poly->owner->get_travel_cost());
-			if (cost < least_cost) {
-				least_cost_id = np->self_id;
-				least_cost = cost;
-			}
-		}
-
-		ERR_BREAK(least_cost_id == -1);
+		// Pop the polygon with the lowest travel cost from the heap of traversable polygons.
+		least_cost_id = traversable_polys.pop()->poly->id;
 
-		// Stores the further reachable end polygon, in case our goal is not reachable.
+		// Store the farthest reachable end polygon in case our goal is not reachable.
 		if (is_reachable) {
-			real_t d = navigation_polys[least_cost_id].entry.distance_to(p_destination);
-			if (reachable_d > d) {
-				reachable_d = d;
+			real_t distance = navigation_polys[least_cost_id].entry.distance_to(p_destination);
+			if (distance_to_reachable_end > distance) {
+				distance_to_reachable_end = distance;
 				reachable_end = navigation_polys[least_cost_id].poly;
 			}
 		}
@@ -943,29 +936,30 @@ void NavMap::sync() {
 		}
 
 		// Resize the polygon count.
-		int count = 0;
+		int polygon_count = 0;
 		for (const NavRegion *region : regions) {
 			if (!region->get_enabled()) {
 				continue;
 			}
-			count += region->get_polygons().size();
+			polygon_count += region->get_polygons().size();
 		}
-		polygons.resize(count);
+		polygons.resize(polygon_count);
 
 		// Copy all region polygons in the map.
-		count = 0;
+		polygon_count = 0;
 		for (const NavRegion *region : regions) {
 			if (!region->get_enabled()) {
 				continue;
 			}
 			const LocalVector<gd::Polygon> &polygons_source = region->get_polygons();
 			for (uint32_t n = 0; n < polygons_source.size(); n++) {
-				polygons[count + n] = polygons_source[n];
+				polygons[polygon_count] = polygons_source[n];
+				polygons[polygon_count].id = polygon_count;
+				polygon_count++;
 			}
-			count += region->get_polygons().size();
 		}
 
-		_new_pm_polygon_count = polygons.size();
+		_new_pm_polygon_count = polygon_count;
 
 		// Group all edges per key.
 		HashMap<gd::EdgeKey, Vector<gd::Edge::Connection>, gd::EdgeKey> connections;
@@ -1136,6 +1130,7 @@ void NavMap::sync() {
 			// If we have both a start and end point, then create a synthetic polygon to route through.
 			if (closest_start_polygon && closest_end_polygon) {
 				gd::Polygon &new_polygon = link_polygons[link_poly_idx++];
+				new_polygon.id = polygon_count++;
 				new_polygon.owner = link;
 
 				new_polygon.edges.clear();

modules/navigation/nav_utils.h

@@ -98,6 +98,9 @@ struct Edge {
 };
 
 struct Polygon {
+	/// Id of the polygon in the map.
+	uint32_t id = UINT32_MAX;
+
 	/// Navigation region or link that contains this polygon.
 	const NavBase *owner = nullptr;
 
@@ -111,9 +114,11 @@ struct Polygon {
 };
 
 struct NavigationPoly {
-	uint32_t self_id = 0;
 	/// This poly.
-	const Polygon *poly;
+	const Polygon *poly = nullptr;
+
+	/// Index in the heap of traversable polygons.
+	uint32_t traversable_poly_index = UINT32_MAX;
 
 	/// Those 4 variables are used to travel the path backwards.
 	int back_navigation_poly_id = -1;
@@ -123,20 +128,44 @@ struct NavigationPoly {
 
 	/// The entry position of this poly.
 	Vector3 entry;
-	/// The distance to the destination.
+	/// The distance traveled until now (g cost).
 	real_t traveled_distance = 0.0;
+	/// The distance to the destination (h cost).
+	real_t distance_to_destination = 0.0;
 
-	NavigationPoly() { poly = nullptr; }
+	/// The total travel cost (f cost).
+	real_t total_travel_cost() const {
+		return traveled_distance + distance_to_destination;
+	}
 
-	NavigationPoly(const Polygon *p_poly) :
-			poly(p_poly) {}
+	bool operator==(const NavigationPoly &p_other) const {
+		return poly == p_other.poly;
+	}
 
-	bool operator==(const NavigationPoly &other) const {
-		return poly == other.poly;
+	bool operator!=(const NavigationPoly &p_other) const {
+		return !(*this == p_other);
 	}
+};
+
+struct NavPolyTravelCostGreaterThan {
+	// Returns `true` if the travel cost of `a` is higher than that of `b`.
+	bool operator()(const NavigationPoly *p_poly_a, const NavigationPoly *p_poly_b) const {
+		real_t f_cost_a = p_poly_a->total_travel_cost();
+		real_t h_cost_a = p_poly_a->distance_to_destination;
+		real_t f_cost_b = p_poly_b->total_travel_cost();
+		real_t h_cost_b = p_poly_b->distance_to_destination;
 
-	bool operator!=(const NavigationPoly &other) const {
-		return !operator==(other);
+		if (f_cost_a != f_cost_b) {
+			return f_cost_a > f_cost_b;
+		} else {
+			return h_cost_a > h_cost_b;
+		}
+	}
+};
+
+struct NavPolyHeapIndexer {
+	void operator()(NavigationPoly *p_poly, uint32_t p_heap_index) const {
+		p_poly->traversable_poly_index = p_heap_index;
 	}
 };
 
@@ -146,6 +175,129 @@ struct ClosestPointQueryResult {
 	RID owner;
 };
 
+template <typename T>
+struct NoopIndexer {
+	void operator()(const T &p_value, uint32_t p_index) {}
+};
+
+/**
+ * A max-heap implementation that notifies of element index changes.
+ */
+template <typename T, typename LessThan = Comparator<T>, typename Indexer = NoopIndexer<T>>
+class Heap {
+	LocalVector<T> _buffer;
+
+	LessThan _less_than;
+	Indexer _indexer;
+
+public:
+	void reserve(uint32_t p_size) {
+		_buffer.reserve(p_size);
+	}
+
+	uint32_t size() const {
+		return _buffer.size();
+	}
+
+	bool is_empty() const {
+		return _buffer.is_empty();
+	}
+
+	void push(const T &p_element) {
+		_buffer.push_back(p_element);
+		_indexer(p_element, _buffer.size() - 1);
+		_shift_up(_buffer.size() - 1);
+	}
+
+	T pop() {
+		ERR_FAIL_COND_V_MSG(_buffer.is_empty(), T(), "Can't pop an empty heap.");
+		T value = _buffer[0];
+		_indexer(value, UINT32_MAX);
+		if (_buffer.size() > 1) {
+			_buffer[0] = _buffer[_buffer.size() - 1];
+			_indexer(_buffer[0], 0);
+			_buffer.remove_at(_buffer.size() - 1);
+			_shift_down(0);
+		} else {
+			_buffer.remove_at(_buffer.size() - 1);
+		}
+		return value;
+	}
+
+	/**
+	 * Update the position of the element in the heap if necessary.
+	 */
+	void shift(uint32_t p_index) {
+		ERR_FAIL_UNSIGNED_INDEX_MSG(p_index, _buffer.size(), "Heap element index is out of range.");
+		if (!_shift_up(p_index)) {
+			_shift_down(p_index);
+		}
+	}
+
+	void clear() {
+		for (const T &value : _buffer) {
+			_indexer(value, UINT32_MAX);
+		}
+		_buffer.clear();
+	}
+
+	Heap() {}
+
+	Heap(const LessThan &p_less_than) :
+			_less_than(p_less_than) {}
+
+	Heap(const Indexer &p_indexer) :
+			_indexer(p_indexer) {}
+
+	Heap(const LessThan &p_less_than, const Indexer &p_indexer) :
+			_less_than(p_less_than), _indexer(p_indexer) {}
+
+private:
+	bool _shift_up(uint32_t p_index) {
+		T value = _buffer[p_index];
+		uint32_t current_index = p_index;
+		uint32_t parent_index = (current_index - 1) / 2;
+		while (current_index > 0 && _less_than(_buffer[parent_index], value)) {
+			_buffer[current_index] = _buffer[parent_index];
+			_indexer(_buffer[current_index], current_index);
+			current_index = parent_index;
+			parent_index = (current_index - 1) / 2;
+		}
+		if (current_index != p_index) {
+			_buffer[current_index] = value;
+			_indexer(value, current_index);
+			return true;
+		} else {
+			return false;
+		}
+	}
+
+	bool _shift_down(uint32_t p_index) {
+		T value = _buffer[p_index];
+		uint32_t current_index = p_index;
+		uint32_t child_index = 2 * current_index + 1;
+		while (child_index < _buffer.size()) {
+			if (child_index + 1 < _buffer.size() &&
+					_less_than(_buffer[child_index], _buffer[child_index + 1])) {
+				child_index++;
+			}
+			if (_less_than(_buffer[child_index], value)) {
+				break;
+			}
+			_buffer[current_index] = _buffer[child_index];
+			_indexer(_buffer[current_index], current_index);
+			current_index = child_index;
+			child_index = 2 * current_index + 1;
+		}
+		if (current_index != p_index) {
+			_buffer[current_index] = value;
+			_indexer(value, current_index);
+			return true;
+		} else {
+			return false;
+		}
+	}
+};
 } // namespace gd
 
 #endif // NAV_UTILS_H

tests/servers/test_navigation_server_3d.h

@@ -31,6 +31,7 @@
 #ifndef TEST_NAVIGATION_SERVER_3D_H
 #define TEST_NAVIGATION_SERVER_3D_H
 
+#include "modules/navigation/nav_utils.h"
 #include "scene/3d/mesh_instance_3d.h"
 #include "scene/resources/3d/primitive_meshes.h"
 #include "servers/navigation_server_3d.h"
@@ -61,6 +62,32 @@ static inline Array build_array(Variant item, Targs... Fargs) {
 	return a;
 }
 
+struct GreaterThan {
+	bool operator()(int p_a, int p_b) const { return p_a > p_b; }
+};
+
+struct CompareArrayValues {
+	const int *array;
+
+	CompareArrayValues(const int *p_array) :
+			array(p_array) {}
+
+	bool operator()(uint32_t p_index_a, uint32_t p_index_b) const {
+		return array[p_index_a] < array[p_index_b];
+	}
+};
+
+struct RegisterHeapIndexes {
+	uint32_t *indexes;
+
+	RegisterHeapIndexes(uint32_t *p_indexes) :
+			indexes(p_indexes) {}
+
+	void operator()(uint32_t p_vector_index, uint32_t p_heap_index) {
+		indexes[p_vector_index] = p_heap_index;
+	}
+};
+
 TEST_SUITE("[Navigation]") {
 	TEST_CASE("[NavigationServer3D] Server should be empty when initialized") {
 		NavigationServer3D *navigation_server = NavigationServer3D::get_singleton();
@@ -788,6 +815,139 @@ TEST_SUITE("[Navigation]") {
 		CHECK_EQ(navigation_mesh->get_vertices().size(), 0);
 	}
 	*/
+
+	TEST_CASE("[Heap] size") {
+		gd::Heap<int> heap;
+
+		CHECK(heap.size() == 0);
+
+		heap.push(0);
+		CHECK(heap.size() == 1);
+
+		heap.push(1);
+		CHECK(heap.size() == 2);
+
+		heap.pop();
+		CHECK(heap.size() == 1);
+
+		heap.pop();
+		CHECK(heap.size() == 0);
+	}
+
+	TEST_CASE("[Heap] is_empty") {
+		gd::Heap<int> heap;
+
+		CHECK(heap.is_empty() == true);
+
+		heap.push(0);
+		CHECK(heap.is_empty() == false);
+
+		heap.pop();
+		CHECK(heap.is_empty() == true);
+	}
+
+	TEST_CASE("[Heap] push/pop") {
+		SUBCASE("Default comparator") {
+			gd::Heap<int> heap;
+
+			heap.push(2);
+			heap.push(7);
+			heap.push(5);
+			heap.push(3);
+			heap.push(4);
+
+			CHECK(heap.pop() == 7);
+			CHECK(heap.pop() == 5);
+			CHECK(heap.pop() == 4);
+			CHECK(heap.pop() == 3);
+			CHECK(heap.pop() == 2);
+		}
+
+		SUBCASE("Custom comparator") {
+			GreaterThan greaterThan;
+			gd::Heap<int, GreaterThan> heap(greaterThan);
+
+			heap.push(2);
+			heap.push(7);
+			heap.push(5);
+			heap.push(3);
+			heap.push(4);
+
+			CHECK(heap.pop() == 2);
+			CHECK(heap.pop() == 3);
+			CHECK(heap.pop() == 4);
+			CHECK(heap.pop() == 5);
+			CHECK(heap.pop() == 7);
+		}
+
+		SUBCASE("Intermediate pops") {
+			gd::Heap<int> heap;
+
+			heap.push(0);
+			heap.push(3);
+			heap.pop();
+			heap.push(1);
+			heap.push(2);
+
+			CHECK(heap.pop() == 2);
+			CHECK(heap.pop() == 1);
+			CHECK(heap.pop() == 0);
+		}
+	}
+
+	TEST_CASE("[Heap] shift") {
+		int values[] = { 5, 3, 6, 7, 1 };
+		uint32_t heap_indexes[] = { 0, 0, 0, 0, 0 };
+		CompareArrayValues comparator(values);
+		RegisterHeapIndexes indexer(heap_indexes);
+		gd::Heap<uint32_t, CompareArrayValues, RegisterHeapIndexes> heap(comparator, indexer);
+
+		heap.push(0);
+		heap.push(1);
+		heap.push(2);
+		heap.push(3);
+		heap.push(4);
+
+		// Shift down: 6 -> 2
+		values[2] = 2;
+		heap.shift(heap_indexes[2]);
+
+		// Shift up: 5 -> 8
+		values[0] = 8;
+		heap.shift(heap_indexes[0]);
+
+		CHECK(heap.pop() == 0);
+		CHECK(heap.pop() == 3);
+		CHECK(heap.pop() == 1);
+		CHECK(heap.pop() == 2);
+		CHECK(heap.pop() == 4);
+
+		CHECK(heap_indexes[0] == UINT32_MAX);
+		CHECK(heap_indexes[1] == UINT32_MAX);
+		CHECK(heap_indexes[2] == UINT32_MAX);
+		CHECK(heap_indexes[3] == UINT32_MAX);
+		CHECK(heap_indexes[4] == UINT32_MAX);
+	}
+
+	TEST_CASE("[Heap] clear") {
+		uint32_t heap_indexes[] = { 0, 0, 0, 0 };
+		RegisterHeapIndexes indexer(heap_indexes);
+		gd::Heap<uint32_t, Comparator<uint32_t>, RegisterHeapIndexes> heap(indexer);
+
+		heap.push(0);
+		heap.push(2);
+		heap.push(1);
+		heap.push(3);
+
+		heap.clear();
+
+		CHECK(heap.size() == 0);
+
+		CHECK(heap_indexes[0] == UINT32_MAX);
+		CHECK(heap_indexes[1] == UINT32_MAX);
+		CHECK(heap_indexes[2] == UINT32_MAX);
+		CHECK(heap_indexes[3] == UINT32_MAX);
+	}
 }
 } //namespace TestNavigationServer3D