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666 lines
24 KiB
C++
666 lines
24 KiB
C++
#include "pathfinding.hpp"
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#include <map>
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#include "OgreMath.h"
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#include "OgreVector3.h"
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#include "../mwbase/world.hpp"
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#include "../mwbase/environment.hpp"
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#include "../mwworld/esmstore.hpp"
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#include "../mwworld/cellstore.hpp"
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namespace
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{
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float distanceZCorrected(ESM::Pathgrid::Point point, float x, float y, float z)
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{
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x -= point.mX;
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y -= point.mY;
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z -= point.mZ;
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return sqrt(x * x + y * y + 0.1 * z * z);
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}
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float distance(ESM::Pathgrid::Point point, float x, float y, float z)
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{
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x -= point.mX;
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y -= point.mY;
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z -= point.mZ;
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return sqrt(x * x + y * y + z * z);
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}
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float distance(ESM::Pathgrid::Point a, ESM::Pathgrid::Point b)
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{
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float x = a.mX - b.mX;
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float y = a.mY - b.mY;
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float z = a.mZ - b.mZ;
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return sqrt(x * x + y * y + z * z);
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}
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// See http://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 * (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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// Slightly cheaper version for comparisons.
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// Caller needs to be careful for very short distances (i.e. less than 1)
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// or when accumuating the results i.e. (a + b)^2 != a^2 + b^2
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//
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float distanceSquared(ESM::Pathgrid::Point point, Ogre::Vector3 pos)
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{
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return Ogre::Vector3(point.mX, point.mY, point.mZ).squaredDistance(pos);
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}
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// Return the closest pathgrid point index from the specified position co
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// -ordinates. NOTE: Does not check if there is a sensible way to get there
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// (e.g. a cliff in front).
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//
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// NOTE: pos is expected to be in local co-ordinates, as is grid->mPoints
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//
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int getClosestPoint(const ESM::Pathgrid* grid, Ogre::Vector3 pos)
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{
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if(!grid || grid->mPoints.empty())
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return -1;
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float distanceBetween = distanceSquared(grid->mPoints[0], pos);
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int closestIndex = 0;
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// TODO: if this full scan causes performance problems mapping pathgrid
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// points to a quadtree may help
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for(unsigned int counter = 1; counter < grid->mPoints.size(); counter++)
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{
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float potentialDistBetween = distanceSquared(grid->mPoints[counter], pos);
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if(potentialDistBetween < distanceBetween)
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{
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distanceBetween = potentialDistBetween;
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closestIndex = counter;
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}
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}
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return closestIndex;
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}
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// Chooses a reachable end pathgrid point. start is assumed reachable.
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std::pair<int, bool> getClosestReachablePoint(const ESM::Pathgrid* grid,
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const MWWorld::CellStore *cell,
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Ogre::Vector3 pos, int start)
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{
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if(!grid || grid->mPoints.empty())
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return std::pair<int, bool> (-1, false);
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float distanceBetween = distanceSquared(grid->mPoints[0], pos);
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int closestIndex = 0;
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int closestReachableIndex = 0;
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// TODO: if this full scan causes performance problems mapping pathgrid
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// points to a quadtree may help
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for(unsigned int counter = 1; counter < grid->mPoints.size(); counter++)
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{
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float potentialDistBetween = distanceSquared(grid->mPoints[counter], pos);
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if(potentialDistBetween < distanceBetween)
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{
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// found a closer one
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distanceBetween = potentialDistBetween;
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closestIndex = counter;
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if (cell->isPointConnected(start, counter))
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{
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closestReachableIndex = counter;
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}
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}
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}
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if(start == closestReachableIndex)
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closestReachableIndex = -1; // couldn't find anyting other than start
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return std::pair<int, bool>
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(closestReachableIndex, closestReachableIndex == closestIndex);
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}
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}
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namespace MWMechanics
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{
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PathFinder::PathFinder()
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: mIsPathConstructed(false),
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mPathgrid(NULL),
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mCell(NULL)
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{
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}
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void PathFinder::clearPath()
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{
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if(!mPath.empty())
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mPath.clear();
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mIsPathConstructed = false;
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}
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/*
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* NOTE: This method may fail to find a path. The caller must check the
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* result before using it. If there is no path the AI routies need to
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* implement some other heuristics to reach the target.
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*
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* NOTE: It may be desirable to simply go directly to the endPoint if for
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* example there are no pathgrids in this cell.
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*
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* NOTE: startPoint & endPoint are in world co-ordinates
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*
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* Updates mPath using aStarSearch() or ray test (if shortcut allowed).
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* mPath consists of pathgrid points, except the last element which is
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* endPoint. This may be useful where the endPoint is not on a pathgrid
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* point (e.g. combat). However, if the caller has already chosen a
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* pathgrid point (e.g. wander) then it may be worth while to call
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* pop_back() to remove the redundant entry.
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*
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* mPathConstructed is set true if successful, false if not
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*
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* NOTE: co-ordinates must be converted prior to calling getClosestPoint()
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*
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* |
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* | cell
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* | +-----------+
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* | | |
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* | | |
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* | | @ |
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* | i | j |
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* |<--->|<---->| |
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* | +-----------+
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* | k
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* |<---------->| world
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* +-----------------------------
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*
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* i = x value of cell itself (multiply by ESM::Land::REAL_SIZE to convert)
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* j = @.x in local co-ordinates (i.e. within the cell)
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* k = @.x in world co-ordinates
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*/
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void PathFinder::buildPath(const ESM::Pathgrid::Point &startPoint,
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const ESM::Pathgrid::Point &endPoint,
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const MWWorld::CellStore* cell,
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bool allowShortcuts)
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{
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mPath.clear();
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if(allowShortcuts)
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{
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// if there's a ray cast hit, can't take a direct path
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if(!MWBase::Environment::get().getWorld()->castRay(startPoint.mX, startPoint.mY, startPoint.mZ,
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endPoint.mX, endPoint.mY, endPoint.mZ))
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{
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mPath.push_back(endPoint);
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mIsPathConstructed = true;
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return;
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}
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}
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if(mCell != cell || !mPathgrid)
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{
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mCell = cell;
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mPathgrid = MWBase::Environment::get().getWorld()->getStore().get<ESM::Pathgrid>().search(*mCell->getCell());
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}
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// Refer to AiWander reseach topic on openmw forums for some background.
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// Maybe there is no pathgrid for this cell. Just go to destination and let
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// physics take care of any blockages.
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if(!mPathgrid || mPathgrid->mPoints.empty())
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{
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mPath.push_back(endPoint);
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mIsPathConstructed = true;
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return;
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}
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// NOTE: getClosestPoint expects local co-ordinates
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float xCell = 0;
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float yCell = 0;
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if (mCell->isExterior())
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{
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xCell = mCell->getCell()->mData.mX * ESM::Land::REAL_SIZE;
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yCell = mCell->getCell()->mData.mY * ESM::Land::REAL_SIZE;
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}
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// NOTE: It is possible that getClosestPoint returns a pathgrind point index
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// that is unreachable in some situations. e.g. actor is standing
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// outside an area enclosed by walls, but there is a pathgrid
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// point right behind the wall that is closer than any pathgrid
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// point outside the wall
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int startNode = getClosestPoint(mPathgrid,
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Ogre::Vector3(startPoint.mX - xCell, startPoint.mY - yCell, startPoint.mZ));
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// Some cells don't have any pathgrids at all
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if(startNode != -1)
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{
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std::pair<int, bool> endNode = getClosestReachablePoint(mPathgrid, cell,
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Ogre::Vector3(endPoint.mX - xCell, endPoint.mY - yCell, endPoint.mZ),
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startNode);
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// this shouldn't really happen, but just in case
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if(endNode.first != -1)
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{
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mPath = mCell->aStarSearch(startNode, endNode.first, mCell->isExterior());
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if(!mPath.empty())
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{
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mIsPathConstructed = true;
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// Add the destination (which may be different to the closest
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// pathgrid point). However only add if endNode was the closest
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// point to endPoint.
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//
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// This logic can fail in the opposite situate, e.g. endPoint may
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// have been reachable but happened to be very close to an
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// unreachable pathgrid point.
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//
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// The AI routines will have to deal with such situations.
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if(endNode.second)
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mPath.push_back(endPoint);
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}
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else
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mIsPathConstructed = false;
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}
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else
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mIsPathConstructed = false;
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}
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else
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mIsPathConstructed = false;
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return;
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}
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float PathFinder::getZAngleToNext(float x, float y) const
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{
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// This should never happen (programmers should have an if statement checking
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// mIsPathConstructed that prevents this call if otherwise).
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if(mPath.empty())
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return 0.;
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const ESM::Pathgrid::Point &nextPoint = *mPath.begin();
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float directionX = nextPoint.mX - x;
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float directionY = nextPoint.mY - y;
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float directionResult = sqrt(directionX * directionX + directionY * directionY);
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return Ogre::Radian(Ogre::Math::ACos(directionY / directionResult) * sgn(Ogre::Math::ASin(directionX / directionResult))).valueDegrees();
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}
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// Used by AiCombat, use Euclidean distance
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float PathFinder::getDistToNext(float x, float y, float z)
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{
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ESM::Pathgrid::Point nextPoint = *mPath.begin();
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return distance(nextPoint, x, y, z);
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}
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bool PathFinder::checkWaypoint(float x, float y, float z)
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{
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if(mPath.empty())
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return true;
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ESM::Pathgrid::Point nextPoint = *mPath.begin();
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if(distanceZCorrected(nextPoint, x, y, z) < 64)
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{
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mPath.pop_front();
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if(mPath.empty()) mIsPathConstructed = false;
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return true;
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}
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return false;
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}
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bool PathFinder::checkPathCompleted(float x, float y, float z)
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{
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if(mPath.empty())
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return true;
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ESM::Pathgrid::Point nextPoint = *mPath.begin();
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if(distanceZCorrected(nextPoint, x, y, z) < 64)
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{
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mPath.pop_front();
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if(mPath.empty())
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{
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mIsPathConstructed = false;
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return true;
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}
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}
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return false;
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}
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// used by AiCombat, see header for the rationale
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void PathFinder::syncStart(const std::list<ESM::Pathgrid::Point> &path)
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{
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if (mPath.size() < 2)
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return; //nothing to pop
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std::list<ESM::Pathgrid::Point>::const_iterator oldStart = path.begin();
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std::list<ESM::Pathgrid::Point>::iterator iter = ++mPath.begin();
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if( (*iter).mX == oldStart->mX
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&& (*iter).mY == oldStart->mY
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&& (*iter).mZ == oldStart->mZ
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&& (*iter).mAutogenerated == oldStart->mAutogenerated
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&& (*iter).mConnectionNum == oldStart->mConnectionNum )
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{
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mPath.pop_front();
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}
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}
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// TODO: Any multi threading concerns?
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PathgridGraph::PathgridGraph()
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: mCell(NULL)
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, mIsGraphConstructed(false)
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, mPathgrid(NULL)
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, mGraph(0)
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, mSCCId(0)
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, mSCCIndex(0)
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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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bool PathgridGraph::initPathgridGraph(const ESM::Cell* cell)
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{
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if(!cell)
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return false;
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mCell = cell;
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mPathgrid = MWBase::Environment::get().getWorld()->getStore().get<ESM::Pathgrid>().search(*cell);
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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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//#if 0
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std::cout << "loading pathgrid " <<
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+"\""+ mPathgrid->mCell +"\""
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+", "+ std::to_string(mPathgrid->mData.mX)
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+", "+ std::to_string(mPathgrid->mData.mY)
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<< std::endl;
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//#endif
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return true;
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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
|
|
* mGraph[v].edges | E (for v) |
|
|
* mSCCIndex | index | tracking smallest unused index
|
|
* mSCCStack | S |
|
|
* mGraph[v].edges[i].index | w |
|
|
*
|
|
*/
|
|
void PathgridGraph::buildConnectedPoints()
|
|
{
|
|
// both of these are set to zero in the constructor
|
|
//mSCCId = 0; // how many strongly connected components in this cell
|
|
//mSCCIndex = 0;
|
|
int pointsSize = mPathgrid->mPoints.size();
|
|
mSCCPoint.resize(pointsSize, std::pair<int, int> (-1, -1));
|
|
mSCCStack.reserve(pointsSize);
|
|
|
|
for(int v = 0; v < static_cast<int> (pointsSize); v++)
|
|
{
|
|
if(mSCCPoint[v].first == -1) // undefined (haven't visited)
|
|
recursiveStrongConnect(v);
|
|
}
|
|
//#if 0
|
|
std::cout << "components: " << std::to_string(mSCCId)
|
|
+", "+ mPathgrid->mCell
|
|
<< std::endl;
|
|
//#endif
|
|
}
|
|
|
|
bool PathgridGraph::isPointConnected(const int start, const int end) const
|
|
{
|
|
return (mGraph[start].componentId == mGraph[end].componentId);
|
|
}
|
|
|
|
/*
|
|
* NOTE: Based on buildPath2(), please check git history if interested
|
|
* Should consider using a 3rd party library version (e.g. boost)
|
|
*
|
|
* Find the shortest path to the target goal using a well known algorithm.
|
|
* Uses mGraph which has pre-computed costs for allowed edges. It is assumed
|
|
* that mGraph is already constructed.
|
|
*
|
|
* Should be possible to make this MT safe.
|
|
*
|
|
* Returns path (a list of pathgrid point indexes) which may be empty.
|
|
*
|
|
* Input params:
|
|
* start, goal - pathgrid point indexes (for this cell)
|
|
* isExterior - used to determine whether to convert to world co-ordinates
|
|
*
|
|
* Variables:
|
|
* openset - point indexes to be traversed, lowest cost at the front
|
|
* closedset - point indexes already traversed
|
|
* gScore - past accumulated costs vector indexed by point index
|
|
* fScore - future estimated costs vector indexed by point index
|
|
*
|
|
* TODO: An intersting exercise might be to cache the paths created for a
|
|
* start/goal pair. To cache the results the paths need to be in
|
|
* pathgrid points form (currently they are converted to world
|
|
* co-ordinates). Essentially trading speed w/ memory.
|
|
*/
|
|
std::list<ESM::Pathgrid::Point> PathgridGraph::aStarSearch(const int start,
|
|
const int goal,
|
|
bool isExterior) const
|
|
{
|
|
std::list<ESM::Pathgrid::Point> path;
|
|
if(!isPointConnected(start, goal))
|
|
{
|
|
return path; // there is no path, return an empty path
|
|
}
|
|
|
|
int graphSize = mGraph.size();
|
|
std::vector<float> gScore;
|
|
gScore.resize(graphSize, -1);
|
|
std::vector<float> fScore;
|
|
fScore.resize(graphSize, -1);
|
|
std::vector<int> graphParent;
|
|
graphParent.resize(graphSize, -1);
|
|
|
|
// gScore & fScore keep costs for each pathgrid point in mPoints
|
|
gScore[start] = 0;
|
|
fScore[start] = costAStar(mPathgrid->mPoints[start], mPathgrid->mPoints[goal]);
|
|
|
|
std::list<int> openset;
|
|
std::list<int> closedset;
|
|
openset.push_back(start);
|
|
|
|
int current = -1;
|
|
|
|
while(!openset.empty())
|
|
{
|
|
current = openset.front(); // front has the lowest cost
|
|
openset.pop_front();
|
|
|
|
if(current == goal)
|
|
break;
|
|
|
|
closedset.push_back(current); // remember we've been here
|
|
|
|
// check all edges for the current point index
|
|
for(int j = 0; j < static_cast<int> (mGraph[current].edges.size()); j++)
|
|
{
|
|
if(std::find(closedset.begin(), closedset.end(), mGraph[current].edges[j].index) ==
|
|
closedset.end())
|
|
{
|
|
// not in closedset - i.e. have not traversed this edge destination
|
|
int dest = mGraph[current].edges[j].index;
|
|
float tentative_g = gScore[current] + mGraph[current].edges[j].cost;
|
|
bool isInOpenSet = std::find(openset.begin(), openset.end(), dest) != openset.end();
|
|
if(!isInOpenSet
|
|
|| tentative_g < gScore[dest])
|
|
{
|
|
graphParent[dest] = current;
|
|
gScore[dest] = tentative_g;
|
|
fScore[dest] = tentative_g + costAStar(mPathgrid->mPoints[dest],
|
|
mPathgrid->mPoints[goal]);
|
|
if(!isInOpenSet)
|
|
{
|
|
// add this edge to openset, lowest cost goes to the front
|
|
// TODO: if this causes performance problems a hash table may help
|
|
std::list<int>::iterator it = openset.begin();
|
|
for(it = openset.begin(); it!= openset.end(); it++)
|
|
{
|
|
if(fScore[*it] > fScore[dest])
|
|
break;
|
|
}
|
|
openset.insert(it, dest);
|
|
}
|
|
}
|
|
} // if in closedset, i.e. traversed this edge already, try the next edge
|
|
}
|
|
}
|
|
|
|
if(current != goal)
|
|
return path; // for some reason couldn't build a path
|
|
|
|
// reconstruct path to return, using world co-ordinates
|
|
float xCell = 0;
|
|
float yCell = 0;
|
|
if (isExterior)
|
|
{
|
|
xCell = mPathgrid->mData.mX * ESM::Land::REAL_SIZE;
|
|
yCell = mPathgrid->mData.mY * ESM::Land::REAL_SIZE;
|
|
}
|
|
|
|
while(graphParent[current] != -1)
|
|
{
|
|
ESM::Pathgrid::Point pt = mPathgrid->mPoints[current];
|
|
pt.mX += xCell;
|
|
pt.mY += yCell;
|
|
path.push_front(pt);
|
|
current = graphParent[current];
|
|
}
|
|
return path;
|
|
}
|
|
}
|
|
|