przeobraenia

Przeobraenia is a Polish term used to describe processes of transformation, change of form, or state across different domains. In common usage it denotes the act or result of turning something into another form, often implying a systematic or observable change.

In mathematics and related disciplines, przeobraenia refers to transformations—functions that map elements from one set to another. Geometric transformations include translations, rotations, reflections, and scaling. More general classes encompass affine transformations (linear parts plus translations) and projective transformations. Transformations may be bijective, preserving structure, and are frequently described by matrices. The composition of transformations corresponds to matrix multiplication, and inverse transformations undo previous effects.

In computer graphics and vision, przeobraenia are essential for manipulating coordinates, shapes, and images. They are typically implemented through matrices and homogeneous coordinates, enabling efficient chaining of operations such as translating, rotating, scaling, and projecting objects onto a viewing plane or screen.

Beyond mathematics and computing, the term also covers broader transformative processes in science and culture. In biology, it can describe developmental changes or metamorphosis; in the arts, it may refer to the alteration of form or style; in physics or chemistry, it can denote state or phase changes. Across contexts, przeobraenia emphasizes how a structure, form, or state is altered, while certain relationships or properties may be preserved or modified as part of the transformation.