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Binary space partitioning 16
together with a Z-buffer, and using the Z-buffer to correctly merge movable objects such as doors and characters
onto the background scene.
BSP trees are often used by 3D computer games, particularly first-person shooters and those with indoor
environments. Probably the earliest game to use a BSP data structure was Doom (see Doom engine for an in-depth
look at Doom's BSP implementation). Other uses include ray tracing and collision detection.
Generation
Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies
one or more requirements. The specific method of division varies depending on its final purpose. For instance, in a
BSP tree used for collision detection, the original object would be partitioned until each part becomes simple enough
to be individually tested, and in rendering it is desirable that each part be convex so that the painter's algorithm can
be used.
The final number of objects will inevitably increase since lines or faces that cross the partitioning plane must be split
into two, and it is also desirable that the final tree remains reasonably balanced. Therefore the algorithm for correctly
and efficiently creating a good BSP tree is the most difficult part of an implementation. In 3D space, planes are used
to partition and split an object's faces; in 2D space lines split an object's segments.
The following picture illustrates the process of partitioning an irregular polygon into a series of convex ones. Notice
how each step produces polygons with fewer segments until arriving at G and F, which are convex and require no
further partitioning. In this particular case, the partitioning line was picked between existing vertices of the polygon
and intersected none of its segments. If the partitioning line intersects a segment, or face in a 3D model, the
offending segment(s) or face(s) have to be split into two at the line/plane because each resulting partition must be a
full, independent object.
1. A is the root of the tree and the entire polygon
2. A is split into B and C
3. B is split into D and E.
4. D is split into F and G, which are convex and hence become leaves on the tree.
Since the usefulness of a BSP tree depends upon how well it was generated, a good algorithm is essential. Most
algorithms will test many possibilities for each partition until they find a good compromise. They might also keep
backtracking information in memory, so that if a branch of the tree is found to be unsatisfactory, other alternative
partitions may be tried. Thus producing a tree usually requires long computations.
BSP trees are also used to represent natural images. Construction methods for BSP trees representing images were
first introduced as efficient representations in which only a few hundred nodes can represent an image that normally