![Vertex normals](https://upload.wikimedia.org/wikipedia/commons/3/3c/Vertex_normals.png)
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 ...
of
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 positio ...
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 on ...
is a directional vector associated with a vertex, intended as a replacement to the true geometric
normal Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
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 at ...
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
In 3D computer graphics, Phong shading, Phong interpolation, or normal-vector interpolation shading is an interpolation technique for surface shading invented by computer graphics pioneer Bui Tuong Phong. Phong shading interpolates surface norm ...
and other
lighting models. Using vertex normals, much smoother shading than
flat shading
Shading refers to the depiction of depth perception in 3D models (within the field of 3D computer graphics) or illustrations (in visual art) by varying the level of darkness. Shading tries to approximate local behavior of light on the object's ...
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
*
Specular highlight
A specular highlight is the bright spot of light that appears on shiny objects when illuminated (for example, see image on right). Specular highlights are important in 3D computer graphics, as they provide a strong visual cue for the shape of a ...
*
Per-pixel lighting
In computer graphics, per-pixel lighting refers to any technique for lighting an image or scene that calculates illumination for each pixel on a rendered image. This is in contrast to other popular methods of lighting such as vertex lighting, whic ...
Shading
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