Affine Spaces

An affine space is a mathematical structure that generalizes the concept of points and directions without fixed origins. Imagine a flat surface like a sheet of paper: points are specific locations, and vectors (arrows) represent directions and distances. In an affine space, you can add a vector to a point to get another point, but there’s no distinguished "starting point" or origin. This flexibility allows us to describe positions and directions consistently, making affine spaces useful in geometry, computer graphics, and physics where absolute positions are less important than relative arrangements.