Normal (geometry)
In geometry, an object such as a line or vector is called a normal to another object if they are perpendicular to each other. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that 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.
The concept has been generalized to differential manifolds of arbitrary dimension embedded in a Euclidean space. The normal vector space or normal space of a manifold at a point P is the set of the vectors which are orthogonal to the tangent space at P. In the case of differential curves, the curvature vector is a normal vector of special interest.
The normal is often used in computer graphics to determine a surface's orientation toward a light source for flat shading, or the orientation of each of the corners (vertices) to mimic a curved surface with Phong shading.
Read more about Normal (geometry): Hypersurfaces in n-dimensional Space, Varieties Defined By Implicit Equations in n-dimensional Space, Uses, Normal in Geometric Optics
Famous quotes containing the word normal:
“Normality highly values its normal man. It educates children to lose themselves and to become absurd, and thus to be normal. Normal men have killed perhaps 100,000,000 of their fellow normal men in the last fifty years.”
—R.D. (Ronald David)