Surface normal

A surface normal, or just normal to a flat surface Surface

In mathematics [i], specifically in topology [i], a surface is a two-dimensional manifold [i]. ...

is a three-dimensional vector which is perpendicular Perpendicular

In geometry [i], two lines [i] are considered perpendicular if one falls on the other in such a way ...

to that surface. A normal to a non-flat surface at a point p on the surface is a vector which is perpendicular to the tangent plane to that surface at p. The word normal is also used as an adjective as well as a noun with this meaning: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalises to orthogonality. Calculating a surface normal

Discussions

Discussion Features

Ask a question about 'Surface normal'

Start a new discussion about 'Surface normal'

Answer questions about 'Surface normal'

'Surface normal' discussion forum

Encyclopedia

A surface normal, or just normal to a
flat surface Surface

In mathematics [i], specifically in topology [i], a surface is a two-dimensional manifold [i]....

is a three-dimensional vector which is perpendicular Perpendicular

Calculating a surface normal

For a polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ...

, a surface normal can be calculated as the vector cross product Cross product

In mathematics [i], the cross product is a binary operation [i] on vector [i]s in a three-dimensi ...

of two edges of the polygon.

For a plane given by the equation , the vector is a normal.

If a surface S is parametrized Coordinate system

In mathematics [i] and applications, a coordinate system is a system for assigning a tuple [i] of number [i]...

by a system of curvilinear coordinates x, with s and t real variables, then a normal is given by the cross product of the partial derivatives

If a surface S is given implicitly, as the set of points satisfying , then, a normal at a point on the surface is given by the gradient Gradient

A generalization of these concepts is the gradient in vector calculus [i]; and this article is mostly ab ...

If a surface does not have a tangent plane at a point, it does not have a normal at that point either. For example, a cone Cone

Cone [i] is a basic geometrical shape. ...

does not have a normal at its tip nor does it have a normal along the edge of its base. However, the normal to the cone is defined almost everywhere. In general, it is possible to define a normal almost everywhere for a surface that is Lipschitz continuous.

Uniqueness of the normal

A normal to a surface does not have a unique direction; the vector pointing in the opposite direction of a surface normal is also a surface normal. For an oriented surface Orientability

Orientability of surfaces

Intuitively, a surface S in the Euclidean space [i] R3 is non-orienta ...

, the surface normal is usually determined by the right-hand rule Right-hand rule

In mathematics [i] and physics [i], the right-hand rule is a convention for determining relative directi...

.

Uses

Surface normals are essential in defining surface integrals of vector field Vector field

In mathematics [i] a vector field is a construction in vector calculus [i] which associates a vector [i] ...

s.
Surface normals are commonly used in 3D computer graphics 3D computer graphics

3D computer graphics are works of graphic art [i] that were created with the aid of digital [i] computer [i] ...

for lighting calculations; see Lambert's cosine law Lambert's cosine law

Lambert's cosine law says that the total radiant power [i] observed from a "Lambertian ...

.

External link

An from Microsoft's MSDN