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314 lines
11 KiB
C++
314 lines
11 KiB
C++
#include "pathgrid.hpp"
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#include <list>
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#include <set>
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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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constexpr size_t NoIndex = static_cast<size_t>(-1);
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}
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namespace MWMechanics
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{
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class PathgridGraph::Builder
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{
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std::vector<Node>& mGraph;
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// variables used to calculate connected components
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int mSCCId = 0;
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size_t mSCCIndex = 0;
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std::vector<size_t> mSCCStack;
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std::vector<std::pair<size_t, size_t>> mSCCPoint; // first is index, second is lowlink
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// v is the pathgrid point index (some call them vertices)
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void recursiveStrongConnect(const size_t 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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size_t w;
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for (const auto& edge : mGraph[v].edges)
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{
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w = edge.index;
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if (mSCCPoint[w].first == NoIndex) // 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, mSCCPoint[w].second);
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}
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else if (std::find(mSCCStack.begin(), mSCCStack.end(), w) != mSCCStack.end())
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mSCCPoint[v].second = std::min(mSCCPoint[v].second, mSCCPoint[w].first);
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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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} while (w != v);
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mSCCId++;
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}
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}
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public:
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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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explicit Builder(PathgridGraph& graph)
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: mGraph(graph.mGraph)
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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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size_t pointsSize = graph.mPathgrid->mPoints.size();
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mSCCPoint.resize(pointsSize, std::pair<size_t, size_t>(NoIndex, NoIndex));
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mSCCStack.reserve(pointsSize);
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for (size_t v = 0; v < pointsSize; ++v)
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{
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if (mSCCPoint[v].first == NoIndex) // undefined (haven't visited)
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recursiveStrongConnect(v);
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}
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}
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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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PathgridGraph::PathgridGraph(const ESM::Pathgrid& pathgrid)
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: mPathgrid(&pathgrid)
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{
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mGraph.resize(mPathgrid->mPoints.size());
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for (const auto& edge : mPathgrid->mEdges)
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{
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ConnectedPoint neighbour;
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neighbour.cost = costAStar(mPathgrid->mPoints[edge.mV0], mPathgrid->mPoints[edge.mV1]);
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// forward path of the edge
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neighbour.index = edge.mV1;
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mGraph[edge.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 = edge.mV0;
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// mGraph[edge.mV1].edges.push_back(neighbour);
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}
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Builder(*this);
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}
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const PathgridGraph PathgridGraph::sEmpty = {};
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bool PathgridGraph::isPointConnected(const size_t start, const size_t 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 size_t index, ESM::Pathgrid::PointList& nodes) const
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{
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for (const auto& edge : mGraph[index].edges)
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{
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if (edge.index != index)
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nodes.push_back(mPathgrid->mPoints[edge.index]);
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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 interesting 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::deque<ESM::Pathgrid::Point> PathgridGraph::aStarSearch(const size_t start, const size_t goal) const
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{
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std::deque<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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size_t graphSize = 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<size_t> graphParent(graphSize, NoIndex);
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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<size_t> openset;
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std::set<size_t> closedset;
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openset.push_back(start);
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size_t current = start;
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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.insert(current); // remember we've been here
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// check all edges for the current point index
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for (const auto& edge : mGraph[current].edges)
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{
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if (!closedset.contains(edge.index))
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{
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// not in closedset - i.e. have not traversed this edge destination
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size_t dest = edge.index;
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float tentative_g = gScore[current] + edge.cost;
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bool isInOpenSet = std::find(openset.begin(), openset.end(), dest) != openset.end();
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if (!isInOpenSet || 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], 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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auto it = openset.begin();
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for (; 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] != NoIndex)
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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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