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Bounding volume 23
Bounding volume
For building code compliance, see Bounding.
In computer graphics and computational geometry, a bounding
volume for a set of objects is a closed volume that completely contains
the union of the objects in the set. Bounding volumes are used to
improve the efficiency of geometrical operations by using simple
volumes to contain more complex objects. Normally, simpler volumes
have simpler ways to test for overlap.
A bounding volume for a set of objects is also a bounding volume for
the single object consisting of their union, and the other way around.
Therefore it is possible to confine the description to the case of a single
object, which is assumed to be non-empty and bounded (finite).
Uses of bounding volumes
Bounding volumes are most often used to accelerate certain kinds of tests.
A three dimensional model with its bounding box
drawn in dashed lines.
In ray tracing, bounding volumes are used in ray-intersection tests, and in many rendering algorithms, they are used
for viewing frustum tests. If the ray or viewing frustum does not intersect the bounding volume, it cannot intersect
the object contained in the volume. These intersection tests produce a list of objects that must be displayed. Here,
displayed means rendered or rasterized.
In collision detection, when two bounding volumes do not intersect, then the contained objects cannot collide, either.
Testing against a bounding volume is typically much faster than testing against the object itself, because of the
bounding volume's simpler geometry. This is because an 'object' is typically composed of polygons or data structures
that are reduced to polygonal approximations. In either case, it is computationally wasteful to test each polygon
against the view volume if the object is not visible. (Onscreen objects must be 'clipped' to the screen, regardless of
whether their surfaces are actually visible.)
To obtain bounding volumes of complex objects, a common way is to break the objects/scene down using a scene
graph or more specifically bounding volume hierarchies like e.g. OBB trees. The basic idea behind this is to organize
a scene in a tree-like structure where the root comprises the whole scene and each leaf contains a smaller subpart.
Common types of bounding volume
The choice of the type of bounding volume for a given application is determined by a variety of factors: the
computational cost of computing a bounding volume for an object, the cost of updating it in applications in which
the objects can move or change shape or size, the cost of determining intersections, and the desired precision of the
intersection test. The precision of the intersection test is related to the amount of space within the bounding volume
not associated with the bounded object, called void space. Sophisticated bounding volumes generally allow for less
void space but are more computationally expensive. It is common to use several types in conjunction, such as a
cheap one for a quick but rough test in conjunction with a more precise but also more expensive type.
The types treated here all give convex bounding volumes. If the object being bounded is known to be convex, this is
not a restriction. If non-convex bounding volumes are required, an approach is to represent them as a union of a
number of convex bounding volumes. Unfortunately, intersection tests become quickly more expensive as the