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Next: <a href="Matrices.html#Matrices" accesskey="n" rel="next">Matrices</a>, Previous: <a href="Rectangles.html#Rectangles" accesskey="p" rel="prev">Rectangles</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html#Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Grid-1"></a>
<h4 class="subsection">2.2.4 Grid</h4>
<p>The <code>(chickadee math grid)</code> module provides a simple spatial
partitioning system for axis-aligned bounding boxes
(see <a href="Rectangles.html#Rectangles">Rectangles</a>) in 2D space. The grid divides the world into
tiles and keeps track of which rectangles occupy which tiles. When
there are lots of moving objects in the game world that need collision
detection, the grid greatly speeds up the process. Instead of
checking collisions of each object against every other object (an
O(n^2) operation), the grid quickly narrows down which objects could
possibly be colliding and only performs collision testing against a
small set of objects.
</p>
<p>In addition to checking for collisions, the grid also handles the
resolution of collisions. Exactly how each collision is resolved is
user-defined. A player bumping into a wall may slide against it. An
enemy colliding with a projectile shot by the player may get pushed
back in the opposite direction. Two players colliding may not need
resolution at all and will just pass through each other. The way this
works is that each time an object (A) is moved within the grid, the
grid looks for an object (B) that may possibly be colliding with A. A
user-defined procedure known as a “filter” is then called with both
A and B. If the filter returns <code>#f</code>, it means that even if A and
B are colliding, no collision resolution is needed. In this case the
grid won’t waste time checking if they really do collide because it
doesn’t matter. If A and B are collidable, then the filter returns a
procedure that implements the resolution technique. The grid will
then perform a collision test. If A and B are colliding, the resolver
procedure is called. It’s the resolvers job to adjust the objects
such that they are no longer colliding. The grid module comes with a
very simple resolution procedure, <code>slide</code>, that adjusts object A
by the smallest amount so that it no longer overlaps with B. By using
this filtering technique, a game can resolve collisions between
different objects in different ways.
</p>
<dl>
<dt><a name="index-make_002dgrid"></a>Procedure: <strong>make-grid</strong> <em>[<var>cell-size</var> 64]</em></dt>
<dd><p>Return a new grid partitioned into <var>cell-size</var> tiles.
</p></dd></dl>
<dl>
<dt><a name="index-grid_003f"></a>Procedure: <strong>grid?</strong> <em><var>obj</var></em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a grid.
</p></dd></dl>
<dl>
<dt><a name="index-cell_003f"></a>Procedure: <strong>cell?</strong> <em><var>obj</var></em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a grid cell.
</p></dd></dl>
<dl>
<dt><a name="index-cell_002dcount"></a>Procedure: <strong>cell-count</strong> <em><var>cell</var></em></dt>
<dd><p>Return the number of items in <var>cell</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dcell_002dsize"></a>Procedure: <strong>grid-cell-size</strong> <em><var>grid</var></em></dt>
<dd><p>Return the cell size of <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dcell_002dcount"></a>Procedure: <strong>grid-cell-count</strong> <em><var>grid</var></em></dt>
<dd><p>Return the number of cells currently in <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002ditem_002dcount"></a>Procedure: <strong>grid-item-count</strong> <em><var>grid</var></em></dt>
<dd><p>Return the number of items in <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dadd"></a>Procedure: <strong>grid-add</strong> <em><var>grid</var> <var>item</var> <var>x</var> <var>y</var> <var>width</var> <var>height</var></em></dt>
<dd>
<p>Add <var>item</var> to <var>grid</var> represented by the axis-aligned bounding
box whose lower-left corner is at (<var>x</var>, <var>y</var>) and is
<var>width</var> x <var>height</var> in size.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dremove"></a>Procedure: <strong>grid-remove</strong> <em><var>grid</var> <var>item</var></em></dt>
<dd><p>Return <var>item</var> from <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dclear"></a>Procedure: <strong>grid-clear</strong> <em><var>grid</var></em></dt>
<dd><p>Remove all items from <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-grid_002dmove"></a>Procedure: <strong>grid-move</strong> <em><var>grid</var> <var>item</var> <var>position</var> <var>filter</var></em></dt>
<dd><p>Attempt to move <var>item</var> in <var>grid</var> to <var>position</var> (a 2D
vector) and check for collisions. For each collision, <var>filter</var>
will be called with two arguments: <var>item</var> and the item it collided
with. If a collision occurs, <var>position</var> may be modified to
resolve the colliding objects.
</p></dd></dl>
<dl>
<dt><a name="index-for_002deach_002dcell"></a>Procedure: <strong>for-each-cell</strong> <em><var>proc</var> <var>grid</var> [<var>rect</var>]</em></dt>
<dd><p>Call <var>proc</var> with each cell in <var>grid</var> that intersects
<var>rect</var>, or every cell if <var>rect</var> is <code>#f</code>.
</p></dd></dl>
<dl>
<dt><a name="index-for_002deach_002ditem"></a>Procedure: <strong>for-each-item</strong> <em><var>proc</var> <var>grid</var></em></dt>
<dd><p>Call <var>proc</var> for each item in <var>grid</var>.
</p></dd></dl>
<dl>
<dt><a name="index-slide"></a>Procedure: <strong>slide</strong> <em><var>item</var> <var>item-rect</var> <var>other</var> <var>other-rect</var> <var>goal</var></em></dt>
<dd>
<p>Resolve the collision that occurs between <var>item</var> and <var>other</var>
when moving <var>item-rect</var> to <var>goal</var> by sliding <var>item-rect</var>
the minimum amount needed to make it no longer overlap
<var>other-rect</var>.
</p></dd></dl>
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