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non-Tk programs successfully. It is a classic memory/speed trade-off.

Lots of information about QTAs can be found on the web. But, very briefly,
a quadtree is a hierarchical data model that recursively decomposes a map into
smaller regions. Each node in the tree has 4 children nodes, each of which
represents one quarter of the area that the parent represents. So, the root
node represents the complete map. This map is then split into 4 equal quarters,
each of which is represented by one child node. Each of these children is now
treated as a parent, and its area is recursively split up into 4 equal areas,
and so on up to a desired depth.

Here is a somewhat crude diagram:

                   ------------------------------
                  |AAA|AAB|       |              |
                  |___AA__|  AB   |              |
                  |AAC|AAD|       |              |
                  |___|___A_______|      B       |
                  |       |       |              |
                  |       |       |              |
                  |   AC  |   AD  |              |
                  |       |       |              |
                   -------------ROOT-------------
                  |               |              |
                  |               |              |
                  |               |              |
                  |      C        |      D       |
                  |               |              |
                  |               |              |
                  |               |              |
                   ------------------------------

Which corresponds to the following quadtree:

                        __ROOT_
                       /  / \  \
                      /  /   \  \
                _____A_  B   C   D
               /  / \  \
              /  /   \  \
        _____AA  AB  AC  AD
       /  / \  \
      /  /   \  \
    AAA AAB AAC AAD

In the above diagrams I show only the nodes through the first branch of
each level. The same structure exists under each node. This quadtree has a
depth of 4.

Each object in the map is assigned to the nodes that it intersects. For example,
if we have an object that overlaps regions I<AAA> and I<AAC>, it will be
assigned to the nodes I<ROOT>, I<A>, I<AA>, I<AAA> and I<AAC>. Now, suppose we
want to find all the objects that intersect a given area. Instead of checking all
objects, we check to see which children of the ROOT node intersect the area. For
each of those nodes, we recursively check I<their> children nodes, and so on
until we reach the leaves of the tree. Finally, we find all the objects that are
assigned to those leaf nodes and check them for overlap with the initial area.

=head1 CLASS METHODS

The following methods are public:

=over 4

=item I<Algorithm::QuadTree>-E<gt>B<new>(I<options>)

This is the constructor. It expects the following options (all mandatory) and
returns an Algorithm::QuadTree object:

=over 8

=item -xmin

This is the X-coordinate of the bottom left corner of the area associated with
the quadtree.

=item -ymin

This is the Y-coordinate of the bottom left corner of the area associated with
the quadtree.

=item -xmax

This is the X-coordinate of the top right corner of the area associated with
the quadtree.

=item -ymax

This is the Y-coordinate of the top right corner of the area associated with
the quadtree.

=item -depth

The depth of the quadtree.

=back

=item I<$qt>-E<gt>B<add>(object, x0, y0, x1, y1)

This method is used to add objects in shape of rectangles to the tree. It has
to be called for every object in the map so that it can properly assigned to
the correct tree nodes. The first argument is an object reference or an
I<unique> ID for the object. The remaining 4 arguments define the outline of
the object (edge coordinates: left, bottom, right, top). This method will
traverse the tree and add the object to the nodes that it overlaps with.

NOTE: The method does B<NOT> check if the object references or IDs passed are
unique or not. It is up to you to make sure they are.

=item I<$qt>-E<gt>B<add>(object, x, y, radius)

Same as above, but for circular objects. C<x> and C<y> are coordinates of object's center.

NOTE: this method called with three coordinates treats the object as a circle,
and with four coordinates as a rectangle. You don't have to worry about
potential empty / undef values in your coordinates, as long as the number of
arguments is right. It will never treat C<< ->add('obj', 1, 2, 3, undef) >> as a
call to the circular version, and instead produce warnings about undef being
treated as a number, hinting you about the problem.

=item I<$qt>-E<gt>B<getEnclosedObjects>(x0, y0, x1, y1)