Game Development Reference
In-Depth Information
and
A ,
A , and A are the unit-length principal axes.
The effective radius ef r with respect to a plane having normal direction N of a
bounding box whose dimensions and orientation are described by the vectors R ,
S , and T is given by
r
=⋅
1
RN SN TN .
+⋅
+⋅
eff
2
Bounding Spheres
A bounding sphere for the set of vertices 12
PP is constructed by locating
the points P and P that produce the least and greatest dot products with the pri-
mary axis R and setting the initial center Q and radius r to
,
,
,
N
PP
+
k
l
Q
=
2
r
=−
PQ .
k
For any point P satisfying
2
2
, we replace the center and radius with
PQ
−>
r
i
the values
GP
+
i
Q
′ =
2
r
=−
PQ ,
i
where G is defined as
PQ
i
G
=−
Q
r
PQ .
i
A bounding sphere having center Q and radius r is not visible if for any view
frustum plane L we have
≤−
r
.
LQ
Bounding Ellipsoids
A bounding ellipsoid for the set of vertices 12
PP is constructed by trans-
forming into a space in which the box bounding the set is a cube, constructing a
bounding sphere in that space, and then performing the reverse transformation to
scale the sphere to the original dimensions of the bounding box.
,
,
,
N
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