void AdjecencyList::Kruskals() {
vector<Edge> path; //the minimal spanning tree of the graph
//sort the edges in the graph, since Kruskals cannot do directed graphs, make
//sure the input file was made as such (it will not crash, just not account extra edges
EdgeSort(EdgeRef);
for(int i = 0; i < EdgeRef.size(); i++) {
//to check if there is a cycle, I will test for it by seeing if both of sides of the new
//edge is within the current minimal spanning tree
bool firstMatch = false; //source is already in path
bool secondMatch = false; //target is already in path
for(int j = 0; j < path.size(); j++) {
//source check
if (EdgeRef[i].source == path[j].source || EdgeRef[i].source == path[j].target) {
firstMatch = true;
}
//target check
if (EdgeRef[i].target == path[j].source || EdgeRef[i].target == path[j].target) {
secondMatch = true;
}
}
//only one or both verticies exist at the moment, adding that edge is legal
if (!firstMatch || !secondMatch) {
path.push_back(EdgeRef[i]);
}
}
cout << "Kruskal's Algorithm: " << endl;
//print out the path
for (int i = 0; i < path.size(); i++) {
cout << path[i].source.value << " -" << path[i].weight << "- " << path[i].target.value << endl;
}
} //do Kruskal's algorithm
void CCmpPathfinder::ComputeShortPath(const IObstructionTestFilter& filter,
entity_pos_t x0, entity_pos_t z0, entity_pos_t r,
entity_pos_t range, const Goal& goal, pass_class_t passClass, Path& path)
{
UpdateGrid(); // TODO: only need to bother updating if the terrain changed
PROFILE("ComputeShortPath");
// ScopeTimer UID__(L"ComputeShortPath");
m_DebugOverlayShortPathLines.clear();
if (m_DebugOverlay)
{
// Render the goal shape
m_DebugOverlayShortPathLines.push_back(SOverlayLine());
m_DebugOverlayShortPathLines.back().m_Color = CColor(1, 0, 0, 1);
switch (goal.type)
{
case CCmpPathfinder::Goal::POINT:
{
SimRender::ConstructCircleOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), 0.2f, m_DebugOverlayShortPathLines.back(), true);
break;
}
case CCmpPathfinder::Goal::CIRCLE:
{
SimRender::ConstructCircleOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), goal.hw.ToFloat(), m_DebugOverlayShortPathLines.back(), true);
break;
}
case CCmpPathfinder::Goal::SQUARE:
{
float a = atan2f(goal.v.X.ToFloat(), goal.v.Y.ToFloat());
SimRender::ConstructSquareOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), goal.hw.ToFloat()*2, goal.hh.ToFloat()*2, a, m_DebugOverlayShortPathLines.back(), true);
break;
}
}
}
// List of collision edges - paths must never cross these.
// (Edges are one-sided so intersections are fine in one direction, but not the other direction.)
std::vector<Edge> edges;
std::vector<Edge> edgesAA; // axis-aligned squares
// Create impassable edges at the max-range boundary, so we can't escape the region
// where we're meant to be searching
fixed rangeXMin = x0 - range;
fixed rangeXMax = x0 + range;
fixed rangeZMin = z0 - range;
fixed rangeZMax = z0 + range;
{
// (The edges are the opposite direction to usual, so it's an inside-out square)
Edge e0 = { CFixedVector2D(rangeXMin, rangeZMin), CFixedVector2D(rangeXMin, rangeZMax) };
Edge e1 = { CFixedVector2D(rangeXMin, rangeZMax), CFixedVector2D(rangeXMax, rangeZMax) };
Edge e2 = { CFixedVector2D(rangeXMax, rangeZMax), CFixedVector2D(rangeXMax, rangeZMin) };
Edge e3 = { CFixedVector2D(rangeXMax, rangeZMin), CFixedVector2D(rangeXMin, rangeZMin) };
edges.push_back(e0);
edges.push_back(e1);
edges.push_back(e2);
edges.push_back(e3);
}
// List of obstruction vertexes (plus start/end points); we'll try to find paths through
// the graph defined by these vertexes
std::vector<Vertex> vertexes;
// Add the start point to the graph
CFixedVector2D posStart(x0, z0);
fixed hStart = (posStart - NearestPointOnGoal(posStart, goal)).Length();
Vertex start = { posStart, fixed::Zero(), hStart, 0, Vertex::OPEN, QUADRANT_NONE, QUADRANT_ALL };
vertexes.push_back(start);
const size_t START_VERTEX_ID = 0;
// Add the goal vertex to the graph.
// Since the goal isn't always a point, this a special magic virtual vertex which moves around - whenever
// we look at it from another vertex, it is moved to be the closest point on the goal shape to that vertex.
Vertex end = { CFixedVector2D(goal.x, goal.z), fixed::Zero(), fixed::Zero(), 0, Vertex::UNEXPLORED, QUADRANT_NONE, QUADRANT_ALL };
vertexes.push_back(end);
const size_t GOAL_VERTEX_ID = 1;
// Add terrain obstructions
{
u16 i0, j0, i1, j1;
NearestTile(rangeXMin, rangeZMin, i0, j0);
NearestTile(rangeXMax, rangeZMax, i1, j1);
AddTerrainEdges(edgesAA, vertexes, i0, j0, i1, j1, r, passClass, *m_Grid);
}
// Find all the obstruction squares that might affect us
CmpPtr<ICmpObstructionManager> cmpObstructionManager(GetSimContext(), SYSTEM_ENTITY);
std::vector<ICmpObstructionManager::ObstructionSquare> squares;
cmpObstructionManager->GetObstructionsInRange(filter, rangeXMin - r, rangeZMin - r, rangeXMax + r, rangeZMax + r, squares);
// Resize arrays to reduce reallocations
vertexes.reserve(vertexes.size() + squares.size()*4);
edgesAA.reserve(edgesAA.size() + squares.size()); // (assume most squares are AA)
// Convert each obstruction square into collision edges and search graph vertexes
for (size_t i = 0; i < squares.size(); ++i)
{
CFixedVector2D center(squares[i].x, squares[i].z);
CFixedVector2D u = squares[i].u;
CFixedVector2D v = squares[i].v;
// Expand the vertexes by the moving unit's collision radius, to find the
// closest we can get to it
CFixedVector2D hd0(squares[i].hw + r + EDGE_EXPAND_DELTA, squares[i].hh + r + EDGE_EXPAND_DELTA);
CFixedVector2D hd1(squares[i].hw + r + EDGE_EXPAND_DELTA, -(squares[i].hh + r + EDGE_EXPAND_DELTA));
// Check whether this is an axis-aligned square
bool aa = (u.X == fixed::FromInt(1) && u.Y == fixed::Zero() && v.X == fixed::Zero() && v.Y == fixed::FromInt(1));
Vertex vert;
vert.status = Vertex::UNEXPLORED;
vert.quadInward = QUADRANT_NONE;
vert.quadOutward = QUADRANT_ALL;
vert.p.X = center.X - hd0.Dot(u); vert.p.Y = center.Y + hd0.Dot(v); if (aa) vert.quadInward = QUADRANT_BR; vertexes.push_back(vert);
vert.p.X = center.X - hd1.Dot(u); vert.p.Y = center.Y + hd1.Dot(v); if (aa) vert.quadInward = QUADRANT_TR; vertexes.push_back(vert);
vert.p.X = center.X + hd0.Dot(u); vert.p.Y = center.Y - hd0.Dot(v); if (aa) vert.quadInward = QUADRANT_TL; vertexes.push_back(vert);
vert.p.X = center.X + hd1.Dot(u); vert.p.Y = center.Y - hd1.Dot(v); if (aa) vert.quadInward = QUADRANT_BL; vertexes.push_back(vert);
// Add the edges:
CFixedVector2D h0(squares[i].hw + r, squares[i].hh + r);
CFixedVector2D h1(squares[i].hw + r, -(squares[i].hh + r));
CFixedVector2D ev0(center.X - h0.Dot(u), center.Y + h0.Dot(v));
CFixedVector2D ev1(center.X - h1.Dot(u), center.Y + h1.Dot(v));
CFixedVector2D ev2(center.X + h0.Dot(u), center.Y - h0.Dot(v));
CFixedVector2D ev3(center.X + h1.Dot(u), center.Y - h1.Dot(v));
if (aa)
{
Edge e = { ev1, ev3 };
edgesAA.push_back(e);
}
else
{
Edge e0 = { ev0, ev1 };
Edge e1 = { ev1, ev2 };
Edge e2 = { ev2, ev3 };
Edge e3 = { ev3, ev0 };
edges.push_back(e0);
edges.push_back(e1);
edges.push_back(e2);
edges.push_back(e3);
}
// TODO: should clip out vertexes and edges that are outside the range,
// to reduce the search space
}
ENSURE(vertexes.size() < 65536); // we store array indexes as u16
if (m_DebugOverlay)
{
// Render the obstruction edges
for (size_t i = 0; i < edges.size(); ++i)
{
m_DebugOverlayShortPathLines.push_back(SOverlayLine());
m_DebugOverlayShortPathLines.back().m_Color = CColor(0, 1, 1, 1);
std::vector<float> xz;
xz.push_back(edges[i].p0.X.ToFloat());
xz.push_back(edges[i].p0.Y.ToFloat());
xz.push_back(edges[i].p1.X.ToFloat());
xz.push_back(edges[i].p1.Y.ToFloat());
SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), true);
}
for (size_t i = 0; i < edgesAA.size(); ++i)
{
m_DebugOverlayShortPathLines.push_back(SOverlayLine());
m_DebugOverlayShortPathLines.back().m_Color = CColor(0, 1, 1, 1);
std::vector<float> xz;
xz.push_back(edgesAA[i].p0.X.ToFloat());
xz.push_back(edgesAA[i].p0.Y.ToFloat());
xz.push_back(edgesAA[i].p0.X.ToFloat());
xz.push_back(edgesAA[i].p1.Y.ToFloat());
xz.push_back(edgesAA[i].p1.X.ToFloat());
xz.push_back(edgesAA[i].p1.Y.ToFloat());
xz.push_back(edgesAA[i].p1.X.ToFloat());
xz.push_back(edgesAA[i].p0.Y.ToFloat());
xz.push_back(edgesAA[i].p0.X.ToFloat());
xz.push_back(edgesAA[i].p0.Y.ToFloat());
SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), true);
}
}
// Do an A* search over the vertex/visibility graph:
// Since we are just measuring Euclidean distance the heuristic is admissible,
// so we never have to re-examine a node once it's been moved to the closed set.
// To save time in common cases, we don't precompute a graph of valid edges between vertexes;
// we do it lazily instead. When the search algorithm reaches a vertex, we examine every other
// vertex and see if we can reach it without hitting any collision edges, and ignore the ones
// we can't reach. Since the algorithm can only reach a vertex once (and then it'll be marked
// as closed), we won't be doing any redundant visibility computations.
PROFILE_START("A*");
PriorityQueue open;
PriorityQueue::Item qiStart = { START_VERTEX_ID, start.h };
open.push(qiStart);
u16 idBest = START_VERTEX_ID;
fixed hBest = start.h;
while (!open.empty())
{
// Move best tile from open to closed
PriorityQueue::Item curr = open.pop();
vertexes[curr.id].status = Vertex::CLOSED;
// If we've reached the destination, stop
if (curr.id == GOAL_VERTEX_ID)
{
idBest = curr.id;
break;
}
// Sort the edges so ones nearer this vertex are checked first by CheckVisibility,
// since they're more likely to block the rays
std::sort(edgesAA.begin(), edgesAA.end(), EdgeSort(vertexes[curr.id].p));
std::vector<EdgeAA> edgesLeft;
std::vector<EdgeAA> edgesRight;
std::vector<EdgeAA> edgesBottom;
std::vector<EdgeAA> edgesTop;
SplitAAEdges(vertexes[curr.id].p, edgesAA, edgesLeft, edgesRight, edgesBottom, edgesTop);
// Check the lines to every other vertex
for (size_t n = 0; n < vertexes.size(); ++n)
{
if (vertexes[n].status == Vertex::CLOSED)
continue;
// If this is the magical goal vertex, move it to near the current vertex
CFixedVector2D npos;
if (n == GOAL_VERTEX_ID)
{
npos = NearestPointOnGoal(vertexes[curr.id].p, goal);
// To prevent integer overflows later on, we need to ensure all vertexes are
// 'close' to the source. The goal might be far away (not a good idea but
// sometimes it happens), so clamp it to the current search range
npos.X = clamp(npos.X, rangeXMin, rangeXMax);
npos.Y = clamp(npos.Y, rangeZMin, rangeZMax);
}
else
{
npos = vertexes[n].p;
}
// Work out which quadrant(s) we're approaching the new vertex from
u8 quad = 0;
if (vertexes[curr.id].p.X <= npos.X && vertexes[curr.id].p.Y <= npos.Y) quad |= QUADRANT_BL;
if (vertexes[curr.id].p.X >= npos.X && vertexes[curr.id].p.Y >= npos.Y) quad |= QUADRANT_TR;
if (vertexes[curr.id].p.X <= npos.X && vertexes[curr.id].p.Y >= npos.Y) quad |= QUADRANT_TL;
if (vertexes[curr.id].p.X >= npos.X && vertexes[curr.id].p.Y <= npos.Y) quad |= QUADRANT_BR;
// Check that the new vertex is in the right quadrant for the old vertex
if (!(vertexes[curr.id].quadOutward & quad))
{
// Hack: Always head towards the goal if possible, to avoid missing it if it's
// inside another unit
if (n != GOAL_VERTEX_ID)
{
continue;
}
}
bool visible =
CheckVisibilityLeft(vertexes[curr.id].p, npos, edgesLeft) &&
CheckVisibilityRight(vertexes[curr.id].p, npos, edgesRight) &&
CheckVisibilityBottom(vertexes[curr.id].p, npos, edgesBottom) &&
CheckVisibilityTop(vertexes[curr.id].p, npos, edgesTop) &&
CheckVisibility(vertexes[curr.id].p, npos, edges);
/*
// Render the edges that we examine
m_DebugOverlayShortPathLines.push_back(SOverlayLine());
m_DebugOverlayShortPathLines.back().m_Color = visible ? CColor(0, 1, 0, 0.5) : CColor(1, 0, 0, 0.5);
std::vector<float> xz;
xz.push_back(vertexes[curr.id].p.X.ToFloat());
xz.push_back(vertexes[curr.id].p.Y.ToFloat());
xz.push_back(npos.X.ToFloat());
xz.push_back(npos.Y.ToFloat());
SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), false);
//*/
if (visible)
{
fixed g = vertexes[curr.id].g + (vertexes[curr.id].p - npos).Length();
// If this is a new tile, compute the heuristic distance
if (vertexes[n].status == Vertex::UNEXPLORED)
{
// Add it to the open list:
vertexes[n].status = Vertex::OPEN;
vertexes[n].g = g;
vertexes[n].h = DistanceToGoal(npos, goal);
vertexes[n].pred = curr.id;
// If this is an axis-aligned shape, the path must continue in the same quadrant
// direction (but not go into the inside of the shape).
// Hack: If we started *inside* a shape then perhaps headed to its corner (e.g. the unit
// was very near another unit), don't restrict further pathing.
if (vertexes[n].quadInward && !(curr.id == START_VERTEX_ID && g < fixed::FromInt(8)))
vertexes[n].quadOutward = ((~vertexes[n].quadInward) & quad) & 0xF;
if (n == GOAL_VERTEX_ID)
vertexes[n].p = npos; // remember the new best goal position
PriorityQueue::Item t = { (u16)n, g + vertexes[n].h };
open.push(t);
// Remember the heuristically best vertex we've seen so far, in case we never actually reach the target
if (vertexes[n].h < hBest)
{
idBest = (u16)n;
hBest = vertexes[n].h;
}
}
else // must be OPEN
{
// If we've already seen this tile, and the new path to this tile does not have a
// better cost, then stop now
if (g >= vertexes[n].g)
continue;
// Otherwise, we have a better path, so replace the old one with the new cost/parent
vertexes[n].g = g;
vertexes[n].pred = curr.id;
// If this is an axis-aligned shape, the path must continue in the same quadrant
// direction (but not go into the inside of the shape).
if (vertexes[n].quadInward)
vertexes[n].quadOutward = ((~vertexes[n].quadInward) & quad) & 0xF;
if (n == GOAL_VERTEX_ID)
vertexes[n].p = npos; // remember the new best goal position
open.promote((u16)n, g + vertexes[n].h);
}
}
}
}
// Reconstruct the path (in reverse)
for (u16 id = idBest; id != START_VERTEX_ID; id = vertexes[id].pred)
{
Waypoint w = { vertexes[id].p.X, vertexes[id].p.Y };
path.m_Waypoints.push_back(w);
}
PROFILE_END("A*");
}
