AStarPathUtil class provides a facility for
* finding a reasonable path between two points in a scene using the
* A* search algorithm.
*
* See the path-finding article on
*
* Gamasutra for more detailed information.
*/
public class AStarPathUtil
{
/**
* Return a list of Point objects representing a path
* from coordinates (ax, by) to (bx, by),
* inclusive, determined by performing an A* search in the given
* scene's base tile layer. Assumes the starting and destination nodes
* are traversable by the specified traverser.
*
* @param scene the scene in which a path is to be computed.
* @param tilewid the scene width in tiles.
* @param tilehei the scene height in tiles.
* @param trav the traverser to follow the path.
* @param ax the starting x-position in tile coordinates.
* @param ay the starting y-position in tile coordinates.
* @param bx the ending x-position in tile coordinates.
* @param by the ending y-position in tile coordinates.
*
* @return the list of points in the path.
*/
public static List getPath (
DisplayMisoScene scene, int tilewid, int tilehei, Traverser trav,
int ax, int ay, int bx, int by)
{
AStarInfo info = new AStarInfo(scene, tilewid, tilehei, trav, bx, by);
// set up the starting node
AStarNode s = info.getNode(ax, ay);
s.g = 0;
s.h = getDistanceEstimate(ax, ay, bx, by);
s.f = s.g + s.h;
// push starting node on the open list
info.open.add(s);
// while there are more nodes on the open list
while (info.open.size() > 0) {
// pop the best node so far from open
AStarNode n = (AStarNode)info.open.first();
info.open.remove(n);
// if node is a goal node
if (n.x == bx && n.y == by) {
// construct and return the acceptable path
return getNodePath(n);
}
// consider each successor of the node
considerStep(info, n, n.x - 1, n.y - 1, DIAGONAL_COST);
considerStep(info, n, n.x, n.y - 1, ADJACENT_COST);
considerStep(info, n, n.x + 1, n.y - 1, DIAGONAL_COST);
considerStep(info, n, n.x - 1, n.y, ADJACENT_COST);
considerStep(info, n, n.x + 1, n.y, ADJACENT_COST);
considerStep(info, n, n.x - 1, n.y + 1, DIAGONAL_COST);
considerStep(info, n, n.x, n.y + 1, ADJACENT_COST);
considerStep(info, n, n.x + 1, n.y + 1, DIAGONAL_COST);
// push the node on the closed list
info.closed.add(n);
}
// no path found
return null;
}
/**
* Consider the step (n.x, n.y) to (x, y)
* for possible inclusion in the path.
*
* @param info the info object.
* @param n the originating node for the step.
* @param x the x-coordinate for the destination step.
* @param y the y-coordinate for the destination step.
*/
protected static void considerStep (
AStarInfo info, AStarNode n, int x, int y, int cost)
{
// skip node if it's outside the map bounds or otherwise impassable
if (!info.isStepValid(n.x, n.y, x, y)) {
return;
}
// if it's offscreen, bang up the cost considerably
if (!info.isCoordinateValid(x, y)) {
cost += OFFSCREEN_COST;
}
// calculate the new cost for this node
int newg = n.g + cost;
// make sure the cost is reasonable (so we don't go crazy computing
// offscreen costs)
if (newg > info.maxcost) {
// Log.info("Rejected costly step.");
return;
}
// retrieve the node corresponding to this location
AStarNode np = info.getNode(x, y);
// skip if it's already in the open or closed list or if its
// actual cost is less than the just-calculated cost
if ((info.open.contains(np) || info.closed.contains(np)) &&
np.g <= newg) {
return;
}
// remove the node from the open list since we're about to
// modify its score which determines its placement in the list
info.open.remove(np);
// update the node's information
np.parent = n;
np.g = newg;
np.h = getDistanceEstimate(np.x, np.y, info.destx, info.desty);
np.f = np.g + np.h;
// remove it from the closed list if it's present
info.closed.remove(np);
// add it to the open list for further consideration
info.open.add(np);
}
/**
* Return a list of Point objects detailing the path
* from the first node (the given node's ultimate parent) to the
* ending node (the given node itself.)
*
* @param n the ending node in the path.
*
* @return the list detailing the path.
*/
protected static List getNodePath (AStarNode n)
{
AStarNode cur = n;
ArrayList path = new ArrayList();
while (cur != null) {
// add to the head of the list since we're traversing from
// the end to the beginning
path.add(0, new Point(cur.x, cur.y));
// advance to the next node in the path
cur = cur.parent;
}
return path;
}
/**
* Return a heuristic estimate of the cost to get from (ax,
* ay) to (bx, by).
*/
protected static int getDistanceEstimate (int ax, int ay, int bx, int by)
{
// we're doing all of our cost calculations based on geometric
// distance times ten
int xsq = bx - ax;
int ysq = by - ay;
return (int) (ADJACENT_COST * Math.sqrt(xsq * xsq + ysq * ysq));
}
/** The standard cost to move between nodes. */
public static final int ADJACENT_COST = 10;
/** The cost to move diagonally. */
public static final int DIAGONAL_COST = (int) Math.sqrt(
(ADJACENT_COST * ADJACENT_COST) * 2);
/** A big old additional cost incurred for offscreen movement. */
public static final int OFFSCREEN_COST = 1000;
}
/**
* A holding class to contain the wealth of information referenced
* while performing an A* search for a path through a tile array.
*/
class AStarInfo
{
/** The scene whose base tile layer is being traversed. */
public DisplayMisoScene scene;
/** The tile array dimensions. */
public int tilewid, tilehei;
/** The traverser moving along the path. */
public Traverser trav;
/** The set of open nodes being searched. */
public SortedSet open;
/** The set of closed nodes being searched. */
public ArrayList closed;
/** The destination coordinates in the tile array. */
public int destx, desty;
/** The maximum cost of any path that we'll consider. */
public int maxcost;
public AStarInfo (
DisplayMisoScene scene, int tilewid, int tilehei, Traverser trav,
int destx, int desty)
{
// save off references
this.scene = scene;
this.tilewid = tilewid;
this.tilehei = tilehei;
this.trav = trav;
this.destx = destx;
this.desty = desty;
// compute the maximum cost as the maximum onscreen path plus
// the maximum offscreen cost
this.maxcost = ((tilewid + tilehei) * AStarPathUtil.ADJACENT_COST) +
MAX_OFFSCREEN * AStarPathUtil.OFFSCREEN_COST;
// construct the open and closed lists
open = new TreeSet();
closed = new ArrayList();
}
/**
* Returns whether the given coordinate is valid based on the
* dimensions of the map being traversed.
*/
protected boolean isCoordinateValid (int x, int y)
{
return (x >= 0 && y >= 0 && x < tilewid && y < tilehei);
}
/**
* Returns whether moving from the given source to destination
* coordinates is a valid move.
*/
protected boolean isStepValid (int sx, int sy, int dx, int dy)
{
// not traversable if the destination itself fails test
if (!isTraversable(dx, dy)) {
return false;
}
// if the step is diagonal, make sure the corners don't impede
// our progress
if ((Math.abs(dx - sx) == 1) && (Math.abs(dy - sy) == 1)) {
return isTraversable(dx, sy) && isTraversable(sx, dy);
}
// non-diagonals are always traversable
return true;
}
/**
* Returns whether the given coordinate is valid and traversable.
*/
protected boolean isTraversable (int x, int y)
{
if (isCoordinateValid(x, y)) {
BaseTile tile = scene.getBaseTile(x, y);
return (tile == null) || trav.canTraverse(tile);
}
return true;
}
/**
* Get or create the node for the specified point.
*/
public AStarNode getNode (int x, int y)
{
// note: this _could_ break for unusual values of x and y.
// perhaps use a IntTuple as a key? Bleah.
int key = (x << 16) | (y & 0xffff);
AStarNode node = (AStarNode) _nodes.get(key);
if (node == null) {
node = new AStarNode(x, y);
_nodes.put(key, node);
}
return node;
}
/** The nodes being considered in the path. */
protected HashIntMap _nodes = new HashIntMap();
/** The maximum number of offscreen points we'll consider. */
protected static final int MAX_OFFSCREEN = 6;
}
/**
* A class that represents a single traversable node in the tile array
* along with its current A*-specific search information.
*/
class AStarNode implements Comparable
{
/** The node coordinates. */
public int x, y;
/** The actual cheapest cost of arriving here from the start. */
public int g;
/** The heuristic estimate of the cost to the goal from here. */
public int h;
/** The score assigned to this node. */
public int f;
/** The node from which we reached this node. */
public AStarNode parent;
/** The node's monotonically-increasing unique identifier. */
public int id;
public AStarNode (int x, int y)
{
this.x = x;
this.y = y;
id = _nextid++;
}
public int compareTo (Object o)
{
int bf = ((AStarNode)o).f;
// since the set contract is fulfilled using the equality results
// returned here, and we'd like to allow multiple nodes with
// equivalent scores in our set, we explicitly define object
// equivalence as the result of object.equals(), else we use the
// unique node id since it will return a consistent ordering for
// the objects.
if (f == bf) {
return (this == o) ? 0 : (id - ((AStarNode)o).id);
}
return f - bf;
}
/** The next unique node id. */
protected static int _nextid = 0;
}