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In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line. In other words, it is an injective affine map from an affine space to the coordinate space , where is the field of scalars, for example, the real numbers R. The most important case of affine coordinates in Euclidean spaces is real-valued Cartesian coordinate system. Orthogonal affine coordinate systems are rectangular, and others are referred to as oblique. A system of coordinates on -dimensional space is defined by a (+1)-tuple of points not belonging to any affine subspace of a lesser dimension. Any given coordinate -tuple gives the point by the formula: : . Note that are ''difference'' vectors with the origin in and ends in . An affine space cannot have a coordinate system with less than its dimension, but may indeed be greater, which means that the coordinate map is not necessary surjective. Examples of -coordinate system in an (−1)-dimensional space are barycentric coordinates and affine "homogeneous" coordinates . In the latter case the 0 coordinate is equal to 1 on all space, but this "reserved" coordinate allows for matrix representation of affine maps similar to one used for projective maps. == See also == * Convex combination * Centroid, can be calculated in affine coordinates * Homogeneous coordinates, a similar concept but without uniqueness of values 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Affine coordinate system」の詳細全文を読む スポンサード リンク
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