Affine is an adjective that relates to or denotes a mathematical function, shape, or transformation that preserves straight lines, parallelism, and ratios of distances. It is derived from the Latin word "affinis," meaning "related" or "connected." In mathematics, this term is commonly used in the field of linear algebra, geometry, and computer graphics.
In linear algebra, an affine transformation refers to a function that maps one vector space into another while preserving lines and ratios of distances. It includes translation, rotation, scaling, and shearing, as well as combinations of these operations. An affine transformation is represented as a matrix multiplication followed by a vector addition.
In geometry, an affine shape is a geometric figure that remains unchanged under an affine transformation. It is characterized by having parallel lines that remain parallel after the transformation and maintains the ratio of distances between points lying on the same line.
In computer graphics and image processing, an affine transformation is widely used to manipulate, transform, or warp images. It allows for operations such as resizing, cropping, rotating, and translating images while preserving their geometric properties.
Overall, the term "affine" describes a relationship, function, or transformation that maintains the fundamental geometric features of a shape or object, such as straight lines, parallelism, and ratios of distances.
