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<p> When I realized my grade as a decorator, I ne'er considered I 'd fetch up penning a blog station about AI. Withal, I took a scissure at inditing an A* ( A-star ) pathfinding algorithm about five ages ago for the avatar move system in the first contemporaries of the <a href="http://lassie.gmacwill.com" title="Lassie Adventure Sudtio">Lassie Engine</a>
( maked employing Macromedia Manager and Slang ). My total root of mention for that first execution was <a href="http://ai-depot.com/Tutorial/PathFinding.html" title="The Beginners" guide="Guide" to="to" pathfinding="Pathfinding" algorithms'="Algorithms'">The Beginner's Guide to Pathfinding Algorithms</a>
If you 're interested in pathfinding theory, that article is an absolute gold mine. I wo n't even sham that I could make a better occupation of explicating the algorithm 's nuts and thunderbolts, so I 'll simply lodge to what an AS3 execution looks like. </p>
<p> Foremost, we require a information construction of a grid to run hunts across. I 'm generally pulled to XML for natural data constructions like this since it Holds easy to compose and keep by manus. Here Holds a simple XML grid of points: </p>
<p><strong> Salvage as: </strong>
grid.xml </p>
<pre><nodes>
<node id="n1" x="25" y="25" join="n2,n3"/>
<node id="n2" x="110" y="110" join="n1,n3,n4"/>
<node id="n3" x="50" y="180" join="n1,n2,n5,n6"/>
<node id="n4" x="225" y="90" join="n2,n5,n6"/>
<node id="n5" x="190" y="160" join="n3,n4"/>
<node id="n6" x="230" y="170" join="n3,n4"/>
</nodes></pre>
<p> The above XML makes a grid that looks like this: </p>
<p style="text-align:center;"><img width="275" alt="demo grid of points" src="http://lassieadventurestudio.files.wordpress.com/2008/12/grid.png?w=275h=219" title="Grid" height="219"></p>
<p> That XML construction is highly simple. Each node is given an Idaho, an Ten and Yttrium co-ordinate, and holds a comma-separated listing of other node ID Holds that it ties to. </p>
<p> Next, we advance to the simple geometry structures that we 'll feed into our guide. First is the Node object. While we 'll lade our grid data as XML, we 'll desire to parse that into typed Objects to give our execution compile-time substantiation. So, we 'd lade our XML so parse the nodes into this construction: </p>
<p><strong> Relieve as: </strong>
com/lassie/player/geom/Node.as </p>
<pre>package com.lassie.player.geom
{
import flash.geom.Point;
public final class Node extends Point
{
// public
public var id:String = "";
// private
private var _neighbors:Array;
public function Node(key:String="", x:int=0, y:int=0):void
{
super(x, y);
id = key;
_neighbors = new Array();
}
/*
* Returns all current data as a new Node object.
*/
public function cloneNode():Node
{
var node:Node = new Node(id, x, y);
node.parseNeighbors(_neighbors.join(","));
return node;
}
/*
* Parses a list of comma-seperated node id's into the array of neighbors.
*/
public function parseNeighbors(csv:String):void
{
for each (var j:String in csv.split(",")) addNeighbor(j);
}
/*
* Adds a new neighbor Id.
*/
public function addNeighbor(id:String):void
{
if (!containsNeighbor(id) && id != "") _neighbors.push(id);
}
/*
* Gets a neightbor Id by numeric index.
*/
public function getNeighbor(index:int):String
{
if (index >= 0 && index < _neighbors.length) return _neighbors[index];
return null;
}
/*
* Gets the number of neighbors assigned to this node.
*/
public function get numNeighbors():int
{
return _neighbors.length;
}
/*
* Tests if the specified node id is among this node's neighbors.
*/
public function containsNeighbor(id:String):Boolean
{
return _neighbors.indexOf(id) > -1;
}
/*
* Appends an additional namespace key onto all Node references. Avoids conflicts during Grid unions.
*/
public function expandNamespace(key:String):void
{
id += key;
for each (var j:String in _neighbors) j += key;
}
/*
* Trace object to string.
*/
public override function toString():String
{
return "[Node] id:"+ id +", x:" + x + ", y:" + y + ", neighbors:(" + _neighbors + ")";
}
}
}</pre>
<p> Now we take a Way object. Ways will be the existent hunting paths that our A* algorithm will make, arm, prioritise, and purgation as it works. Here Holds the Way category: </p>
<p><strong> Salve as: </strong>
com/lassie/player/geom/Path.as </p>
<pre>package com.lassie.player.geom
{
public final class Path
{
// public
public var length:int = -1;
public var bestCase:int = -1;
public var nodes:Array;
// private
private var _path:Array;
public function Path($length:Number=-1, $bestCase:Number=-1, $path:Array=null):void
{
length = $length;
bestCase = $bestCase;
_path = ($path != null) ? $path : new Array();
}
public function destroy():void
{
_path = null;
nodes = null;
}
/*
* Returns all current data as a new Path object.
*/
public function clone():Path
{
return new Path(length, bestCase, _path.slice());
}
/*
* Tests if path has been initialized with actual pathing data.
*/
public function get hasLength():Boolean
{
return length + bestCase >= 0;
}
/*
* Returns the last node id contained within the path.
*/
public function get lastElement():String
{
return _path.slice(-1)[0];
}
/*
* Tests if this path contains a node Id.
*/
public function containsNode($id:String):Boolean
{
return _path.indexOf($id) > -1;
}
/*
* Adds a node to the path if not already present.
*/
public function addNode($id:String):void
{
if (!containsNode($id)) _path.push($id);
}
/*
* Trace object to string.
*/
public function toString():String
{
return "[Path] length:"+ length +", nodes:("+ _path +")";
}
}
}</pre>
<p> And eventually we ask a grid family. A Grid will keep Nodes, keyed by their respective Idaho 's, and will hold the existent A* execution within it to make the heavy lifting of grid hunts. </p>
<p><strong> Relieve as: </strong>
com/lassie/player/geom/Grid.as </p>
<pre>package com.lassie.player.geom
{
import flash.geom.Point;
public final class Grid extends Object
{
private var _nodes:Object;
public function Grid():void
{
super();
_nodes = new Object();
}
/*
* Parses an XML structure into the grid object.
*/
public function parseXML($xml:XML):void
{
// loop through all <node> XML items
for each (var $nodeXML in $xml.children())
{
// create a new Node object for each XML item
var $node:Node = new Node($nodeXML.@id, $nodeXML.@x, $nodeXML.@y);
$node.parseNeighbors($nodeXML.@join);
// register node by Id within the grid
_nodes[$node.id] = $node;
}
}
/*
* Gets a node object by ID name
*/
public function getNodeById($id:String):Node
{
if (_nodes[$id] != undefined) return _nodes[$id] as Node;
return null;
}
/*
* Finds the shortest path between two nodes.
*/
public function findPath($startId:String, $goalId:String):Path
{
// queue of paths to search
var $stack:Array = new Array(new Path(0, 0, [$startId]));
// best path to goal
var $best:Path = new Path();
// shortest distance to each node reached thus far
var $reachedNodes:Object = new Object();
// cycle counter (for debug and optimization)
var $cyc:int = 0;
// UNTIL ALL SEARCH PATHS HAVE BEEN ELIMINATED
while ($stack.length > 0)
{
// pull the first path out from the search stack
var $searchPath:Path = $stack.shift() as Path;
// pull the last node element from the path
var $searchNode:Node = getNodeById($searchPath.lastElement);
// EXTEND PATH ONE STEP TO ALL NEIGHBORS
// creating X new paths
for (var j:int=0; j < $searchNode.numNeighbors; j++)
{
// Branch: duplicate current search path as a new branch
var $branch:Path = $searchPath.clone();
// Pull and expand upon each of searchNode's neighbor Id's.
var $expandNode:String = $searchNode.getNeighbor(j);
// REJECT PATHS WITH LOOPS
// if branch does NOT already contain next search node
if (!$branch.containsNode($expandNode))
{
// get coordinates of previous, current, and goal nodes
var $prevCoord:Node = getNodeById($branch.lastElement);
var $currentCoord:Node = getNodeById($expandNode);
var $goalCoord:Node = getNodeById($goalId);
// extend branch after having referenced last end-point.
$branch.addNode($expandNode);
// UPDATE BRANCH LENGTH AND UNDERESTIMATE
$branch.length += Point.distance($prevCoord, $currentCoord);
$branch.bestCase = $branch.length + Point.distance($currentCoord, $goalCoord);
// TRACK SHORTEST DISTANCE TO EACH NODE REACHED
// attempt to pull a distance-to-node from the register of reached nodes.
// if node has not yet been reached, register it with the current branch length.
var $shortest:Number = $reachedNodes[$expandNode];
if (isNaN($shortest)) $shortest = $branch.length;
// TEST IF PATH IS WORTH KEEPING (keep if:)
// - if branch is as short or shorter than the best distance to the current expansion node
// - and if a best-path has not been found yet, OR if this branch's best case scenario is still shorter than the best path.
if ($branch.length <= $shortest && (!$best.hasLength || $branch.bestCase < $best.length))
{
// log as best path to current search node
$reachedNodes[$expandNode] = $branch.length;
// If the expansion node is the goal, save branch as the parth to beat.
// Otherwise, add the branch back into the search stack.
if ($expandNode == $goalId) $best = $branch;
else $stack.push($branch);
}
}
}
// PRIORITIZE SEARCH PATHS
// sort paths by best-case scenario so that most likely paths are searched first.
var $priority:Function = function($a:Path, $b:Path):int
{
if ($a.bestCase < $b.bestCase) return -1;
else if ($a.bestCase > $b.bestCase) return 1;
else return 0;
}
$stack.sort($priority);
$cyc++;
}
return $best;
}
}
}</pre>
<p> Now allow 's set all that together. Make a new Flash papers in the root of your family way and layed that ``grid.xml '' file in with it. So in frame-1 actions of the root timeline, merely add the followers: </p>
<pre>import com.lassie.player.geom.Grid;
var $xmlLoader:URLLoader = new URLLoader();
$xmlLoader.addEventListener(Event.COMPLETE, this._onXMLLoaded);
$xmlLoader.load(new URLRequest("grid.xml"));
function _onXMLLoaded($event:Event):void
{
// retrieve the loaded XML data
var $xml:XML = new XML($event.target.data);
// create a new grid and parse the loaded XML into it.
var $grid:Grid = new Grid();
$grid.parseXML($xml);
// find a path between two node Id's
trace($grid.findPath("n1", "n5"));
trace($grid.findPath("n1", "n6"));
}</pre>
<p> If you run that playscript as is, you should get the undermentioned output: </p>
<pre>[Path] length:298, nodes:(n1,n3,n5)
[Path] length:316, nodes:(n1,n2,n4,n6)</pre>
<p> Those are hints of two separate way huntings meet the grid. The first hunting linked n1 and n5 to one another through their common neighbour of n3. The 2nd hunt took a dramatically different itinerary from n1 to n6 that ramified through n2 and n4. Why? Because it was slightly shorter to run through two connexion instead take the individual connexion through n3. </p>
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