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<span id="Path-Finding"></span><div class="header">
<p>
Previous: <a href="Bezier-Curves.html" accesskey="p" rel="prev">Bezier Curves</a>, Up: <a href="Math.html" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html" title="Index" rel="index">Index</a>]</p>
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<hr>
<span id="Path-Finding-1"></span><h4 class="subsection">2.2.9 Path Finding</h4>
<p>Most game worlds have maps. Often, these games have a need to move
non-player characters around in an unscripted fashion. For example,
in a real-time strategy game, the player may command one of their
units to attack something in the enemy base. To do so, the unit must
calculate the shortest route to get there. It wouldn’t be a very fun
game if units didn’t know how to transport themselves efficiently.
This is where path finding algorithms come in handy. The
<code>(chickadee math path-finding)</code> module provides a generic
implementation of the popular A* path finding algorithm. Just add a
map implementation!
</p>
<p>The example below defines a very simple town map and finds the
quickest way to get from the town common to the school.
</p>
<div class="example">
<pre class="example">(define world-map
'((town-common . (town-hall library))
(town-hall . (town-common school))
(library . (town-common cafe))
(school . (town-hall cafe))
(cafe . (library school))))
(define (neighbors building)
(assq-ref town-map building))
(define (cost a b) 1)
(define (distance a b) 1)
(define pf (make-path-finder))
(a* pf 'town-common 'school neighbors cost distance)
</pre></div>
<p>In this case, the <code>a*</code> procedure will return the list
<code>(town-common town-hall school)</code>, which is indeed the shortest
route. (The other possible route is <code>(town-common library cafe
school)</code>.)
</p>
<p>The <code>a*</code> procedure does not know anything about about any kind of
map and therefore must be told how to look up neighboring nodes, which
is what the <code>neighbors</code> procedure in the example does. To
simulate different types of terrain, a cost procedure is used. In
this example, it is just as easy to move between any two nodes because
<code>cost</code> always returns 1. In a real game, perhaps moving from
from a field to a rocky hill would cost a lot more than moving from
one field to another. Finally, a heuristic is used to calculate an
approximate distance between two nodes on the map. In this simple
association list based graph it is tough to calculate a distance
between nodes, so the <code>distance</code> procedure isn’t helpful and
always returns 1. In a real game with a tile-based map, for example,
the heuristic could be a quick Manhattan distance calculation based on
the coordinates of the two map tiles. Choose an appropriate heuristic
for optimal path finding!
</p>
<dl>
<dt id="index-make_002dpath_002dfinder">Procedure: <strong>make-path-finder</strong></dt>
<dd><p>Return a new path finder object.
</p></dd></dl>
<dl>
<dt id="index-path_002dfinder_003f">Procedure: <strong>path-finder?</strong> <em>obj</em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a path finder.
</p></dd></dl>
<dl>
<dt id="index-a_002a">Procedure: <strong>a*</strong> <em>path-finder start goal neighbors cost distance</em></dt>
<dd>
<p>Return a list of nodes forming a path from <var>start</var> to <var>goal</var>
using <var>path-finder</var> to hold state. <var>neighbors</var> is a procedure
that accepts a node and returns a list of nodes that neighbor it.
<var>cost</var> is a procedure that accepts two neighboring nodes and
returns the cost of moving from the first to the second as a real
number. <var>distance</var> is a procedure that accepts two nodes and
returns an approximate distance between them.
</p></dd></dl>
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