affine transformation
- noun
- /əˈfaɪn trænʃəˈfɔrmeɪʃən/
- Specialized
:
transformación afín
- An affine transformation can be used to stretch an image while keeping its proportions intact.
Examples
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In computer graphics, an affine transformation often combines rotation, scaling, and translation to position an object on the screen.
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If the user's preferences are robust to small variations in the structure of Q, then the determinant Q is a reasonable measure of the rate or velocity of information obsolescence in a single period, up to an affine transformation aQ + b.
Academic text (1992) -
The central insight is that if we consider the sub-mixture corresponding to just the two narrow Gaussians, then we can rescale the space by applying an affine transformation so that the resulting mean and variance are zero and one, respectively, in every direction.
Academic text (2012) -
To align the two datasets perfectly, we applied an affine transformation that adjusted their coordinate systems.
Surface Forms
Morphology
The phrase is compositionally clear: it denotes a kind or class of 'transformation', so a learner can infer it refers to a specific type of transformation. However, 'affine' is a technical mathematical qualifier whose precise implications (preserving lines, parallelism, combinations of rotation/translation/scaling) are not predictable from everyday vocabulary, so the full meaning requires specialist knowledge.
Etymology
The noun affine transformation creates a clear picture: imagine drawing a shape on a clear sheet and then translate, which means slide, rotate, which means turn, scale, which means stretch, or reflect, which means flip; the shape's lines stay straight and points keep their order. So, an affine transformation is a change that 'keeps lines straight and flat surfaces the same', which is why the term means a transformation that preserves points, straight lines, and planes.
