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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