In the

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

, a vertex normal at a

vertex Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

of a

polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all o ...

is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of the surface. Commonly, it is computed as the normalized average of the

surface normal In geometry, a normal is an object such as a line, ray, or vector that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the (infinite) line perpendicular to the tangent line to the curve ...

s of the

faces The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...

that contain that vertex. The average can be weighted for example by the area of the face or it can be unweighted. Vertex normals can also be computed for polygonal approximations to surfaces such as

NURBS Non-uniform rational basis spline (NURBS) is a mathematical model using B-spline, basis splines (B-splines) that is commonly used in computer graphics for representing curves and Surface (mathematics), surfaces. It offers great flexibility and pr ...

, or specified explicitly for artistic purposes. Vertex normals are used in

Gouraud shading Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes. In practice, Gouraud shading is most often used to achieve continuous li ...

, Phong shading and other lighting models. Using vertex normals, much smoother shading than flat shading can be achieved; however, without some modifications, it cannot produce a sharp edge.Max Wagner, Generating Vertex Normals, https://web.archive.org/web/20130531101356/http://www.emeyex.com/site/tuts/VertexNormals.pdf

References

See also