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The data structure relationships of the Non-Manifold 3D Winged-Edge Topology are summarized in the object model shown in Figure 17.11. References to geometry are omitted for clarity. There are five main VPF+ primitives: Entity node. Used to represent isolated features. Connected node. Used as endpoints to define edges. Edge. An arc used to represent linear features or borders of faces. Face. A two-dimensional primitive used to represent a facet of a three-dimensional object such as the wall of a building, or to represent a two-dimensional area feature such as a lake. Eface. Describes a use of a face by an edge. Inside the primitive directory, a mandatory Minimum Bounding Box (MBB) table (not shown in Figure 17.11) is associated with each edge and face primitive. Because of its simple shape, an MBB is easier to handle than its corresponding primitive. The primitives shown in Figure 17.11, except for the eface, have an optional spatial index. The spatial index is based on an adaptive-grid-based 3D binary tree, which reduces searching for a primitive down to binary search. Due to its variable length records, the connected node table has a mandatory associated variable length index. The ring table identifies the ring forming the outer boundary and all internal rings of a face primitive. This table allows (along with the face table) the extraction of all of the edges that form the outer boundary and that form the internal rings of a face prim-
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itive. The entity node and the internal and external rings are not essential to the understanding of the VPF+ data structure, and as such, will not be discussed further. The eface is a new structure that is introduced in VPF+ to resolve some of the ambiguities resulting from the absence of a fixed number of faces adjacent to an edge. Efaces describe the use of a face by an edge and allow maintenance of the adjacency relationships between an edge and zero, one, two, or more faces incident to an edge. This is accomplished by linking each edge to all faces connected along the edge through a circular linked list of efaces. As shown in Figure 17.12, each eface in the list identifies the face with which it is associated, the next eface in the list, and the "next" edge about the face with which the eface is associated. Efaces are also radially ordered in the linked list in a clockwise direction about the edge. The purpose for the ordering is to make traversal from one face to the radially closest adjacent face a simple list operation. Additionally, VPF's Connected Node Table is modified to allow for nonmanifold nodes. This requires that a node point to one edge in each object connected solely through the node and to each dangling edge. This allows the retrieval of all edges and all faces in each object, and the retrieval of all dangling edges connected to the nonmanifold node. Unlike traditional VPF's Level 3 topology, the "universe face" is absent in VPF+'s full 3D topology since VPF+ is intended primarily for 3D modeling. Additionally, since 3D modeling is intended, faces may be one- or two-sided. A two-sided face, for example, might be used to represent the wall of a building with one side used for the outside of the building and the other side for the inside of the building. Feature attribute information would be used to render the two different surface textures and color. A one-sided face might be used to represent a portion of a terrain surface. Orientation of the interior and exterior of 3D objects is organized in relation to the normal vector of faces forming the surface boundary of closed objects. Faces may also be embedded within a 3D object.
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