linear. Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, hyperbolic rotation, shear mapping,...

types of affine geometry correspond to what interpretation is taken for rotation. Euclidean geometry corresponds to the ordinary idea of rotation, while...

inversion are each a special case of improper rotation. Any improper rotation is an affine transformation and, in cases that keep the coordinate origin fixed...

are sometimes referred to as affine rotations (although the term is misleading), whereas the latter are vector rotations. See the article below for details...

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent...

origin fixed are linear, including rotation, scaling, shearing, reflection, and orthogonal projection; if an affine transformation is not a pure translation...

properties from Euclidean space are no longer relevant. For example, in affine space, there is no concept of distance, so there are no reflections or motions...

understand "pure" rotations as linear maps in a vector space equipped with Euclidean structure, not as maps of points of a corresponding affine space. In other...

there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object...

of a linear transformation (such as rotation, shear, extension and compression) and a rigid body translation. Affine deformations are also called homogeneous...