# Normal (geometry)

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 the point.
A normal vector may have length one (a unit vector) or its length may represent the curvature of the object (a *curvature vector*); its algebraic sign may indicate sides (interior or exterior).

In three dimensions, a **surface normal**, or simply **normal**, to a surface at point is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line *normal* to a plane, the *normal* component of a force, the **normal vector**, etc. The concept of normality generalizes to orthogonality (right angles).

The concept has been generalized to differentiable manifolds of arbitrary dimension embedded in a Euclidean space. The **normal vector space** or **normal space** of a manifold at point is the set of vectors which are orthogonal to the tangent space at
Normal vectors are of special interest in the case of smooth curves and smooth surfaces.

The normal is often used in 3D computer graphics (notice the singular, as only one normal will be defined) to determine a surface's orientation toward a light source for flat shading, or the orientation of each of the surface's corners (vertices) to mimic a curved surface with Phong shading.

The **normal distance** of a point *Q* to a curve or to a surface is the Euclidean distance between *Q* and its perpendicular projection on the object (at the point *P* on the object where the normal contains *Q*). The normal distance is a type of *perpendicular distance* generalizing the distance from a point to a line and the distance from a point to a plane. It can be used for curve fitting and for defining offset surfaces.