Polygon Mesh - Representations

Representations

Polygon meshes may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:

• Face-vertex meshes: A simple list of vertices, and a set of polygons that point to the vertices it uses.
• Winged-edge meshes, in which each edge points to two vertices, two faces, and the four (clockwise and counterclockwise) edges that touch it. Winged-edge meshes allow constant time traversal of the surface, but with higher storage requirements.
• Half-edge meshes: Similar to winged-edge meshes except that only half the edge traversal information is used. (see OpenMesh)
• Quad-edge meshes, which store edges, half-edges, and vertices without any reference to polygons. The polygons are implicit in the representation, and may be found by traversing the structure. Memory requirements are similar to half-edge meshes.
• Corner-tables, which store vertices in a predefined table, such that traversing the table implicitly defines polygons. This is in essence the "triangle fan" used in hardware graphics rendering. The representation is more compact, and more efficient to retrieve polygons, but operations to change polygons are slow. Furthermore, corner-tables do not represent meshes completely. Multiple corner-tables (triangle fans) are needed to represent most meshes.
• Vertex-vertex meshes: A "VV" mesh represents only vertices, which point to other vertices. Both the edge and face information is implicit in the representation. However, the simplicity of the representation allows for many efficient operations to be performed on meshes.

Each of the representations above have particular advantages and drawbacks, further discussed in Smith (2006).

The choice of the data structure is governed by the application, the performance required, size of the data, and the operations to be performed. For example, it is easier to deal with triangles than general polygons, especially in computational geometry. For certain operations it is necessary to have a fast access to topological information such as edges or neighboring faces; this requires more complex structures such as the winged-edge representation. For hardware rendering, compact, simple structures are needed; thus the corner-table (triangle fan) is commonly incorporated into low-level rendering APIs such as DirectX and OpenGL.