Figure 8.10 shows one the first difficulties with collision detection, in terms of two triangles in a 2D world. The first two cases (Figures 8.10(a) and 8.10(b)) show obvious cases; however, the third case, Figure 8.10(c), could be ambiguous. If one triangle is wholly inside of another, then is this a collision? If we interpret the outer triangle as a solid model, then YES. If the outer triangle is only the boundary edges, and is meant to have an empty interior, then the answer is NO. This is why emphasis was placed on having a coherent model in Section 3.1; otherwise, the boundary might not be established well enough to distinguish the inside from the outside.

Steven M LaValle 2020-11-11