Game Engine Architecture

616 12. Collision and Rigid Body Dynamics

axis is the one parallel to the center-to-center line segment. As the spheres

move apart, we can rotate the separating axis more and more in either direc-

tion. This is shown in Figure 12.11.

12.3.5.4. AABB versus AABB

To determine whether two AABBs are intersecting, we can again apply the

separating axis theorem. The fact that the faces of both AABBs are guaranteed

to lie parallel to a common set of coordinate axes tells us that if a separating

axis exists, it will be one of these three coordinate axes.

So, to test for intersections between two AABBs, which we’ll call A and B,

we merely inspect the minimum and maximum coordinates of the two boxes

along each axis independently. Along the x-axis, we have the two intervals

[xminA , xmaxA ] and [xBmin, xmaxB ], and we have corresponding intervals for the y- and

z-axes. If the intervals overlap along all three axes, then the two AABBs are in-

tersecting—in all other cases, they are not. Examples of intersecting and non-

intersecting AABBs are shown in Figure 12.12 (simplifi ed to two dimensions

for the purposes of illustration). For an in-depth discussion of AABB collision,

see htt p://www.gamasutra.com/features/20000203/lander_01.htm.

Separatin

g

Line/Plane

Separatin

gAxis Many

Separati

ngAxes

Many

Separatin

g

Lines/Pla

nes

Figure 12.11. When two spheres are an infi nitesimal distance apart, the only separating axis

lies parallel to the line segment formed by the two spheres’ center points.

y

x

y

x

Figure 12.12. A two-dimensional example of intersecting and non-intersecting AABBs. Notice

that even though the second pair of AABBs are intersecting along the x-axis, they are not

intersecting along the y-axis.