Game Development Reference

In-Depth Information

Once the effective radius is known, we proceed in exactly the same manner as we

would to test an ellipsoid. For each frustum plane
L
, we calculate the 4D dot

product between the plane and the center
Q
of the bounding box. If for any plane

eff

L Q
, then the box is not visible.

In the case that the length of
R
is much greater than the lengths of
S
and
T
, a

box may not be rejected in many situations when it lies far outside the view frus-

tum. An instance of this case is demonstrated in Figure 8.8. To circumvent this

problem, we can reduce the box intersection test to a line segment intersection, as

is done for cylinders.

In terms of the bounding box center
Q
and its primary axis
R
, we can express

the endpoints

⋅

≤−

r

Q
and

Q
of the line segment representing the box as

QQ R

Q

=+

=−

1

1

2

1

QR
.

(8.48)

2

2

The effective radius
eff

r

with respect to a plane having unit normal direction
N
is

given by

r

=⋅

(

SN

+⋅

TN
,

)

(8.49)

1

eff

2

S

R

Figure 8.8.
This example demonstrates that using the point test for a box having one di-

mension much larger than the other two can result in the failure to reject a box that lies a

significant distance outside the view frustum.

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