In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More...
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include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific...
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Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and...
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Shear mapping (redirect from Shear transformation)
parallel to the direction of displacement. This geometric transformation is a linear transformation of R n {\displaystyle \mathbb {R} ^{n}} that...
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Isometry (redirect from Length-preserving transformation)
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...
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geometry Infinitesimal transformation, a limiting case of a geometrical transformation Chemical transformation Phase transformation, a physical transition...
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mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that...
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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...
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Eigenvalues and eigenvectors (redirect from Geometric multiplicity)
\lambda } . Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates...
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when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to...
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The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It...
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often possible to translate to and from eigenbases. Most common geometric transformations that keep the origin fixed are linear, including rotation, scaling...
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Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative...
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Data augmentation (section Geometric Transformations)
of techniques, including geometric transformations, color space adjustments, and noise injection. Geometric transformations alter the spatial properties...
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Translation (geometry) (category Transformation (function))
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...
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Procrustes transformation is a geometric transformation that involves only translation, rotation, uniform scaling, or a combination of these transformations. Hence...
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Dual polyhedron (redirect from Geometric dual)
also isotoxal. Duality is closely related to polar reciprocity, a geometric transformation that, when applied to a convex polyhedron, realizes the dual polyhedron...
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Glide reflection (category Transformation (function))
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")...
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unitary transformation U {\textstyle U} satisfies U U ∗ = I {\textstyle UU^{*}=I} . Taking the determinant ( N {\textstyle N} -th power of the geometric mean)...
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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...
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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...
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Symmetry (redirect from Symmetry transformation)
time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects...
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Blowing up (redirect from Monoidal transformation)
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...
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generalize easily to A = P D P − 1 {\displaystyle A=PDP^{-1}} . The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation...
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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....
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64 GFLOPS EFU) Tri-strip geometric transformation (VU0+VU1): 150 million vertices per second 3D CG geometric transformation with raw 3D perspective operations...
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spaces. A reflection across a hyperplane is a kind of motion (geometric transformation preserving distance between points), and the group of all motions...
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Squeeze mapping (redirect from Squeeze transformation)
Möbius transformations, the squeeze transformations are the hyperbolic elements in the classification of elements. A geometric transformation is called...
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homographies and Möbius transformations, when considered as transformations of a projective space. Until the end of the 19th century, geometric spaces were defined...
64 KB (7,780 words) - 04:31, 11 August 2024