An affine space is a geometric structure that generalizes the concept of a vector space. It consists of a set of points and a vector space that describes the relationships between these points. In an affine space, there is no fixed origin; instead, points can be translated using vectors, allowing for the representation of geometric transformations without a specific reference point. In an affine space, the operations of addition and scalar multiplication are not defined for points directly. Instead, one can only perform operations on vectors that connect pairs of points. This framework is useful in various fields, including computer graphics, robotics, and geometry, where understanding the relative positions of objects is essential.