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3D Game Engine Design, 2nd Edition
book

3D Game Engine Design, 2nd Edition

by David Eberly
November 2006
Intermediate to advanced content levelIntermediate to advanced
1040 pages
26h 31m
English
CRC Press
Content preview from 3D Game Engine Design, 2nd Edition
8.1 The Method of Separating Axes 439
The algebraic condition that describes the separated intervals in Figure 8.17 (a)
is |γ
1
γ
0
| >r
0
+ r
1
. In words, this says that the distance between the centers of the
projected intervals is larger than the sum of the radii of the intervals. The intervals in
the bottom image of the figure overlap, so |γ
1
γ
0
| <r
0
+ r
1
. If the intervals are just
touching, |γ
1
γ
0
|=r
0
+ r
1
. This last case is important when dealing with moving
OBBs.
Define r =|γ
1
γ
0
|. A closer look at the algebraic condition for separation of the
projected intervals shows that
r =|γ
1
γ
0
|=|D
.
(C
1
Q) D
.
(C
0
Q)|=|D
.
(C
1
C
0
)|
This means we need to specify only the direction D and not worry about providing a
point Q on the line. Also,
r
0
=
2
i=0
a
i
|D
.
A
i
|, r
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Publisher Resources

ISBN: 9781482267303