Graphics Reference
In-Depth Information
or new target coordinate systems. Caching of updated bounding volumes has the
drawback of nearly doubling the required storage space, as most fields of a bounding
volume representation are changed during an update.
Some bounding volumes, such as spheres or convex hulls, naturally trans-
form into any coordinate system, as they are not restricted to specific orientations.
Consequently, they are called nonaligned or (freely) oriented bounding volumes.
In contrast, aligned bounding volumes (such as AABBs) are restricted in what ori-
entations they can assume. The aligned bounding volumes must be realigned as
they become unaligned due to object rotation during motion. For updating or
reconstructing the AABB, there are four common strategies:
Utilizing a fixed-size loose AABB that always encloses the object
●
Computing a tight dynamic reconstruction from the original point set
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Computing a tight dynamic reconstruction using hill climbing
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Computing an approximate dynamic reconstruction from the rotated AABB
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The next four sections cover these approaches in more detail.
4.2.3
AABB from the Object Bounding Sphere
The first method completely circumvents the need to reshape the AABB by making it
large enough to contain the object at any orientation. This fixed-size encompassing
AABB is computed as the bounding box of the bounding sphere of the contained
object
A
. The bounding sphere, in turn, is centered in the pivot point
P
that
A
rotates
about. Its radius
r
is the distance to the farthest object vertex from this center (as
illustrated in Figure 4.5). By making sure the object pivot
P
lies in the center of the
object, the sphere radius is minimized.
The benefit of this representation is that during update this AABB simply need be
translated (by the same translation applied to the bounded object), and any object
rotation can be completely ignored. However, the bounding sphere itself (which has
a better sound than the AABB) would also have this property. Thus, bounding spheres
should be considered a potential better choice of bounding volume in this case.
4.2.4
AABB Reconstructed from Original Point Set
The update strategy described in this section (as well as the remaining two update
strategies to be described) dynamically resizes the AABB as it is being realigned with
the coordinate system axes. For a tightly fitted bounding box, the underlying geometry
of the bounded object is examined and the box bounds are established by finding
the extreme vertices in all six directions of the coordinate axes. The straightforward
approach loops through all vertices, keeping track of the vertex most distant along
