Game Physics Engine Development, 2nd Edition

18.8 Summary 473

The SAT works as well for 2D as 3D. In the 2D case, however , the only ax es we need

to check are those that are normal to each edge in the model. This is an important

result. In the 3D case, we had to check each face normal and the direction given by

the cross-product of each pair of edges. So the work we needed to do grew with the

square ofthenumberofedges.ThismadetheSATslowforcomplexgeometry.

In the 3D case, the number of axes to test depends only on the number of edges

in each model; there is no squared term. This makes SAT tractable for much more

complex geometries. To collide two rectangles, we need to check just four axes (again

assuming opposite edges in a box are parallel, so there are only two distinct axes to

check per