In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More...

include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific...

Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and...

parallel to the direction of displacement. This geometric transformation is a linear transformation of ⁠ R n {\displaystyle \mathbb {R} ^{n}} ⁠ that...

metron meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion. Given a metric...

geometry Infinitesimal transformation, a limiting case of a geometrical transformation Chemical transformation Phase transformation, a physical transition...

generalized in transformation geometry, which studies the properties of geometric objects that are preserved by different kinds of transformations. Classical...

mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that...

pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to...

\lambda } . Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates...

when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to...

The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It...

often possible to translate to and from eigenbases. Most common geometric transformations that keep the origin fixed are linear, including rotation, scaling...

Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative...

of techniques, including geometric transformations, color space adjustments, and noise injection. Geometric transformations alter the spatial properties...

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction...

Procrustes transformation is a geometric transformation that involves only translation, rotation, uniform scaling, or a combination of these transformations. Hence...

also isotoxal. Duality is closely related to polar reciprocity, a geometric transformation that, when applied to a convex polyhedron, realizes the dual polyhedron...

In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")...

unitary transformation U {\textstyle U} satisfies U U ∗ = I {\textstyle UU^{*}=I} . Taking the determinant ( N {\textstyle N} -th power of the geometric mean)...

to the distance and a + or − sign chosen based on direction). A geometric transformation of the line can be represented by a function of a real variable...

In mathematics, a geometric algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors...

time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects...

In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with the space of all directions...

generalize easily to A = P D P − 1 {\displaystyle A=PDP^{-1}} . The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation...

In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out....

64 GFLOPS EFU) Tri-strip geometric transformation (VU0+VU1): 150 million vertices per second 3D CG geometric transformation with raw 3D perspective operations...

spaces. A reflection across a hyperplane is a kind of motion (geometric transformation preserving distance between points), and the group of all motions...

Möbius transformations, the squeeze transformations are the hyperbolic elements in the classification of elements. A geometric transformation is called...

homographies and Möbius transformations, when considered as transformations of a projective space. Until the end of the 19th century, geometric spaces were defined...