/* Copyright (C) 2010 Wildfire Games. * This file is part of 0 A.D. * * 0 A.D. is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 2 of the License, or * (at your option) any later version. * * 0 A.D. is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with 0 A.D. If not, see . */ #include "precompiled.h" #include "simulation2/system/Component.h" #include "ICmpPathfinder.h" #include "simulation2/MessageTypes.h" #include "graphics/Terrain.h" #include "maths/FixedVector2D.h" #include "maths/MathUtil.h" #include "ps/Overlay.h" #include "ps/Profile.h" #include "renderer/TerrainOverlay.h" class CCmpPathfinder; struct PathfindTile; // Basic 2D array, for storing tile data // (TODO: Maybe this could use a more cache-friendly data layout or something?) template class Grid { public: Grid(u16 w, u16 h) : m_W(w), m_H(h) { m_Data = new T[m_W * m_H]; reset(); } ~Grid() { delete[] m_Data; } void reset() { memset(m_Data, 0, m_W*m_H*sizeof(T)); } void set(size_t i, size_t j, const T& value) { debug_assert(i < m_W && j < m_H); m_Data[j*m_W + i] = value; } T& get(size_t i, size_t j) { debug_assert(i < m_W && j < m_H); return m_Data[j*m_W + i]; } u16 m_W, m_H; T* m_Data; }; // Externally, tags are opaque non-zero positive integers // Internally, they are tagged (by shape) indexes into shape lists #define TAG_IS_CIRCLE(tag) (((tag) & 1) == 0) #define TAG_IS_SQUARE(tag) (((tag) & 1) == 1) #define CIRCLE_INDEX_TO_TAG(idx) ((((idx)+1) << 1) | 0) #define SQUARE_INDEX_TO_TAG(idx) ((((idx)+1) << 1) | 1) #define TAG_TO_INDEX(tag) (((tag) >> 1)-1) /** * Internal representation of circle shapes */ struct Circle { entity_pos_t x, z, r; }; /** * Internal representation of square shapes */ struct Square { entity_pos_t x, z; entity_angle_t a; entity_pos_t w, h; }; /** * Terrain overlay for pathfinder debugging. * Renders a representation of the most recent pathfinding operation. */ class PathfinderOverlay : public TerrainOverlay { NONCOPYABLE(PathfinderOverlay); public: CCmpPathfinder& m_Pathfinder; PathfinderOverlay(CCmpPathfinder& pathfinder) : m_Pathfinder(pathfinder) { } virtual void EndRender(); virtual void ProcessTile(ssize_t i, ssize_t j); }; /** * Implementation of ICmpPathfinder */ class CCmpPathfinder : public ICmpPathfinder { public: static void ClassInit(CComponentManager& UNUSED(componentManager)) { } DEFAULT_COMPONENT_ALLOCATOR(Pathfinder) const CSimContext* m_Context; bool m_GridDirty; // whether m_Grid is invalid u16 m_MapSize; // tiles per side Grid* m_Grid; // terrain/passability information // Debugging - output from last pathfind operation: Grid* m_DebugGrid; u32 m_DebugSteps; Path* m_DebugPath; PathfinderOverlay* m_DebugOverlay; // TODO: using std::map is stupid and inefficient std::map m_Circles; std::map m_Squares; virtual void Init(const CSimContext& context, const CParamNode& UNUSED(paramNode)) { m_Context = &context; m_GridDirty = true; m_MapSize = 0; m_Grid = NULL; m_DebugOverlay = new PathfinderOverlay(*this); m_DebugGrid = NULL; m_DebugPath = NULL; } virtual void Deinit(const CSimContext& UNUSED(context)) { delete m_Grid; delete m_DebugOverlay; delete m_DebugGrid; delete m_DebugPath; } virtual void Serialize(ISerializer& serialize) { // TODO: do something here // (Do we need to serialise the pathfinder state, or is it fine to regenerate it from // the original entities after deserialisation?) } virtual void Deserialize(const CSimContext& context, const CParamNode& paramNode, IDeserializer& deserialize) { Init(context, paramNode); // TODO } virtual tag_t AddCircle(entity_pos_t x, entity_pos_t z, entity_pos_t r) { Circle c = { x, z, r }; size_t id = m_Circles.size(); m_Circles[id] = c; m_GridDirty = true; return CIRCLE_INDEX_TO_TAG(id); } virtual tag_t AddSquare(entity_pos_t x, entity_pos_t z, entity_angle_t a, entity_pos_t w, entity_pos_t h) { Square s = { x, z, a, w, h }; size_t id = m_Squares.size(); m_Squares[id] = s; m_GridDirty = true; return SQUARE_INDEX_TO_TAG(id); } virtual void MoveShape(tag_t tag, entity_pos_t x, entity_pos_t z, entity_angle_t a) { if (TAG_IS_CIRCLE(tag)) { Circle& c = m_Circles[TAG_TO_INDEX(tag)]; c.x = x; c.z = z; } else { Square& s = m_Squares[TAG_TO_INDEX(tag)]; s.x = x; s.z = z; s.a = a; } m_GridDirty = true; } virtual void RemoveShape(tag_t tag) { if (TAG_IS_CIRCLE(tag)) m_Circles.erase(TAG_TO_INDEX(tag)); else m_Squares.erase(TAG_TO_INDEX(tag)); m_GridDirty = true; } virtual bool CanMoveStraight(entity_pos_t x0, entity_pos_t z0, entity_pos_t x1, entity_pos_t z1, entity_pos_t r, u32& cost); virtual void ComputePath(entity_pos_t x0, entity_pos_t z0, const Goal& goal, Path& ret); virtual void SetDebugPath(entity_pos_t x0, entity_pos_t z0, const Goal& goal) { delete m_DebugGrid; m_DebugGrid = NULL; delete m_DebugPath; m_DebugPath = new Path(); ComputePath(x0, z0, goal, *m_DebugPath); } /** * Returns the tile containing the given position */ void NearestTile(entity_pos_t x, entity_pos_t z, u16& i, u16& j) { i = clamp((x / CELL_SIZE).ToInt_RoundToZero(), 0, m_MapSize-1); j = clamp((z / CELL_SIZE).ToInt_RoundToZero(), 0, m_MapSize-1); } /** * Returns the position of the center of the given tile */ void TileCenter(u16 i, u16 j, entity_pos_t& x, entity_pos_t& z) { x = entity_pos_t::FromInt(i*CELL_SIZE + CELL_SIZE/2); z = entity_pos_t::FromInt(j*CELL_SIZE + CELL_SIZE/2); } /** * Regenerates the grid based on the shape lists, if necessary */ void UpdateGrid() { PROFILE("UpdateGrid"); // Initialise the terrain data when first needed if (!m_Grid) { // TOOD: these bits should come from ICmpTerrain ssize_t size = m_Context->GetTerrain().GetTilesPerSide(); debug_assert(size >= 1 && size <= 0xffff); // must fit in 16 bits m_MapSize = size; m_Grid = new Grid(m_MapSize, m_MapSize); } if (m_GridDirty) { // TODO: this is all hopelessly inefficient // What we should perhaps do is have some kind of quadtree storing Shapes so it's // quick to invalidate and update small numbers of tiles m_Grid->reset(); for (std::map::iterator it = m_Circles.begin(); it != m_Circles.end(); ++it) { // TODO: need to handle larger circles (r != 0) u16 i, j; NearestTile(it->second.x, it->second.z, i, j); m_Grid->set(i, j, 1); } for (std::map::iterator it = m_Squares.begin(); it != m_Squares.end(); ++it) { // TODO: need to handle rotations (a != 0) entity_pos_t x0 = it->second.x - it->second.w/2; entity_pos_t z0 = it->second.z - it->second.h/2; entity_pos_t x1 = it->second.x + it->second.w/2; entity_pos_t z1 = it->second.z + it->second.h/2; u16 i0, j0, i1, j1; NearestTile(x0, z0, i0, j0); // TODO: should be careful about rounding on edges NearestTile(x1, z1, i1, j1); for (u16 j = j0; j <= j1; ++j) for (u16 i = i0; i <= i1; ++i) m_Grid->set(i, j, 1); } m_GridDirty = false; } } }; REGISTER_COMPONENT_TYPE(Pathfinder) u32 g_CostPerTile = 256; // base cost to move between adjacent tiles // Detect intersection between ray (0,0)-L and circle with center M radius r // (Only counts intersections from the outside to the inside) static bool IntersectRayCircle(CFixedVector2D l, CFixedVector2D m, entity_pos_t r) { // TODO: this should all be checked and tested etc, it's just a rough first attempt for now... // Intersections at (t * l.X - m.X)^2 * (t * l.Y - m.Y) = r^2 // so solve the quadratic for t: #define DOT(u, v) ( ((i64)u.X.GetInternalValue()*(i64)v.X.GetInternalValue()) + ((i64)u.Y.GetInternalValue()*(i64)v.Y.GetInternalValue()) ) i64 a = DOT(l, l); if (a == 0) return false; // avoid divide-by-zero later i64 b = DOT(l, m)*-2; i64 c = DOT(m, m) - r.GetInternalValue()*r.GetInternalValue(); i64 d = b*b - 4*a*c; // TODO: overflow breaks stuff here if (d < 0) // no solutions return false; // Find the time of first intersection (entering the circle) i64 t2a = (-b - isqrt64(d)); // don't divide by 2a explicitly, to avoid rounding errors if ((a > 0 && t2a < 0) || (a < 0 && t2a > 0)) // if t2a/2a < 0 then intersection was before the ray return false; if (t2a >= 2*a) // intersection was after the ray return false; // printf("isct (%f,%f) (%f,%f) %f a=%lld b=%lld c=%lld d=%lld t2a=%lld\n", l.X.ToDouble(), l.Y.ToDouble(), m.X.ToDouble(), m.Y.ToDouble(), r.ToDouble(), a, b, c, d, t2a); return true; } bool CCmpPathfinder::CanMoveStraight(entity_pos_t x0, entity_pos_t z0, entity_pos_t x1, entity_pos_t z1, entity_pos_t r, u32& cost) { PROFILE("CanMoveStraight"); // TODO: this is all very inefficient, it should use kind of spatial data structures // Ray-circle intersections for (std::map::iterator it = m_Circles.begin(); it != m_Circles.end(); ++it) { if (IntersectRayCircle(CFixedVector2D(x1 - x0, z1 - z0), CFixedVector2D(it->second.x - x0, it->second.z - z0), it->second.r + r)) return false; } // Ray-square intersections for (std::map::iterator it = m_Squares.begin(); it != m_Squares.end(); ++it) { // XXX need some kind of square intersection code if (IntersectRayCircle(CFixedVector2D(x1 - x0, z1 - z0), CFixedVector2D(it->second.x - x0, it->second.z - z0), it->second.w/2 + r)) return false; } // Calculate the exact movement cost // (TODO: this needs to care about terrain costs etc) cost = (CFixedVector2D(x1 - x0, z1 - z0).Length() * g_CostPerTile).ToInt_RoundToZero(); return true; } /** * Tile data for A* computation */ struct PathfindTile { enum { STATUS_UNEXPLORED = 0, STATUS_OPEN = 1, STATUS_CLOSED = 2 }; u8 status; // (TODO: this only needs 2 bits) u16 pi, pj; // predecessor on best path (TODO: this only needs 2 bits) u32 cost; // g (cost to this tile) u32 step; // step at which this tile was last processed (TODO: this should only be present for debugging) }; void PathfinderOverlay::EndRender() { if (m_Pathfinder.m_DebugPath) { std::vector& wp = m_Pathfinder.m_DebugPath->m_Waypoints; for (size_t n = 0; n < wp.size(); ++n) { u16 i, j; m_Pathfinder.NearestTile(wp[n].x, wp[n].z, i, j); RenderTileOutline(CColor(1, 1, 1, 1), 2, false, i, j); } } } void PathfinderOverlay::ProcessTile(ssize_t i, ssize_t j) { if (m_Pathfinder.m_Grid && m_Pathfinder.m_Grid->get(i, j)) RenderTile(CColor(1, 0, 0, 0.6f), false); if (m_Pathfinder.m_DebugGrid) { PathfindTile& n = m_Pathfinder.m_DebugGrid->get(i, j); float c = clamp(n.step / (float)m_Pathfinder.m_DebugSteps, 0.f, 1.f); if (n.status == PathfindTile::STATUS_OPEN) RenderTile(CColor(1, 1, c, 0.6f), false); else if (n.status == PathfindTile::STATUS_CLOSED) RenderTile(CColor(0, 1, c, 0.6f), false); } } /* * A* pathfinding implementation * * This is currently all a bit rubbish and hasn't been tested for correctness or efficiency; * the intention is to demonstrate the interface that the pathfinder can use, and improvements * to the implementation shouldn't affect that interface much. */ struct QueueItem { u16 i, j; u32 rank; // g+h (estimated total cost of path through here) }; struct QueueItemPriority { bool operator()(const QueueItem& a, const QueueItem& b) { if (a.rank > b.rank) // higher costs are lower priority return true; if (a.rank < b.rank) return false; // Need to tie-break to get a consistent ordering // TODO: Should probably tie-break on g or h or something, but don't bother for now if (a.i < b.i) return true; if (a.i > b.i) return false; if (a.j < b.j) return true; if (a.j > b.j) return false; debug_warn(L"duplicate tiles in queue"); return false; } }; // Priority queue implementation, based on std::priority_queue but with O(n) find/update functions // TODO: this is all a bit rubbish and slow class PriorityQueue { public: void push(const QueueItem& item) { m_Heap.push_back(item); push_heap(m_Heap.begin(), m_Heap.end(), QueueItemPriority()); } void fixheap() { make_heap(m_Heap.begin(), m_Heap.end(), QueueItemPriority()); } QueueItem* find(u16 i, u16 j) { for (size_t n = 0; n < m_Heap.size(); ++n) { if (m_Heap[n].i == i && m_Heap[n].j == j) return &m_Heap[n]; } return NULL; } void remove(u16 i, u16 j) { for (size_t n = 0; n < m_Heap.size(); ++n) { if (m_Heap[n].i == i && m_Heap[n].j == j) { m_Heap.erase(m_Heap.begin() + n); fixheap(); // XXX: this is slow return; } } } const QueueItem& top() { debug_assert(m_Heap.size()); return m_Heap.front(); } void pop() { debug_assert(m_Heap.size()); pop_heap(m_Heap.begin(), m_Heap.end(), QueueItemPriority()); m_Heap.pop_back(); } bool empty() { return m_Heap.empty(); } std::vector m_Heap; }; #define USE_DIAGONAL_MOVEMENT // Calculate heuristic cost from tile i,j to destination // (This ought to be an underestimate for correctness) static u32 CalculateHeuristic(u16 i, u16 j, u16 iGoal, u16 jGoal, u16 rGoal, bool aimingInwards) { #ifdef USE_DIAGONAL_MOVEMENT CFixedVector2D pos (CFixed_23_8::FromInt(i), CFixed_23_8::FromInt(j)); CFixedVector2D goal (CFixed_23_8::FromInt(iGoal), CFixed_23_8::FromInt(jGoal)); CFixed_23_8 dist = (pos - goal).Length(); // TODO: the heuristic could match the costs better - it's not really Euclidean movement CFixed_23_8 rdist = dist - CFixed_23_8::FromInt(rGoal); if (!aimingInwards) rdist = -rdist; if (rdist < CFixed_23_8::FromInt(0)) return 0; return (rdist * g_CostPerTile).ToInt_RoundToZero(); #else return (abs((int)i - (int)iGoal) + abs((int)j - (int)jGoal)) * g_CostPerTile; #endif } // Calculate movement cost from predecessor tile pi,pj to tile i,j static u32 CalculateCostDelta(u16 pi, u16 pj, u16 i, u16 j, Grid* tempGrid) { u32 dg = g_CostPerTile; #ifdef USE_DIAGONAL_MOVEMENT // XXX: Probably a terrible hack: // For simplicity, we only consider horizontally/vertically adjacent neighbours, but // units can move along arbitrary lines. That results in ugly square paths, so we want // to prefer diagonal paths. // Instead of solving this nicely, I'll just special-case 45-degree and 30-degree lines // by checking the three predecessor tiles (which'll be in the closed set and therefore // likely to be reasonably stable) and reducing the cost, and use a Euclidean heuristic. // At least this makes paths look a bit nicer for now... PathfindTile& p = tempGrid->get(pi, pj); if (p.pi != i && p.pj != j) dg = dg*(sqrt(2.0)/2.0); // XXX: shouldn't use floats here else { PathfindTile& pp = tempGrid->get(p.pi, p.pj); int di = abs(i - pp.pi); int dj = abs(j - pp.pj); if ((di == 1 && dj == 2) || (di == 2 && dj == 1)) dg = dg*(sqrt(5.0)-sqrt(2.0)); // XXX: shouldn't use floats here } #endif return dg; } struct PathfinderState { u32 steps; // number of algorithm iterations u16 iGoal, jGoal; // goal tile u16 rGoal; // radius of goal (around tile center) bool aimingInwards; // whether we're moving towards the goal or away PriorityQueue open; // (there's no explicit closed list; it's encoded in PathfindTile::status) Grid* tiles; Grid* terrain; u32 hBest; // heuristic of closest discovered tile to goal u16 iBest, jBest; // closest tile }; // Do the A* processing for a neighbour tile i,j. static void ProcessNeighbour(u16 pi, u16 pj, u16 i, u16 j, u32 pg, PathfinderState& state) { // Reject impassable tiles if (state.terrain->get(i, j)) return; u32 h = CalculateHeuristic(i, j, state.iGoal, state.jGoal, state.rGoal, state.aimingInwards); u32 dg = CalculateCostDelta(pi, pj, i, j, state.tiles); u32 g = pg + dg; // cost to this tile = cost to predecessor + delta from predecessor // Remember the best tile we've seen so far, in case we never actually reach the target if (h < state.hBest) { state.hBest = h; state.iBest = i; state.jBest = j; } PathfindTile& n = state.tiles->get(i, j); // If we've already added this tile to the open list: if (n.status == PathfindTile::STATUS_OPEN) { // If this a better path, replace the old one with the new cost/parent if (g < n.cost) { n.cost = g; n.pi = pi; n.pj = pj; n.step = state.steps; state.open.find(i, j)->rank = g + h; state.open.fixheap(); // XXX: this is slow } return; } // If we've already found the 'best' path to this tile: if (n.status == PathfindTile::STATUS_CLOSED) { // If this is a better path (possible when we use inadmissible heuristics), reopen it if (g < n.cost) { // (don't return yet) } else { return; } } // Add it to the open list: n.status = PathfindTile::STATUS_OPEN; n.cost = g; n.pi = pi; n.pj = pj; n.step = state.steps; QueueItem t = { i, j, g + h }; state.open.push(t); } static bool AtGoal(u16 i, u16 j, u16 iGoal, u16 jGoal, u16 rGoal, bool aimingInwards) { // If we're aiming towards a point, stop when we get there if (aimingInwards && rGoal == 0) return (i == iGoal && j == jGoal); // Otherwise compute the distance and compare to desired radius i32 dist2 = ((i32)i-iGoal)*((i32)i-iGoal) + ((i32)j-jGoal)*((i32)j-jGoal); if (aimingInwards && (dist2 <= rGoal*rGoal)) return true; if (!aimingInwards && (dist2 >= rGoal*rGoal)) return true; return false; } void CCmpPathfinder::ComputePath(entity_pos_t x0, entity_pos_t z0, const Goal& goal, Path& path) { UpdateGrid(); PROFILE("ComputePath"); PathfinderState state; // Convert the start/end coordinates to tile indexes u16 i0, j0; NearestTile(x0, z0, i0, j0); NearestTile(goal.x, goal.z, state.iGoal, state.jGoal); // If we start closer than min radius, aim for the min radius // If we start further than max radius, aim for the max radius // Otherwise we're there already CFixed_23_8 initialDist = (CFixedVector2D(x0, z0) - CFixedVector2D(goal.x, goal.z)).Length(); if (initialDist < goal.minRadius) { state.aimingInwards = false; state.rGoal = (goal.minRadius / CELL_SIZE).ToInt_RoundToZero(); // TODO: what rounding mode is appropriate? } else if (initialDist > goal.maxRadius) { state.aimingInwards = true; state.rGoal = (goal.maxRadius / CELL_SIZE).ToInt_RoundToZero(); // TODO: what rounding mode is appropriate? } else { return; } state.steps = 0; state.tiles = new Grid(m_MapSize, m_MapSize); state.terrain = m_Grid; state.iBest = i0; state.jBest = j0; state.hBest = CalculateHeuristic(i0, j0, state.iGoal, state.jGoal, state.rGoal, state.aimingInwards); QueueItem start = { i0, j0, 0 }; state.open.push(start); state.tiles->get(i0, j0).status = PathfindTile::STATUS_OPEN; state.tiles->get(i0, j0).pi = i0; state.tiles->get(i0, j0).pj = j0; state.tiles->get(i0, j0).cost = 0; while (1) { ++state.steps; // Hack to avoid spending ages computing giant paths, particularly when // the destination is unreachable if (state.steps > 5000) break; // If we ran out of tiles to examine, give up if (state.open.empty()) break; // Move best tile from open to closed QueueItem curr = state.open.top(); state.open.pop(); state.tiles->get(curr.i, curr.j).status = PathfindTile::STATUS_CLOSED; // If we've reached the destination, stop if (AtGoal(curr.i, curr.j, state.iGoal, state.jGoal, state.rGoal, state.aimingInwards)) { state.iBest = curr.i; state.jBest = curr.j; state.hBest = 0; break; } u32 g = state.tiles->get(curr.i, curr.j).cost; if (curr.i > 0) ProcessNeighbour(curr.i, curr.j, curr.i-1, curr.j, g, state); if (curr.i < m_MapSize-1) ProcessNeighbour(curr.i, curr.j, curr.i+1, curr.j, g, state); if (curr.j > 0) ProcessNeighbour(curr.i, curr.j, curr.i, curr.j-1, g, state); if (curr.j < m_MapSize-1) ProcessNeighbour(curr.i, curr.j, curr.i, curr.j+1, g, state); } // Reconstruct the path (in reverse) u16 ip = state.iBest, jp = state.jBest; while (ip != i0 || jp != j0) { PathfindTile& n = state.tiles->get(ip, jp); entity_pos_t x, z; TileCenter(ip, jp, x, z); Waypoint w = { x, z, n.cost }; path.m_Waypoints.push_back(w); // Follow the predecessor link ip = n.pi; jp = n.pj; } // Save this grid for debug display delete m_DebugGrid; m_DebugGrid = state.tiles; m_DebugSteps = state.steps; }