#pragma warning disable 414 using System.Collections.Generic; using UnityEngine; namespace Pathfinding { public enum HeuristicOptimizationMode { None, Random, RandomSpreadOut, Custom } /// /// Implements heuristic optimizations. /// /// See: heuristic-opt /// See: Game AI Pro - Pathfinding Architecture Optimizations by Steve Rabin and Nathan R. Sturtevant /// [System.Serializable] public class EuclideanEmbedding { /// /// If heuristic optimization should be used and how to place the pivot points. /// See: heuristic-opt /// See: Game AI Pro - Pathfinding Architecture Optimizations by Steve Rabin and Nathan R. Sturtevant /// public HeuristicOptimizationMode mode; public int seed; /// All children of this transform will be used as pivot points public Transform pivotPointRoot; public int spreadOutCount = 1; [System.NonSerialized] public bool dirty; /// /// Costs laid out as n*[int],n*[int],n*[int] where n is the number of pivot points. /// Each node has n integers which is the cost from that node to the pivot node. /// They are at around the same place in the array for simplicity and for cache locality. /// /// cost(nodeIndex, pivotIndex) = costs[nodeIndex*pivotCount+pivotIndex] /// uint[] costs = new uint[8]; int maxNodeIndex; int pivotCount; GraphNode[] pivots; /* * Seed for random number generator. * Must not be zero */ const uint ra = 12820163; /* * Seed for random number generator. * Must not be zero */ const uint rc = 1140671485; /* * Parameter for random number generator. */ uint rval; System.Object lockObj = new object(); /// /// Simple linear congruential generator. /// See: http://en.wikipedia.org/wiki/Linear_congruential_generator /// uint GetRandom () { rval = (ra*rval + rc); return rval; } void EnsureCapacity (int index) { if (index > maxNodeIndex) { lock (lockObj) { if (index > maxNodeIndex) { if (index >= costs.Length) { var newCosts = new uint[System.Math.Max(index*2, pivots.Length*2)]; for (int i = 0; i < costs.Length; i++) newCosts[i] = costs[i]; costs = newCosts; } maxNodeIndex = index; } } } } public uint GetHeuristic (int nodeIndex1, int nodeIndex2) { nodeIndex1 *= pivotCount; nodeIndex2 *= pivotCount; if (nodeIndex1 >= costs.Length || nodeIndex2 >= costs.Length) { EnsureCapacity(nodeIndex1 > nodeIndex2 ? nodeIndex1 : nodeIndex2); } uint mx = 0; for (int i = 0; i < pivotCount; i++) { uint d = (uint)System.Math.Abs((int)costs[nodeIndex1+i] - (int)costs[nodeIndex2+i]); if (d > mx) mx = d; } return mx; } void GetClosestWalkableNodesToChildrenRecursively (Transform tr, List nodes) { foreach (Transform ch in tr) { var info = AstarPath.active.GetNearest(ch.position, NNConstraint.Default); if (info.node != null && info.node.Walkable) { nodes.Add(info.node); } GetClosestWalkableNodesToChildrenRecursively(ch, nodes); } } /// /// Pick N random walkable nodes from all nodes in all graphs and add them to the buffer. /// /// Here we select N random nodes from a stream of nodes. /// Probability of choosing the first N nodes is 1 /// Probability of choosing node i is min(N/i,1) /// A selected node will replace a random node of the previously /// selected ones. /// /// See: https://en.wikipedia.org/wiki/Reservoir_sampling /// void PickNRandomNodes (int count, List buffer) { int n = 0; var graphs = AstarPath.active.graphs; // Loop through all graphs for (int j = 0; j < graphs.Length; j++) { // Loop through all nodes in the graph graphs[j].GetNodes(node => { if (!node.Destroyed && node.Walkable) { n++; if ((GetRandom() % n) < count) { if (buffer.Count < count) { buffer.Add(node); } else { buffer[(int)(GetRandom()%buffer.Count)] = node; } } } }); } } GraphNode PickAnyWalkableNode () { var graphs = AstarPath.active.graphs; GraphNode first = null; // Find any node in the graphs for (int j = 0; j < graphs.Length; j++) { graphs[j].GetNodes(node => { if (node != null && node.Walkable && first == null) { first = node; } }); } return first; } public void RecalculatePivots () { if (mode == HeuristicOptimizationMode.None) { pivotCount = 0; pivots = null; return; } // Reset the random number generator rval = (uint)seed; // Get a List from a pool var pivotList = Pathfinding.Util.ListPool.Claim(); switch (mode) { case HeuristicOptimizationMode.Custom: if (pivotPointRoot == null) throw new System.Exception("heuristicOptimizationMode is HeuristicOptimizationMode.Custom, " + "but no 'customHeuristicOptimizationPivotsRoot' is set"); GetClosestWalkableNodesToChildrenRecursively(pivotPointRoot, pivotList); break; case HeuristicOptimizationMode.Random: PickNRandomNodes(spreadOutCount, pivotList); break; case HeuristicOptimizationMode.RandomSpreadOut: if (pivotPointRoot != null) { GetClosestWalkableNodesToChildrenRecursively(pivotPointRoot, pivotList); } // If no pivot points were found, fall back to picking arbitrary nodes if (pivotList.Count == 0) { GraphNode first = PickAnyWalkableNode(); if (first != null) { pivotList.Add(first); } else { Debug.LogError("Could not find any walkable node in any of the graphs."); Pathfinding.Util.ListPool.Release(ref pivotList); return; } } // Fill remaining slots with null int toFill = spreadOutCount - pivotList.Count; for (int i = 0; i < toFill; i++) pivotList.Add(null); break; default: throw new System.Exception("Invalid HeuristicOptimizationMode: " + mode); } pivots = pivotList.ToArray(); Pathfinding.Util.ListPool.Release(ref pivotList); } public void RecalculateCosts () { if (pivots == null) RecalculatePivots(); if (mode == HeuristicOptimizationMode.None) return; pivotCount = 0; for (int i = 0; i < pivots.Length; i++) { if (pivots[i] != null && (pivots[i].Destroyed || !pivots[i].Walkable)) { throw new System.Exception("Invalid pivot nodes (destroyed or unwalkable)"); } } if (mode != HeuristicOptimizationMode.RandomSpreadOut) for (int i = 0; i < pivots.Length; i++) if (pivots[i] == null) throw new System.Exception("Invalid pivot nodes (null)"); Debug.Log("Recalculating costs..."); pivotCount = pivots.Length; System.Action startCostCalculation = null; int numComplete = 0; OnPathDelegate onComplete = (Path path) => { numComplete++; if (numComplete == pivotCount) { // Last completed path ApplyGridGraphEndpointSpecialCase(); } }; startCostCalculation = (int pivotIndex) => { GraphNode pivot = pivots[pivotIndex]; FloodPath floodPath = null; floodPath = FloodPath.Construct(pivot, onComplete); floodPath.immediateCallback = (Path _p) => { // Handle path pooling _p.Claim(this); // When paths are calculated on navmesh based graphs // the costs are slightly modified to match the actual target and start points // instead of the node centers // so we have to remove the cost for the first and last connection // in each path var meshNode = pivot as MeshNode; uint costOffset = 0; if (meshNode != null && meshNode.connections != null) { for (int i = 0; i < meshNode.connections.Length; i++) { costOffset = System.Math.Max(costOffset, meshNode.connections[i].cost); } } var graphs = AstarPath.active.graphs; // Process graphs in reverse order to raise probability that we encounter large NodeIndex values quicker // to avoid resizing the internal array too often for (int j = graphs.Length-1; j >= 0; j--) { graphs[j].GetNodes(node => { int idx = node.NodeIndex*pivotCount + pivotIndex; EnsureCapacity(idx); PathNode pn = ((IPathInternals)floodPath).PathHandler.GetPathNode(node); if (costOffset > 0) { costs[idx] = pn.pathID == floodPath.pathID && pn.parent != null ? System.Math.Max(pn.parent.G-costOffset, 0) : 0; } else { costs[idx] = pn.pathID == floodPath.pathID ? pn.G : 0; } }); } if (mode == HeuristicOptimizationMode.RandomSpreadOut && pivotIndex < pivots.Length-1) { // If the next pivot is null // then find the node which is furthest away from the earlier // pivot points if (pivots[pivotIndex+1] == null) { int best = -1; uint bestScore = 0; // Actual number of nodes int totCount = maxNodeIndex/pivotCount; // Loop through all nodes for (int j = 1; j < totCount; j++) { // Find the minimum distance from the node to all existing pivot points uint mx = 1 << 30; for (int p = 0; p <= pivotIndex; p++) mx = System.Math.Min(mx, costs[j*pivotCount + p]); // Pick the node which has the largest minimum distance to the existing pivot points // (i.e pick the one furthest away from the existing ones) GraphNode node = ((IPathInternals)floodPath).PathHandler.GetPathNode(j).node; if ((mx > bestScore || best == -1) && node != null && !node.Destroyed && node.Walkable) { best = j; bestScore = mx; } } if (best == -1) { Debug.LogError("Failed generating random pivot points for heuristic optimizations"); return; } pivots[pivotIndex+1] = ((IPathInternals)floodPath).PathHandler.GetPathNode(best).node; } // Start next path startCostCalculation(pivotIndex+1); } // Handle path pooling _p.Release(this); }; AstarPath.StartPath(floodPath, true); }; if (mode != HeuristicOptimizationMode.RandomSpreadOut) { // All calculated in parallel for (int i = 0; i < pivots.Length; i++) { startCostCalculation(i); } } else { // Recursive and serial startCostCalculation(0); } dirty = false; } /// /// Special case necessary for paths to unwalkable nodes right next to walkable nodes to be able to use good heuristics. /// /// This will find all unwalkable nodes in all grid graphs with walkable nodes as neighbours /// and set the cost to reach them from each of the pivots as the minimum of the cost to /// reach the neighbours of each node. /// /// See: ABPath.EndPointGridGraphSpecialCase /// void ApplyGridGraphEndpointSpecialCase () { #if !ASTAR_NO_GRID_GRAPH var graphs = AstarPath.active.graphs; for (int i = 0; i < graphs.Length; i++) { var gg = graphs[i] as GridGraph; if (gg != null) { // Found a grid graph var nodes = gg.nodes; // Number of neighbours as an int int mxnum = gg.neighbours == NumNeighbours.Four ? 4 : (gg.neighbours == NumNeighbours.Eight ? 8 : 6); for (int z = 0; z < gg.depth; z++) { for (int x = 0; x < gg.width; x++) { var node = nodes[z*gg.width + x]; if (!node.Walkable) { var pivotIndex = node.NodeIndex*pivotCount; // Set all costs to reach this node to maximum for (int piv = 0; piv < pivotCount; piv++) { costs[pivotIndex + piv] = uint.MaxValue; } // Loop through all potential neighbours of the node // and set the cost to reach it as the minimum // of the costs to reach any of the adjacent nodes for (int d = 0; d < mxnum; d++) { int nx, nz; if (gg.neighbours == NumNeighbours.Six) { // Hexagon graph nx = x + gg.neighbourXOffsets[GridGraph.hexagonNeighbourIndices[d]]; nz = z + gg.neighbourZOffsets[GridGraph.hexagonNeighbourIndices[d]]; } else { nx = x + gg.neighbourXOffsets[d]; nz = z + gg.neighbourZOffsets[d]; } // Check if the position is still inside the grid if (nx >= 0 && nz >= 0 && nx < gg.width && nz < gg.depth) { var adjacentNode = gg.nodes[nz*gg.width + nx]; if (adjacentNode.Walkable) { for (int piv = 0; piv < pivotCount; piv++) { uint cost = costs[adjacentNode.NodeIndex*pivotCount + piv] + gg.neighbourCosts[d]; costs[pivotIndex + piv] = System.Math.Min(costs[pivotIndex + piv], cost); //Debug.DrawLine((Vector3)node.position, (Vector3)adjacentNode.position, Color.blue, 1); } } } } // If no adjacent nodes were found // set the cost to reach it back to zero for (int piv = 0; piv < pivotCount; piv++) { if (costs[pivotIndex + piv] == uint.MaxValue) { costs[pivotIndex + piv] = 0; } } } } } } } #endif } public void OnDrawGizmos () { if (pivots != null) { for (int i = 0; i < pivots.Length; i++) { Gizmos.color = new Color(159/255.0f, 94/255.0f, 194/255.0f, 0.8f); if (pivots[i] != null && !pivots[i].Destroyed) { Gizmos.DrawCube((Vector3)pivots[i].position, Vector3.one); } } } } } }