Now consider the question of whether the object interior is part of the model (recall Figure 3.2). Suppose the mesh triangles fit together perfectly so that every edge borders exactly two triangles and no triangles intersect unless they are adjacent along the surface. In this case, the model forms a complete barrier between the inside and outside of the object. If we were to hypothetically fill the inside with a gas, then it could not leak to the outside. This is an example of a coherent model. Such models are required if the notion of inside or outside is critical to the VWG. For example, a penny could be inside of the dolphin, but not intersecting with any of its boundary triangles. Would this ever need to be detected? If we remove a single triangle, then the hypothetical gas would leak out. There would no longer be a clear distinction between the inside and outside of the object, making it difficult to answer the question about the penny and the dolphin. In the extreme case, we could have a single triangle in space. There is clearly no natural inside or outside. At an extreme, the model could be as bad as polygon soup, which is a jumble of triangles that do not fit together nicely and could even have intersecting interiors. In conclusion, be careful when constructing models so that the operations you want to perform later will be logically clear. If you are using a high-level design tool, such as Blender or Maya, to make your models, then coherent models will be automatically built.
Steven M LaValle 2016-12-31