Polygon Mesh - Elements of Mesh Modeling

Elements of Mesh Modeling

Objects created with polygon meshes must store different types of elements. These include vertices, edges, faces, polygons and surfaces. In many applications, only vertices, edges and either faces or polygons are stored. A renderer may support only 3-sided faces, so polygons must be constructed of many of these, as shown in Figure 1. However, many renderers either support quads and higher-sided polygons, or are able to triangulate polygons to triangles on the fly, making it unnecessary to store a mesh in a triangulated form. Also, in certain applications like head modeling, it is desirable to be able to create both 3- and 4-sided polygons.

A vertex is a position along with other information such as color, normal vector and texture coordinates. An edge is a connection between two vertices. A face is a closed set of edges, in which a triangle face has three edges, and a quad face has four edges. A polygon is a set of faces. In systems that support multi-sided faces, polygons and faces are equivalent. However, most rendering hardware supports only 3- or 4-sided faces, so polygons are represented as multiple faces. Mathematically a polygonal mesh may be considered an unstructured grid, or undirected graph, with additional properties of geometry, shape and topology.

Surfaces, more often called smoothing groups, are useful, but not required to group smooth regions. Consider a cylinder with caps, such as a soda can. For smooth shading of the sides, all surface normals must point horizontally away from the center, while the normals of the caps must point in the +/-(0,0,1) directions. Rendered as a single, Phong-shaded surface, the crease vertices would have incorrect normals. Thus, some way of determining where to cease smoothing is needed to group smooth parts of a mesh, just as polygons group 3-sided faces. As an alternative to providing surfaces/smoothing groups, a mesh may contain other data for calculating the same data, such as a splitting angle (polygons with normals above this threshold are either automatically treated as separate smoothing groups or some technique such as splitting or chamfering is automatically applied to the edge between them). Additionally, very high resolution meshes are less subject to issues that would require smoothing groups, as their polygons are so small as to make the need irrelevant. Further, another alternative exists in the possibility of simply detaching the surfaces themselves from the rest of the mesh. Renderers do not attempt to smooth edges across noncontiguous polygons.

Mesh format may or may not define other useful data. Groups may be defined which define separate elements of the mesh and are useful for determining separate sub-objects for skeletal animation or separate actors for non-skeletal animation. Generally materials will be defined, allowing different portions of the mesh to use different shaders when rendered. Most mesh formats also suppose some form of UV coordinates which are a separate 2d representation of the mesh "unfolded" to show what portion of a 2-dimensional texture map to apply to different polygons of the mesh.