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# Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. 

65 relations: Affine space, Almost everywhere, Angle of incidence (optics), Boundary (topology), Complex-analytic variety, Computer graphics, Cone, Convex set, Coordinate system, Cross product, Curvilinear coordinates, Differentiable function, Differentiable manifold, Differential geometry of curves, Digital compositing, Dimension, Dual space, Euclidean space, Euclidean vector, Force, Function (mathematics), Geometry, Gradient, Hyperplane, Hypersurface, Implicit function, Implicit function theorem, Jacobian matrix and determinant, Kernel (linear algebra), Lambert's cosine law, Lighting, Line (geometry), Lipschitz continuity, List of mathematical jargon, Local property, Manifold, Neighbourhood, Normal mapping, Optical medium, Orientability, Orthogonality, Partial derivative, Perpendicular, Phong shading, Plane (geometry), Plane of incidence, Polygon, Pseudovector, Ray (optics), Real number, ... Expand index (15 more) »

## Affine space

In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

## Almost everywhere

In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.

## Angle of incidence (optics)

In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

## Boundary (topology)

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

## Complex-analytic variety

In mathematics, specifically complex geometry, a complex-analytic variety is defined locally as the set of common zeros of finitely many analytic functions.

## Computer graphics

Computer graphics are pictures and films created using computers.

## Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

## Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

## Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

## Cross product

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.

## Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.

## Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

## Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

## Differential geometry of curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

## Digital compositing

Digital compositing is the process of digitally assembling multiple images to make a final image, typically for print, motion pictures or screen display.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Dual space

In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

## Force

In physics, a force is any interaction that, when unopposed, will change the motion of an object.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

In mathematics, the gradient is a multi-variable generalization of the derivative.

## Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

## Hypersurface

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

## Implicit function

In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).

## Implicit function theorem

In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables.

## Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

## Kernel (linear algebra)

In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which, where 0 denotes the zero vector in W. That is, in set-builder notation,.

## Lambert's cosine law

In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal.

## Lighting

Lighting or illumination is the deliberate use of light to achieve a practical or aesthetic effect.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

## List of mathematical jargon

The language of mathematics has a vast vocabulary of specialist and technical terms.

## Local property

In mathematics, a phenomenon is sometimes said to occur locally if, roughly speaking, it occurs on sufficiently small or arbitrarily small neighborhoods of points.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Neighbourhood

A neighbourhood (British English), or neighborhood (American English; see spelling differences), is a geographically localised community within a larger city, town, suburb or rural area.

## Normal mapping

In 3D computer graphics, normal mapping, or Dot3 bump mapping, is a technique used for faking the lighting of bumps and dents – an implementation of bump mapping.

## Optical medium

An optical medium is material through which electromagnetic waves propagate.

## Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

## Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

## Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

## Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

Phong shading refers to an interpolation technique for surface shading in 3D computer graphics.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

## Plane of incidence

In describing reflection and refraction in optics, the plane of incidence (also called the meridional plane) is the plane which contains the surface normal and the propagation vector of the incoming radiation.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Pseudovector

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.

## Ray (optics)

In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Reflection (physics)

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.

## Render layers

When creating computer-generated imagery, final scenes appearing in movies and television productions are usually produced by rendering more than one "layer" or "pass," which are multiple images designed to be put together through digital compositing to form a completed frame.

## Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.

## Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.

Shading refers to depicting depth perception in 3D models or illustrations by varying levels of darkness.

## Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

## Surface integral

In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces.

## Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

## Tangent space

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

## Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## Vertex normal

In the geometry of computer graphics, a vertex normal at a vertex of a polyhedron is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of the surface.

## 3D computer graphics

3D computer graphics or three-dimensional computer graphics, (in contrast to 2D computer graphics) are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes of performing calculations and rendering 2D images.

## References

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