Affine group

The affine group is a mathematical concept that describes transformations combining linear changes, like rotations or scaling, with translations, such as shifting an object’s position. Imagine moving a shape on a piece of paper: you can make it bigger or smaller, rotate it, or slide it to a different spot—all these combined actions form an affine transformation. The affine group consists of all such transformations, ensuring that straight lines remain straight and parallel lines stay parallel after the transformation. It’s fundamental in geometry and computer graphics for modeling how objects change position and shape without distortion.