Affine transformations are geometric operations that map points to new points while preserving collinearity (lines remain straight lines) and distance ratios. Examples include scaling, rotation, translation, reflection, and shearing.

In computer graphics and linear algebra, these are represented using homogeneous coordinates:

• 2D: Represented as $3 \times 3$ matrices acting on coordinates $[x, y, 1]^T$.
• 3D: Represented as $4 \times 4$ matrices acting on coordinates $[x, y, z, 1]^T$.