
8.5 Pathfinding to Avoid Collisions 499
Figure 8.39 The current vertex is V
0
and has two adjacent vertices A
0
and A
1
.
A
1
P
(a) (b)
P
VV
A
1
A
0
A
0
Figure 8.40 (a) The vertex V is a convex vertex relative to the other vertices A
0
and A
1
. (b) The
vertex V is a reflex vertex relative to the other vertices. In both cases, a vector P − V
between vectors A
0
− V and A
1
− V is shown in blue.
In the case where V is convex with respect to its neighbors, D is between D
0
and
D
1
when the cross products E × E
1
and E
0
× E both have positive z-components.
That is, if you put your right hand in the direction E with your thumb up (out of the
plane of the page), and rotate your fingers ...