# Loop subdivision surface

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Loop_subdivision_surface
> Markdown URL: https://mediated.wiki/source/Loop_subdivision_surface.md
> Source: https://en.wikipedia.org/wiki/Loop_subdivision_surface
> Source revision: 1353927679
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

This computing article is a stub. You can help Wikipedia by adding missing information.

- [v](https://en.wikipedia.org/wiki/Template:Compu-stub)
- [t](/source/Template_talk%3ACompu-stub)
- [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:Compu-stub)

Subdivision surface derived from a triangular mesh

Loop subdivision of an [icosahedron](/source/Icosahedron); refinement steps zero, one, and two

In [computer graphics](/source/Computer_graphics), the **Loop method** for [subdivision surfaces](/source/Subdivision_surface) is an approximating subdivision scheme developed by Charles Loop in 1987 for [triangular meshes](/source/Triangle_mesh).[1] Prior methods, namely [Catmull-Clark](/source/Catmull-Clark)[2] and [Doo-Sabin](/source/Doo-Sabin_subdivision_surface),[3] focused on [quad meshes](/source/Polygon_mesh).

Loop subdivision [surfaces](/source/Computer_representation_of_surfaces) are defined recursively, dividing each triangle into four smaller ones. The method is based on a [quartic](/source/Quartic_function) [box spline](/source/Box_spline). It generates [C2](/source/Parametric_continuity) continuous limit surfaces everywhere except at extraordinary vertices, where they are [C1](/source/Parametric_continuity) continuous.[4]

## See also

- [Geodesic polyhedron](/source/Geodesic_polyhedron)

- [Catmull-Clark subdivision surface](/source/Catmull-Clark_subdivision_surface)

- [Doo-Sabin subdivision surface](/source/Doo-Sabin_subdivision_surface)

## References

1. **[^](#cite_ref-1)** Loop, Charles (1987). [*Smooth Subdivision Surfaces Based on Triangles*](https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/thesis-10.pdf) (PDF). Retrieved 8 March 2026.

1. **[^](#cite_ref-2)** Catmull, E.; Clark, J. (November 1978). "Recursively generated B-spline surfaces on arbitrary topological meshes". *Computer-Aided Design*. **10** (6): 350–355. [doi](/source/Doi_(identifier)):[10.1016/0010-4485(78)90110-0](https://doi.org/10.1016%2F0010-4485%2878%2990110-0).

1. **[^](#cite_ref-3)** Doo, D.; Sabin, M. (November 1978). "Behaviour of recursive division surfaces near extraordinary points". *Computer-Aided Design*. **10** (6): 356–360. [doi](/source/Doi_(identifier)):[10.1016/0010-4485(78)90111-2](https://doi.org/10.1016%2F0010-4485%2878%2990111-2).

1. **[^](#cite_ref-4)** Wiliam A. P. Smith (2020). "6. 3D Data Representation, Storage and Processing". *3D Imaging, Analysis and Applications* (2nd 2020 ed.). Springer International Publishing. pp. 298–299. [ISBN](/source/ISBN_(identifier)) [978-3030440701](https://en.wikipedia.org/wiki/Special:BookSources/978-3030440701).

---
Adapted from the Wikipedia article [Loop subdivision surface](https://en.wikipedia.org/wiki/Loop_subdivision_surface) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Loop_subdivision_surface?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.