# Vertex normal

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Directional vector associated with a vertex

Vertex normals of a [dodecahedral](/source/Dodecahedral) [mesh](/source/Polygon_mesh).

In the [geometry](/source/Geometry) of [computer graphics](/source/Computer_graphics), a **vertex normal** at a [vertex](/source/Vertex_(geometry)) of a [polyhedron](/source/Polyhedron) is a directional vector associated with a vertex, intended as a replacement to the true geometric [normal](/source/Normal_(geometry)) of the surface. Commonly, it is computed as the [normalized](/source/Unit_vector) average of the [surface normals](/source/Surface_normal) of the [faces](/source/Face_(geometry)) that contain that vertex.[1][2] The [average can be weighted](/source/Weighted_average) for example by the area of the face or it can be unweighted.[3][4] Vertex normals can also be computed for polygonal approximations to surfaces such as [NURBS](/source/NURBS), or specified explicitly for artistic purposes. Vertex normals are used in [Gouraud shading](/source/Gouraud_shading), [Phong shading](/source/Phong_shading) and other [lighting models](/source/Lighting_model). Using vertex normals, much smoother shading than [flat shading](/source/Flat_shading) can be achieved; however, without some modifications to topology such as support loops, it cannot produce a sharper edge.[5]

## See also

- [Specular highlight](/source/Specular_highlight)

- [Per-pixel lighting](/source/Per-pixel_lighting)

## References

1. **[^](#cite_ref-1)** Henri Gouraud. "Continuous Shading of Curved Surfaces." IEEE Transactions on Computers, C-20(6) : 623--629 (June 1971).

1. **[^](#cite_ref-2)** Andrew Glassner, I.6 Building vertex normals from a unstructured polygon list, in Graphics Gems IV, edited by Paul S. Heckbert, Morgan Kaufmann, 1994. pp. 60--74

1. **[^](#cite_ref-3)** Nelson Max, Weights for Computing Vertex Normals from Facet Normals, Journal of Graphics Tools, Volume 4, Issue 2, 1999 p. 1-6

1. **[^](#cite_ref-4)** Grit Thürrner and Charles A. Wüthrich, Computing Vertex Normals from Polygonal Facets. Journal of Graphics Tools, Volume 3, Issue 1, 1998. pp. 43-46

1. **[^](#cite_ref-5)** Max Wagner, Generating Vertex Normals, [https://web.archive.org/web/20130531101356/http://www.emeyex.com/site/tuts/VertexNormals.pdf](https://web.archive.org/web/20130531101356/http://www.emeyex.com/site/tuts/VertexNormals.pdf)

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