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344 lines
12 KiB
C++
344 lines
12 KiB
C++
#include "pathgrid.hpp"
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#include "../mwbase/world.hpp"
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#include "../mwbase/environment.hpp"
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#include "../mwworld/cellstore.hpp"
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#include "../mwworld/esmstore.hpp"
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namespace
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{
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// See https://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html
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//
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// One of the smallest cost in Seyda Neen is between points 77 & 78:
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// pt x y
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// 77 = 8026, 4480
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// 78 = 7986, 4218
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//
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// Euclidean distance is about 262 (ignoring z) and Manhattan distance is 300
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// (again ignoring z). Using a value of about 300 for D seems like a reasonable
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// starting point for experiments. If in doubt, just use value 1.
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//
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// The distance between 3 & 4 are pretty small, too.
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// 3 = 5435, 223
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// 4 = 5948, 193
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//
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// Approx. 514 Euclidean distance and 533 Manhattan distance.
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//
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float manhattan(const ESM::Pathgrid::Point& a, const ESM::Pathgrid::Point& b)
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{
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return 300.0f * (abs(a.mX - b.mX) + abs(a.mY - b.mY) + abs(a.mZ - b.mZ));
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}
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// Choose a heuristics - Note that these may not be the best for directed
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// graphs with non-uniform edge costs.
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//
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// distance:
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// - sqrt((curr.x - goal.x)^2 + (curr.y - goal.y)^2 + (curr.z - goal.z)^2)
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// - slower but more accurate
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//
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// Manhattan:
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// - |curr.x - goal.x| + |curr.y - goal.y| + |curr.z - goal.z|
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// - faster but not the shortest path
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float costAStar(const ESM::Pathgrid::Point& a, const ESM::Pathgrid::Point& b)
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{
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//return distance(a, b);
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return manhattan(a, b);
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}
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}
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namespace MWMechanics
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{
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PathgridGraph::PathgridGraph(const MWWorld::CellStore *cell)
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: mCell(NULL)
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, mPathgrid(NULL)
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, mIsExterior(0)
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, mGraph(0)
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, mIsGraphConstructed(false)
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, mSCCId(0)
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, mSCCIndex(0)
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{
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load(cell);
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}
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/*
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* mGraph is populated with the cost of each allowed edge.
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*
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* The data structure is based on the code in buildPath2() but modified.
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* Please check git history if interested.
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*
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* mGraph[v].edges[i].index = w
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*
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* v = point index of location "from"
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* i = index of edges from point v
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* w = point index of location "to"
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*
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*
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* Example: (notice from p(0) to p(2) is not allowed in this example)
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*
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* mGraph[0].edges[0].index = 1
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* .edges[1].index = 3
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*
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* mGraph[1].edges[0].index = 0
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* .edges[1].index = 2
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* .edges[2].index = 3
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*
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* mGraph[2].edges[0].index = 1
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*
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* (etc, etc)
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*
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*
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* low
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* cost
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* p(0) <---> p(1) <------------> p(2)
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* ^ ^
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* | |
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* | +-----> p(3)
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* +---------------->
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* high cost
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*/
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bool PathgridGraph::load(const MWWorld::CellStore *cell)
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{
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if(!cell)
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return false;
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if(mIsGraphConstructed)
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return true;
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mCell = cell->getCell();
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mIsExterior = cell->getCell()->isExterior();
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mPathgrid = MWBase::Environment::get().getWorld()->getStore().get<ESM::Pathgrid>().search(*cell->getCell());
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if(!mPathgrid)
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return false;
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mGraph.resize(mPathgrid->mPoints.size());
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for(int i = 0; i < static_cast<int> (mPathgrid->mEdges.size()); i++)
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{
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ConnectedPoint neighbour;
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neighbour.cost = costAStar(mPathgrid->mPoints[mPathgrid->mEdges[i].mV0],
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mPathgrid->mPoints[mPathgrid->mEdges[i].mV1]);
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// forward path of the edge
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neighbour.index = mPathgrid->mEdges[i].mV1;
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mGraph[mPathgrid->mEdges[i].mV0].edges.push_back(neighbour);
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// reverse path of the edge
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// NOTE: These are redundant, ESM already contains the required reverse paths
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//neighbour.index = mPathgrid->mEdges[i].mV0;
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//mGraph[mPathgrid->mEdges[i].mV1].edges.push_back(neighbour);
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}
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buildConnectedPoints();
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mIsGraphConstructed = true;
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return true;
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}
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const ESM::Pathgrid *PathgridGraph::getPathgrid() const
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{
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return mPathgrid;
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}
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// v is the pathgrid point index (some call them vertices)
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void PathgridGraph::recursiveStrongConnect(int v)
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{
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mSCCPoint[v].first = mSCCIndex; // index
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mSCCPoint[v].second = mSCCIndex; // lowlink
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mSCCIndex++;
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mSCCStack.push_back(v);
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int w;
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for(int i = 0; i < static_cast<int> (mGraph[v].edges.size()); i++)
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{
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w = mGraph[v].edges[i].index;
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if(mSCCPoint[w].first == -1) // not visited
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{
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recursiveStrongConnect(w); // recurse
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mSCCPoint[v].second = std::min(mSCCPoint[v].second,
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mSCCPoint[w].second);
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}
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else
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{
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if(find(mSCCStack.begin(), mSCCStack.end(), w) != mSCCStack.end())
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mSCCPoint[v].second = std::min(mSCCPoint[v].second,
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mSCCPoint[w].first);
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}
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}
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if(mSCCPoint[v].second == mSCCPoint[v].first)
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{ // new component
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do
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{
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w = mSCCStack.back();
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mSCCStack.pop_back();
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mGraph[w].componentId = mSCCId;
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}
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while(w != v);
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mSCCId++;
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}
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return;
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}
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/*
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* mGraph contains the strongly connected component group id's along
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* with pre-calculated edge costs.
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*
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* A cell can have disjointed pathgrids, e.g. Seyda Neen has 3
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*
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* mGraph for Seyda Neen will therefore have 3 different values. When
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* selecting a random pathgrid point for AiWander, mGraph can be checked
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* for quickly finding whether the destination is reachable.
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*
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* Otherwise, buildPath can automatically select a closest reachable end
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* pathgrid point (reachable from the closest start point).
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*
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* Using Tarjan's algorithm:
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*
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* mGraph | graph G |
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* mSCCPoint | V | derived from mPoints
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* mGraph[v].edges | E (for v) |
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* mSCCIndex | index | tracking smallest unused index
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* mSCCStack | S |
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* mGraph[v].edges[i].index | w |
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*
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*/
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void PathgridGraph::buildConnectedPoints()
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{
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// both of these are set to zero in the constructor
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//mSCCId = 0; // how many strongly connected components in this cell
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//mSCCIndex = 0;
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int pointsSize = static_cast<int> (mPathgrid->mPoints.size());
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mSCCPoint.resize(pointsSize, std::pair<int, int> (-1, -1));
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mSCCStack.reserve(pointsSize);
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for(int v = 0; v < pointsSize; v++)
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{
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if(mSCCPoint[v].first == -1) // undefined (haven't visited)
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recursiveStrongConnect(v);
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}
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}
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bool PathgridGraph::isPointConnected(const int start, const int end) const
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{
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return (mGraph[start].componentId == mGraph[end].componentId);
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}
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void PathgridGraph::getNeighbouringPoints(const int index, ESM::Pathgrid::PointList &nodes) const
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{
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for(int i = 0; i < static_cast<int> (mGraph[index].edges.size()); i++)
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{
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int neighbourIndex = mGraph[index].edges[i].index;
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if (neighbourIndex != index)
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nodes.push_back(mPathgrid->mPoints[neighbourIndex]);
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}
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}
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/*
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* NOTE: Based on buildPath2(), please check git history if interested
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* Should consider using a 3rd party library version (e.g. boost)
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*
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* Find the shortest path to the target goal using a well known algorithm.
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* Uses mGraph which has pre-computed costs for allowed edges. It is assumed
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* that mGraph is already constructed.
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*
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* Should be possible to make this MT safe.
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*
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* Returns path which may be empty. path contains pathgrid points in local
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* cell coordinates (indoors) or world coordinates (external).
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*
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* Input params:
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* start, goal - pathgrid point indexes (for this cell)
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*
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* Variables:
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* openset - point indexes to be traversed, lowest cost at the front
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* closedset - point indexes already traversed
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* gScore - past accumulated costs vector indexed by point index
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* fScore - future estimated costs vector indexed by point index
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*
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* TODO: An intersting exercise might be to cache the paths created for a
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* start/goal pair. To cache the results the paths need to be in
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* pathgrid points form (currently they are converted to world
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* coordinates). Essentially trading speed w/ memory.
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*/
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std::list<ESM::Pathgrid::Point> PathgridGraph::aStarSearch(const int start,
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const int goal) const
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{
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std::list<ESM::Pathgrid::Point> path;
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if(!isPointConnected(start, goal))
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{
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return path; // there is no path, return an empty path
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}
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int graphSize = static_cast<int> (mGraph.size());
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std::vector<float> gScore (graphSize, -1);
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std::vector<float> fScore (graphSize, -1);
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std::vector<int> graphParent (graphSize, -1);
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// gScore & fScore keep costs for each pathgrid point in mPoints
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gScore[start] = 0;
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fScore[start] = costAStar(mPathgrid->mPoints[start], mPathgrid->mPoints[goal]);
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std::list<int> openset;
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std::list<int> closedset;
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openset.push_back(start);
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int current = -1;
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while(!openset.empty())
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{
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current = openset.front(); // front has the lowest cost
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openset.pop_front();
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if(current == goal)
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break;
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closedset.push_back(current); // remember we've been here
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// check all edges for the current point index
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for(int j = 0; j < static_cast<int> (mGraph[current].edges.size()); j++)
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{
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if(std::find(closedset.begin(), closedset.end(), mGraph[current].edges[j].index) ==
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closedset.end())
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{
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// not in closedset - i.e. have not traversed this edge destination
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int dest = mGraph[current].edges[j].index;
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float tentative_g = gScore[current] + mGraph[current].edges[j].cost;
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bool isInOpenSet = std::find(openset.begin(), openset.end(), dest) != openset.end();
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if(!isInOpenSet
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|| tentative_g < gScore[dest])
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{
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graphParent[dest] = current;
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gScore[dest] = tentative_g;
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fScore[dest] = tentative_g + costAStar(mPathgrid->mPoints[dest],
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mPathgrid->mPoints[goal]);
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if(!isInOpenSet)
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{
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// add this edge to openset, lowest cost goes to the front
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// TODO: if this causes performance problems a hash table may help
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std::list<int>::iterator it = openset.begin();
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for(it = openset.begin(); it!= openset.end(); ++it)
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{
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if(fScore[*it] > fScore[dest])
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break;
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}
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openset.insert(it, dest);
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}
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}
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} // if in closedset, i.e. traversed this edge already, try the next edge
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}
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}
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if(current != goal)
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return path; // for some reason couldn't build a path
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// reconstruct path to return, using local coordinates
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while(graphParent[current] != -1)
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{
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path.push_front(mPathgrid->mPoints[current]);
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current = graphParent[current];
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}
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// add first node to path explicitly
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path.push_front(mPathgrid->mPoints[start]);
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return path;
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}
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}
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