Editing Polygon mesh (section)

== Elements ==
[[File:mesh overview.svg|Elements of polygonal 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 above. However, many renderers either support quads and higher-sided polygons, or are able to convert polygons to triangles on the fly, making it unnecessary to store a mesh in a [[surface triangulation|triangulated]] form. 

{{term|vertex}} {{defn|A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates.}}
{{term|edge}} {{defn|A connection between two vertices.}}
{{term|face}} {{defn|A closed set of edges, in which a ''triangle face'' has three edges, and a ''quad face'' has four edges. A '''polygon''' is a [[coplanar]] 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.}}

{{term|surfaces}} {{defn|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 normal]]s must point horizontally away from the center, while the normals of the caps must point straight up and down. Rendered as a single, [[Phong shading|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.}}

{{term|groups}}
{{defn|Some mesh formats contain '''groups''', 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. }}

{{term|materials}}
{{defn|Generally '''materials''' will be defined, allowing different portions of the mesh to use different [[shaders]] when rendered. }}

{{term|UV coordinates|content=[[UV coordinates]]}}
{{defn|Most mesh formats also support some form of '''[[UV coordinates]]''' which are a separate 2d representation of the mesh "unfolded" to show what portion of a two-dimensional [[texture map]] to apply to different polygons of the mesh. It is also possible for meshes to contain other such vertex ''attribute'' information such as colour, tangent vectors, [[Weighting|weight maps]] to control [[Skeletal animation|animation]], etc. (sometimes also called ''channels'').}}