Editing Subdivision surface (section)

==Overview==
[[File:Cube simple subdivisions (0-3).png|thumb|Simple subdivision of a cube up to 3]]
[[File:Tesselation pipeline.svg|thumb|right|upright=1.3|A [[tessellation (computer graphics)|tessellation]] pipeline using a subdivision method]]
A subdivision surface algorithm is [[recursive]] in nature. The process starts with a base level polygonal mesh. A '''refinement scheme''' is then applied to this mesh. This process takes that mesh and subdivides it, creating new vertices and new faces. The positions of the new vertices in the mesh are computed based on the positions of nearby old vertices, edges, and/or faces. In many refinement schemes, the positions of old vertices are also altered (possibly based on the positions of new vertices).

This process produces a ''denser'' mesh than the original one, containing more polygonal faces (often by a factor of 4). This resulting mesh can be passed through the same refinement scheme again and again to produce more and more refined meshes. Each iteration is often called a subdivision ''level'', starting at zero (before any refinement occurs).

The ''limit'' subdivision surface is the surface produced from this process being iteratively applied infinitely many times. In practical use however, this algorithm is only applied a limited, and fairly small (<math>\leq 5</math>), number of times.

Mathematically, the [[Neighbourhood (mathematics)|neighborhood]] of an ''extraordinary vertex'' (non-4-[[Degree (graph theory)|valent]] node for quad refined meshes) of a subdivision surface is a [[Spline (mathematics)|spline]] with a parametrically [[singular point of a curve|singular point]].<ref name="PetersBook">J. Peters and U. Reif: ''Subdivision Surfaces'', Springer series Geometry and Computing monograph 3, 2008, [http://dx.doi.org/10.1007/978-3-540-76406-9 doi]</ref>