Affine

In mathematics, particularly geometry and linear algebra, 'affine' describes a geometric transformation that preserves collinearity (points lying on a line remain on a line) and ratios of distances between points on a line. affine transformations include translations, rotations, scalings, shears, and reflections. Crucially, an affine transformation does *not* necessarily preserve angles or distances. The term can also be used more broadly in computer graphics and image processing to describe transformations that maintain parallel lines. It signifies a relationship or connection, especially through family or marriage, or in a less strict sense, a similarity or resemblance.

Affine meaning with examples

• In computer graphics, an affine transformation can be applied to a 3D model to move, rotate, or scale it. This is a core concept in rendering pipelines, enabling realistic animations. For instance, a character's arm could be transformed by an affine function to simulate bending at the elbow, maintaining the arm's structural integrity through preserving collinearity. The function ensures all the model's components move consistently.
• The mathematical definition of affine space is built on the notion of affine transformations preserving the structure of the space. This is central to understanding how points can be transformed in a way that maintains the relationships between them. affine functions can also be combined to perform complex shape manipulations, crucial for the modeling of complex surfaces, like a car's chassis
• During image processing, an affine transformation can be used for image registration, where two or more images are aligned. For example, a satellite image can be rotated, translated, or sheared to fit a map based on features and the coordinate system. This approach guarantees the original feature layout is always maintained relative to the image's structure.
• Considering the use of the word 'affine' outside of a strict mathematical context: 'the two families were now affine by marriage' or perhaps 'The design elements of this architecture were affine, with common stylistic choices.' This shows a relational sense and implies connections are present and the same.