Vector
Vector | Vectorelement of the linear space. Describes one or more numbers (vector from one number is a scalar). In computer graphics are commonly used vectors of 2, 3, and 4 numbers. The vector has a length, which is calculated using the Pythagorean theorem (the square root of the sum of the squares of all elements of the vector). Vectors are all basic arithmetic operations (Addition, subtraction, multiplication, division). The section of mathematics, studying the operations on vectors is called the vector algebra (she, in turn, is a special case of a more general directions - linear algebra).
Using a vector can be described as a point in the Euclidean space and the direction corresponding to the "look" at this point from the beginning of the coordinates. The direction is typically set to a specified, or a single vector (i.e., a vector with the length equal to 1). Any non-zero vector can be нормировать, separating the покомпонентно on its length. The direction is not equivalent to the turn - to get a full rotation, there are three mutually perpendicular vectors, forming the so-called basis. The basis is an integral part of the affine transformation matrix.
affine transformation are carried out over the space of affine vectors. Аффинный vector is a vector of 4 numbers, as symbolised by the XYZW, where XYZ - normal евклидовый vector, and the additional coordinate W allows you to express infinitely remote point (where W is equal to 0). Conventional terms have the W is equal to 1.
See also Matrix, 1.